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How to find the rotational mode shapes using an accelerometer that can measure the translational mode shape only in the modal analysis experiment for a cantilever beam?
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I would say that you need more than one sensing point to describe your shape; then you may derive the shape spatially. This is what I achieved with full-field measurements, please have a look to:
If the spatial description is too coarse, other authors have tried with closely spaced accereometers to get the same spatial derivation I did with non contacting measurements.
Best regards,
Alessandro
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Using Python, I would like to convert PSD (G2/Hz vs Frequency) diagrams to Acceleration vs Time diagrams. Would someone be able to provide some insight into this matter, because I would like to know first whether or not this can be accomplished and if so, how?
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DearRavi Patel:
At the first, and as you know we can say the following information:
Vibration Research software uses Welch’s method for power spectral density (PSD) estimation. This method applies the fast Fourier transform (FFT) algorithm to the estimation of power spectra.
In regards to his method, Peter D. Welch said, “[the] principal advantages of this method are a reduction in the number of computations and in required core storage, and convenient application in non-stationarity tests.”
The process begins with Gaussian-distributed time-domain input data—i.e., a time history file.
Relying on the above، you can benefit from this valuable article about your topic:
"Calculating PSD from a Time History File"
I hope it will be helpful ...
Best regards ...
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How can I get the second and third natural frequency of a cantilever beam experimentally??
The problem that I am facing is that I got only the first natural frequency.. I can't get other frequencies..
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To expand on the answer provided by Vyacheslav Ryaboy, when performing the increasing-frequency sine sweep test, you would pass through the first resonance frequency of the cantilever beam. This is what is referred to as "hitting" the first resonance frequency. If you continue to increase the frequency, you will eventually reach and pass through the second resonance frequency. If you continue to increase the frequency further, you will eventually reach and pass through the third resonance frequency.
Depending on the equipment at your disposal, you may wish to use an impact hammer to simultaneously excite a number of modes of vibration. The measurement system would likely have the ability to compute the transfer function between the response and the excitation force. The frequency response curve would generally show the first few natural frequencies of vibration of the cantilever beam, dependent somewhat on the bandwidth of the force impulse and also the point of application of the transient excitation force.
The links provided by Om Prakash Chhangani and Mohamed-Mourad Lafifi give the formulas for the first three natural frequencies of a cantilever beam, as well as a graphical representation of the associated mode shapes. There are some suggestions for how to go about experimental testing there too.
What test equipment do you have available to conduct the experiments with?
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Hello everyone,
Recently, I've been trying to conduct a vibration test to obtain the quality factor of a specimen. However, the support boundary inevitably affects the results.
I have tried elastic strips and EPE foams (supporting near the nodal points), but the quality factor varies (~10%) from test to test due to the slight difference in support. The quality factor of the specimen is about 10,000.
I wonder if there are practical treatments to minimize the variation of boundary effect so that the obtained quality factor can be more stable (~1%) during different tests?
Thanks a lot.
Hao
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I assume you are using flexural vibration of the specimen in this test. To get consistent results, the specimen must be vibration-isolated from the surrounding structures. This means that the natural frequency of the specimen bouncing on its supports as a rigid body should be much lower than the frequency of its resonance flexural vibration. For large structures, this kind of test is done by supporting the structure on soft pneumatic isolators with frequencies as low as 1 Hz. I understand your specimen is rather small, so pneumatics would be not suitable, but you can use the soft vibration-isolating elements such as long rubber strings suspended from above, or very soft "negative stiffness" springs. Vibration Control for Optomechanical Systems, by V.M. Ryaboy, ISBN 9789811237331, has some discussion of these issues, in particular, pages 76-85 and 130-132.
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What is lattice mode in RAMAN vibration mode? In general, can you help me about what the lattice mode is in the RAMAN analysis?
I'm working on Sb2S3 thin films. During the Raman analysis, I saw that there are lattice mode vibrational modes. How is it different from symmetric S–Sb–S stretching or symmetric S–Sb–S bending? In General, can you help me about what the lattice mode is in the RAMAN analysis?
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Thank you so much for your reply, and have a nice day. Best regard.
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I have data from shake table random vibration testing. the results are in terms of power spectral density vs frequency. how to convert psd to accelertion ?
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Hi
By acceleration, I am guessing that you ask for the RMS value? It is a common output from PSDs.
I am guessing that you measure acceleration and thus, have acceleration as acc2/Hz, which is PSD. You might have acc/sqrt(Hz), if so, you simply square data to get PSD.
The RMS value can be derived from the PSD by numerical integration, ie
RMS = sqrt(sum(PSD*df)), which can be made crude as a sum or more elaborate using, say Simpson integration.
Assuming the crest factor, you can estimate Peak as Sqrt(2)*RMS and Peak-to-Peak as 2*sqrt(2)*RMS. This should be a reasonable guess as your data is from a test bench at which noise probably was used as excitation source signal.
Hope this helps
Claes
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How the vibration testing is used to detect damage in aerospace components using modal parameters?
What will be the accuracy, if only natural frequencies are used in damage detection?
Are natural frequencies upto 10th mode enough to detect damage and estimate severity?
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Hi
I am no expert neither on aerospace, not on Structural Health Monitoring (SHM).
However, I do know that modes and damping are weak damage indicators, ie damage needs to be severe before it truly shows.
Therefore, in SHM, one tend to use point to point transfer functions instead as these readily show whenever the relative motion changes.
The points are situated next to each other, so for a line of, say four points #1-#4, one would look at transfer functions for #1/#2, #3&#2 and #4/#3. Points can be placed also across joints.
The approach s pretty straightforward. Just plot the transfer functions as a function of time to detect changes,
I've used both simple comparison of autopectra when impacting on structures as well as FRFs. The latter is more precise. The former is HillaBilly but way faster when looking for problem areas as one then can move excitation around more easily.
Hope this helps.
Sincerely
Claes
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I am doing testing of inertial sensors and I need what kind of processor is used for getting the data into my system and do some related calculation.
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Something to consider is that when using the Arduino approach you might not have adequate circuit protection if you're using certain sensors (e.g. 24v IMU type sensors). USB data-logging interfaces are cheap, it might be worth investing in one - you can always chain that into an Arduino if you want to intercept it before the PC.
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Hello
I am trying to perform a sine sweep test using OROS 38 DAQ, Modal analysis software and The modal shop shaker 2100E11. The DAQ software allows to specifying the peak to peak voltage from 0 to 10V and I am using natural air cooling for the shaker so the sine peak force is 220 N.
Only accelerometers are available to get the data and no force sensors are available. Is there any way to measure approximate values of force corresponding to the given peak voltage in the DAQ system?
Please help me out with this.
Thank you
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Mr. Shaik:
I am not familiar with the specific equipment you use, but if your vibration exciter is a permanent magnet electromagnetic shaker, it might be possible that you can correlate the current input into the shaker’s coil with the output force. If you can set up the power amplifier so that it is in a controlled-current mode, then the current would be proportional to the voltage input to the power amplifier, and the force output of the shaker might be a predictable function of frequency and the current and voltage. I did something like this as reported in an article published in 1989, “Experimental active vibration damping of a plane truss using hybrid actuation,” which is posted on ResearchGate.
You might also find help in a detailed article (perhaps even a series of articles) about shakers written by George Fox Lang, published in the magazine “Sound and Vibration.” I don’t recall when Lang’s articles were published and I can’t find them in a quick look into my files, but I think they came out sometime between 1990 and 2010.
As you are probably aware, the conventional and most reliable method of measuring shaker force output is to position a dynamic force sensor between the shaker sting and the attachment point to the structure.
Yours is a well written question. Good luck finding a satisfactory solution.
William Hallauer
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I am running a real-time hybrid simulation by using an electric linear motor. I am trying to perform the free vibration test and in this process, I am measuring the inertia force of the specimen with a load cell. If I do not feed the force in the system it becomes a cyclic test. Under the cyclic test, the system delay is around 2ms and the measured frequency and the input frequency are the same and no damping is observed. However, When I am feeding the measured force into the system then observing a higher delay around 10/12ms and a higher frequency than the input frequency. Can anyone help me with the problem?
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Hello Sir,
What are you trying to do ?. Built a servo system ?.
- For a servo system, conventional technique is to do the design in the frequency domain, using a Bode diagram.
- As far as I can see, you have following system equations.
1. F = k*<input> (force produced by the actuator is proportional to the input signal.)
2. F = m*a (Newtons law. Force equals mass*acceleration.)
3. a = d2 x/dt2 (the accelerations is equal to the second derivative of the positinon)
4. a = (jw)**2 * x (same, but in the frequency domain.)
5. m * (jw)**2 * x = k * <input> (combining 1, 2 and 4.)
- Typically, when you want to make a control loop, you have a sensor, producing delta-x
(the deviation of the intended position of the mass.)
- As you see, the 'problem' here is the response of the system (in Bode diagram) goes down with
slope -2, and phase is constant at -180 degree.
- The controller used of this, is typically a PID-controller.
input (to actuator) =
k1 * Integral(delta-x) + k2 * delta-x + k3 * d(delta-x)/dt.
k1: integral term
k2 : proportional term
k3 : differential term.
On top, to limit noise, there usually is a low-pass filter to limit the differentiator producing
too much noise.
Best Regards,
Henri.
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Good afternoon, I would like to ask you the method to get acceleration PSD profile from time-acceleration data which was obtained through vibration test.
First of all, I though that the time-acceleration data should be changed to frequency-acceleration data. Therefore, I used FFT.
And then, I though that transformed data to frequency-acceleration data should be squared and divided by their own frequency. Because as seeing Acceleration graph, the parameter of X-axis is frequency(Hz) and that of Y-axis is (g^2/Hz).
So, I wrote matlab code like below;
(Here, THM is the time-acceleration data)
time1=THM(:,1);
t_leng1=length(time1);
dt1=time1(2)-time1(1);
Freq1=(0:t_leng1-1)/dt1/t_leng1;
x=THM(:,2);
xft=fft(x);
xft=xft(1:t_leng1/2+1);
psdx = (abs(xft).^2/Freq1');
psdx = 2*psdx(2:end-1);
figure(1)
plot(time1, x);
hold
xlabel('Time(sec)');
ylabel('Acclearation(g)');
title('Time-domain Accelaration of X axis');
figure(2)
plot(Freq1(2:t_leng1),abs(psdx(2:end-1)))
hold
xlim([2 200])
xlabel('Frequency (Hz)');
ylabel('Accelaration (g)');
title('Frequency-domain Accelaration of X axis');
Freqq=Freq1(2:t_leng1)';
Xresopons=abs(xft(2:t_leng1))/t_leng1*2;
However, when running this code, the errors appear like below;
Error using plot
Vectors must be the same length.
Error in FFT_PSd (line 59)
plot(Freq1(2:t_leng1),abs(psdx(2:end-1)))
Here are my questions.
1. Is the correct method to obtain the acceleration PSD graph?
2. if it is correct, how can I solve this matlab error.
3. If it is incorrect, please let me know the method.
Thank you.
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You have to simulate your model to get the acceleration as a function of time.
Once you get the acceleration as a function of time you proceed as described in this forum to get psd using fft.
Best wishes
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Hi,
Can we use FDD algorithm for forced vibration response (sinusoidal response produced from eccentric mass vibrator)?
Thanks
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The OMA or output-only method is basically used to identify the modal characteristics of structure during operation without the need to measure the input excitation or in cased where the input excitation is not deterministic. The main concern is that the excitation must be approximately stochastic with as many excitation sources as possible, preferably more the number of degrees of freedom. The resulting Operational Deflection Shapes (ODS) contain the overall dynamic response of a structure due to forced and resonant vibration.
As for your question, the FDD is an output-only modal identification algorithm and doesn’t directly produce the forced vibration response. As the input excitation is not measured, the collected data cannot be directly interpreted as the excitation. In fact, the excitation needs to be backtracked form the data collecting process, in which both the structure and the measurements systems add and remove components from the excitations. That is the structure will add modal characteristics, while the measurements add noise, aliasing and other phenomena; all such contributions are to be taken into consideration in the analysis of data.
Finally, in your proposed system of an eccentric mass excitation (deterministic input), you can easily measure the forced response at any point on the structure.
I hope this answer would shed some light on your question.
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I am dealing with vibration signals which were acquired from different systems. They are mostly non-stationary and in some cases cyclostationary. What are the less expensive methods for removing noise from the signals? It can be parametric or non-parametric.
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Ijaz Durrani
Thank you so much for providing me with useful information.
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During the correlation of vibration measurement and FE frequency response simulation data, the MAC value can be calculated in 2 ways, with and without considering the effect of phase data. These are called real and complex MAC values respectively. The real MAC value calculation is relatively simple and takes into account only the directional vector magnitudes. How can the phase data be included so as to get a more accurate correlation?
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Hi Arun
The Modal Assurance Criterion is defined as
MAC = (V1*(conj(V2)))2/(abs(V1)2*abs(V2)2)
, where conj is the complex conjugate and abs is the absolute value and Vx is the modal vector x.
You may regard the MAC as a 3D version of the Coherence function.
For real valued modes (standing waves), the modal vectors V1 and V2 can contain positive and/or negative data, i.e. show a 180 degree phase shift. The MAC value then is real valued.
For complex modes (where there is a net energy flow across the system), the modal vectors contain complex (real & imaginary) data. The MAC value can then be complex.
As you can see, phase is part of both a real and a complex valued mode. The difference is that a real valued mode has a shape that stands still while the complex valued mode changes with time. This is readily seen in that node points (zero motion) stand still for the former and move for the latter.
Hope this helps
Claes
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Good morning
I would like to perform a ground vibration test (GVT) on a wing model. Can a someone suggest a good material on that (including how to perform it)?
Thank you in advance for your input and time.
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I am currently working on my Masterthesis and i am about to make some tests about vibration. I have searched many biological and psycho-physical Articles. But i didn't find any data when it comes to vibration thresholds. I know they are hard to measure, but is there any data, in order to have a guideline?
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I am working on vibration test.
my question is how much 'g' level can we accept for a automotive components when it is subjected to forced vibration in terms of 10-40 'g' at various frequencies range of -0-2000 Hz.
eg: input is 10g at 500 Hz, and output vibration level is 200 g at 500 Hz , Is it accepted or on what basis can we have any criteria?
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It is a very interested question
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Please let me know the standard procedure or acceptable procedure for validating the vibration test fixtures.
1. My argument is that the only fixtures are to be validated in the test frequency range for any resonance condition and resonance should not occur with in the test frequency range. It is not meant for fixtures along with the units.
2. My QA agency says that when validating fixture means along with the unit. And says that when accelerometer monitoring is on the unit, resonance condition should not occur. If at all occurs, the transmissibility at resonance frequency should not be more than
3.But I am totally not agreeing with my QA.Who is correct?Please explain. Thanks
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Hi Gowtham,
This is a very interesting question. I am afraid I am not aware of any standard describing what you are after. The only thing I can tell you is that in my case, working with electrodynamic shaker before (in two different setups) I had to be sure that the resonance of the fixture was out of the in-scope frequency range. The only way I could do it was to use as much mass as possible, designing a quite heavy fixture compared with the examined specimen (fixture's mass/specimen's mass>50). Additionally, the shaker was mounted on the fixture, so it was designed to be very stiff on the mounting point.
I don't know if I am helping you somehow...
All the best,
Theofanis Ampatzidis.
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We showed the explicit analytical expression of the complex wave number of a longitudinal wave in a viscoelastic rod and a flexural wave in a viscoelastic beam. (1)
Frequency response functions (FRFs), such as the mobility, are evaluated using the complex wave number calculated by the proposed formulas. This means the direct problems. (Estimation of the frequency response functions from the given viscoelastic data)
On the other hand, there might be inverse problems. (Estimation of the viscoelastic data from a given frequency response function)
We tried to estimate the viscoelasticity from the mobility data of a beam specimen numerically. We searched for the viscoelasticity (E, eta) to minimize the root mean squared residual error of the absolute mobility. But the derived viscoelasticity had the different frequency dependency from the original one. Then we calculated the mobility by using the derived viscoelasticity. The results agreed with the originally measured one.
It seems that the solution of the inverse problem is not unique. Do you have any idea to solve this kind of inverse problem?
If this type of inverse problem can be solved properly, I think it can be applied to the measurement techniques. We are looking forward to your answer and advice.
(References)
(1)Propagation of stress waves in viscoelastic rods and plates
Ryuzo Horiguchi, Yoshiro Oda and Takao Yamaguchi
Journal of Technology and Social Science, Vol.2, No.1, pp.24-39, 2018.
(2) Stress Waves in Viscoelastic rods beams and plates_ICMEMIS2017.pptx
(Presentation slides)
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Hi ,Everybody
I agree with all the above answer.
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From my experience, I know that amplitude vs frequency curves are generated as output from measurement points in a shaker test. (Amplitude can be displacement, velocity or acceleration. Acceleration is obtained by default from the accelerometer, which can be internally converted into displacement or velocity by the data acquisition system). 
I have seen certain test results where curves are generated for different engine orders and these have been plotted on the Campbell diagram against the engine rpm. I have also observed that for the same frequency, at the same measurement point, the amplitude of acceleration/displacement is different for different engine orders. How is this data extracted from the default amplitude vs frequency data ?
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I have been wanting to add this for a long time, but kept procrastinating......In the question that I asked above, the test results which I found were not from shaker test. The Campbell diagrams were plotted from an engine test where the input was in the form of engine revolutions per minute (from a roller dynamometer and car engine). Now I could understand how the amplitudes (for same frequency) were different for different engine orders.
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What can be some new and innovative ways to develop a condition monitoring set-up using Vibration Signature of any system (say a coupling, an engine)
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Because I could only use the compression type accelerometer which is more sensitive to the zero shift in the impact test, I cannot obtain the accurate signal, and thus cannot obtain the correct velocity, displacement using common integration approach as well. The velocity and displacement shows unrealistic trend to increase continuously without approaching zero.
So my problem is how to process the acceleration correctly with matlab (preferred) or any other software, the detrend function in matlab seems to be unable to handle this problem.
After reading several relevant literatures I found that the discrete wavelet transform (DWT) method and the empirical mode decomposition (EMD) method may be appropriate to be applied. Have you ever met similar problem during the impact tests? Looking forward to hearing your experiences and thanks in advance.
The brief introduction is enclosed as attachment.
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Hi
This is a classic problem & a nuisance. 
Try these steps. 
  1. Select a time record with zero offset at start and zero offset  at end. 
  2. If you do not have such a record, apply exponential weighting to get zero offset at the end. 
  3. You should now have a saw tooth pulse of duration tau seconds and hence, 90% of its energy below 2/tau Hz. 
  4. Take a FFT of the whole signal. 
  5. Delete any spectral components below 2/tau Hz. 
  6. Apply integration using jw as appropriate. 
  7. Take a FFT of the whole signal to return to the time domain.
  8. Plot the signal. 
The FFT is cyclic so, doing 2x FFTs in a row only returns your original time signal - try it. Note that you need long time records for the approach to work at least so so. 
The above can be done in Matlab.  
A better way, if you can repeat your test, is to use mechanical filters to remove the high frequency content that upsets the sensor. Take a look here. 
/Claes
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The guitar tuning is the initial state on guitar by which all possible states are known.  The guitar tuning is a point in tuning space represented by a 6-digit number such as 0 7 5 3 4 5, commonly known as Open D Minor when intonated at D2 pitch level as D A D F A D.
In guitar tuning space every tuning is one step away from every other tuning because for any two tuning vectors there is a difference vector which changes one tuning into another using a single operator.
Given unknown tablature for the song “Happy Birthday” written in an unknown tuning there is one and only tuning which makes sense of the unknown tab, which otherwise seems to be nonsense for every other tuning.  Clearly if every possible tuning is used to interrogate the unknown tab, the authentic tuning will be found.  Also, if the tuning used to write the tab is D A D F A D, and the tab is interrogated using D A D F# A D, the song will be recognizable but every note falling on the F# string will be off-key and the error can be used to deduce the string should be tuned to F, not F#.
Most common tunings are within 3 strings of each other, but clearly there cannot be more than five steps to go from any tuning to any other.
In affine theory and music copyright law every possible guitar tuning is a simple mathematic derivative of music that any trained musician can make, but clearly there is one and only one authentic guitar tuning used to compose and record guitar.  Finding the tuning used to record guitar is possible by interrogating the music, but an additional step is required to determine both tuning and intonation, which surprisingly is only slightly more difficult than find the tuning for unknown tabs.
I see this question as similar to the 3-color map problem in topology because the guitar is finite so there must be a way to learn the tuning from a record.   If there is a way to learn the guitar tuning, then there must be a deductive system of logic and implication that can find the best-possible tuning.
Tablature makes more sense as the number of tunings considered increases but clearly considering every possible tuning is not required.  In practice, there is certainly a maximum number of tunings that are used in popular music, on a order of magnitude between 10 and 100.  The number of useful tunings is clearly highly determined, but how? Why isn't every tuning just as good as any tuning?
If it is possible to learn guitar by auditor surveillance of a record, then can anyone calculate the minimum number of guitar tunings that must be considered?  How many times does tablature need to be re-written until the sequence of tabs converges on the best-possible?  I realize that there is no way to prove the absolute best but in any specific collection the best is always clear.  Can tabs just get better and better in definitely?
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I don't know about music, but I liked the question. I think, it is more like solving-pnp problem than map-coloring.
Hope it would be helpful for you.
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I am doing a 1D FE code for a simple expansion chamber, but at the expansion and contraction area jumps, i cannot use my regular shape functions, beacuse they just take length into account, in order to consider area jump i was trying to use an impedance element, since the impedance will change depending on the area, but i am confused on the point that how to give it correctly into code and what all variables i should use while defining the impedance element. Also, i am doing just 1 degree of freedom model i.e, pressure.
thank you
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Hi
I believe that you find all your questions answered in the book written by M.L. Munjal, Acoustics of Ducts and Mufflers
I suggest that you get a copy. 
To answer your question, you need to ensure continuity of mass, or rather mass flow across impedance junctions to get things right. 
Sincerely
Claes
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Hi everybody,
I'm going to do dynamic analysis of a vibrating string in ABAQUS. The string is vibrating at a specific frequency and at time t1 boundary conditions are altered in such a way that tension is released while the string is still vibrating. How to model it in ABAQUS?
Thanks for your time
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Thanks for your answer William!
I'm using Static (General), Frequency and finally Modal Dynamic steps in succession. In the Modal Dynamic step, while the string is vibrating, tension is released by returning the boundary displacements to the zero point. 
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Hi all,
I was simulating Eigenfrequencies of an sign post 3D object. I obtained many frequency values including pure imaginary,for the first natural frequency.
It shows the pure imaginary frequency for rotation (attached image), but I don't understand the meaning of pure imaginary frequencies.
Would anybody help me to understand this obtained result? Or is this wrong result?
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Hi Mojtaba,
that mode looks like a rigid body rotation, i.e. the plate can rotate freely around one axis without performing work. In the undamped case, this eigenfrequency should theoretically turn out to be zero. I assume the small imaginary part is due to material damping or simply an inaccurate solution of the eigenvalue solver. However, the solution is not physically meaningful. You should try and add constraints in a realistic way such that rigid body motions are avoided.
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I'm using the ERA/OKID algorithm for the identification of a real structure from noisy experimental data (full scale free vibration tests).
The algorithm provides at least two real-valued modes for which damping=100%. How can I interpret this result?
Thank you , 
Anastasia
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 Dear Anastasia. 
Damping is a sensitive parameter to estimate. There are several explanations for why unreasonable damping estimates are obtained by ERA/OKID or any other output-only system identification technique assuming white noise excitation. One possible explantation is wheather the dynamic model assumed in the technique is representative of the vibrations of the structure in question. If you find that the model is a good approximation, the remaining explanations to the damping ratio estimated could be related to the identification procedure i.e. what model order was chosen, how many time lags did you include for the construction of the block-Hankel matrices. 
Anela
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Hello, I am trying to calculate the element modal strain energy for a simple mass spring system as shown in the attachment. I have calculated the first 3 modal frequencies as [4.4504,12.4698, 18.0194] rad/s. The values i calculated for mode shapes of the first mode are [2.3305, 1.8689, 1.0372], while the second and third modes have a mode shape of [-1.8689,1.0372, 2.3305] and [1.0372, -2.3305,1.8689] respectively. Currently I am unable to match the modal strain energy ratio for each member at the first three modal frequencies, and i need some help understanding the process of calculating the modal strain energy. 
Thank You.
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Hi Timi
You might like this link for basic understanding
(Look at the sdof link). 
If you start with a single dof mass-spring system, then 
potential (modal) energy (PE) is 1/2KX2 and kinetic (modal) energy (KE) is 1/2MV2,
where K is spring stiffness, M is mass, X is displacement and V is velocity. 
I write (modal) as the modal energy exists only at the natural frequency w = sqrt(K/M), i.e. when PE = KE. 
For harmonic vibration V = jwX, where w = 2*pi*frequency. 
The ratios shown in your Table is % per spring of 100% modal strain. Most FE software is able to output Modal Strain Energy for the element groups you define. Some also output Kinetic Energy. You then need to sum this energy per group. Again, some FE software does the job for you. 
Sincerely
Claes
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Method1: I have the time domain acceleration data at a specific measurement point obtained from hammer testing. I also have the excitation data in time domain from the hammer used (method is roving accelerometer method). I do all the necessary filtering to remove noise and convert both data into frequency domain (FFT) and then take the ratio (output/input), which would be the FRF. 
Method 2: After this, I use the shaker to directly compute FRF (using data acquisiton systems) at the same measurement point.
Will the 2 FRF curves using the above methods be similar (not necessarily in amplitude level, but in terms of behavior and peaks)? As per my understanding, it should be the same. Just wanted to make sure.
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Hi
Just to make sure - I hope you are computing Frequency Response Functions (aka Transfer Functions) & Coherence, not simply dividing the response and force spectra with each other?
They should be the same, but the methods differ in the kind of systematic measurement errors they introduce. They can be quite close though. 
The hammer tip has a mass which is accelerated and influence the magnitude/phase of the force signal. Also, the hammer picks up force before and after the impact & you can get double impacts. A hammer blow never is exactly the same twice, as it varies in strength, orientation and location when landing on the object. Therefore, the rule of thumb is that it does not pay to average more than about 9 hammer impacts.
A force sensor excited by a shaker also has a mass that is accelerated, but this acceleratoin can be measured and compensated for. The shaker places an inertial load on the object, and if it is a thin shelled object, rotational intertia loading can affect results. Depending on the mechanical setup, non-driving dofs of the shaker may add damping to the object you are studiying. 
Comparing FRFs obtained with the respective methods, expect the largerst differences to arise at anti-resonance, as this is where phase errors matter the most. 
For a locally reacting material, i.e. for a material where the response close to the load greatly varies (think of a soft sponge and your loading it with your finger to get an idea of what it looks like when locally reacting), there may be large differences between the methods, partially as the excitation surface (size, shape and loading plate stiffness) affects the local FRF magnitude. Concrete is a locally reacting material. 
Then, of course, you have the question of what happens when/if you move acceleroemeters across the measurement object during acquisition of your FRFs ,
You might want to take a look here as well
Hope this helps
Claes
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I have results for repeated vibration test (excitation and response) in time domain. I need to calculate average frf (using cpsd 'Sxy/Sxx') of these test results.
  • when i use [abs{(sum(Sxy) / number of test) / (sum(Sxx) / number of test)}] i got something different than what i have for the single test, also it looks much noise.
  • but when i use [{(sum(abs(Sxy)) / number of test) / (sum(abs(Sxx)) / number of test)}] i got better smooth results.
which one of these two methods is true and is there a nice reference to read in deep ?
thank you
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Dear Ahmed,
Actually there are three often considered approaches for averaging the frequency response functions. The so-called H1, H2 and Hv estimator, all three are techniques to average out the spectrum all three have their underlying assumption to avoid a bias (No noise on input / No noise on output / noise on both input and output). 
An interesting read might be the second chapter, especially section 2.5, of the PhD of Peter Verboven (See link). 
I hope this helped to answer your question. Feel free to contact me if you have further questions.
Kind regards,
Wout
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We are developing a new evaluation of acoustics properties of wood and wood panels with small dimensions and in the free-free scheme for vibration testing is necessary a microphone to pick up the signal. 
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I would suggest measurements with a laser vibrometer! If available...
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  1. For study of  vibration of cylindrical shell i need to find Governing equation by using energy function with Ritz method.
  2. Use of Hooks law ,strain vectors ,resultant force and moment relation and strain energy and kinetic energy find the equation for frequency.
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Hi
Here are good classic references for plates and shells
Leissa - Vibration of plates: http://ntrs.nasa.gov/search.jsp?R=19700009156
Leissa - Vibration of shells: http://ntrs.nasa.gov/search.jsp?R=19730018197
I believe that you find what you are looking for in the Leissa books. 
Sincerely
Claes
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I know that commonly random vibration analysis is performed as implicit analysis and uses modal superposition method, but can it be performed as explicit analysis? How can we do that? and what are the pros and cons relative to implicit analysis? Any cited sources would be greatly appreaciated
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Why don't you try to see the problem also from the real testing side?
I suggest you these books:
Modal Analysis Theory and Testing, Ward Heylen, Stefan Lammens, Paul Sas
Katholieke Universiteit Leuven, Faculty of Engineering, Department of Mechanical Engineering, Division of Production Engineering, Machine Design and Automation, 1998 - 340 pages
Modal Testing, Theory, Practice, and Application, 2nd Edition, by D.j. Ewins
Have a nice day,
Alessandro
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Daniel Bernoulli established the principle that the number of modes of vibration in a system is equal to the degrees of freedom.  In his method of hanging weights on a string, I assume without any weights the string has one mode.  Clearly, a system can have at most one fundamental.  But the problem is how can the string be defined by a fundamental frequency while radiating a complex sinusoidal wave?
I am confused, therefore, about how to count the degrees of freedom of movement that exist in a string detained between two point with constant tension, length, mass, and composition.  We assume the parameters allow the string to be subject to harmonic motion when deformed.  The question seems a simple geometric problem.
I seems to me that the string has only one mode of vibration which is d2y/dt2 = 0 but then there is a second mode, which you can see with the naked eye, where the shape of the string concatenation is not a circle in cross-section so the axis of the string elliptic rotates.
This makes me ask if d2z/dt2 = 0 is also a boundary condition?
If we imagine the string is plucked so the deformation vector is only in the direction of the y-axis, then clearly the concatenary does not remain in the x-y plane.  But the string does not necessarily assume a circular cross section either.  In fact, I cannot see any reason why the cross-section would be circular at all.
Some say the string has n modes or even an infinite number of modes at the same time,  which I think more closely applies to air and electromagnetic fields that have a broad frequency response but not to the detained string defined on the interval 0 to 1 where x is fixed and there must be a fixed point.
I have an intuitive answer for the degrees of freedom of string movement that I hope someone can state formally.  There must be two modes of string vibration, a dominant and subdominant string mode.  Then we have the string tone and overtones as two sets.
I think the string has only 2 possible modes of vibration, perhaps dy/dt and dz/dt, or it may be a radial and rotational mode, but such that the fundamental has only one mode possible at a time, but there is a secondary mode induced by the fundamental on any mode in the frequency expression that is not isochronus because d2y/dt2 is not zero  Perhaps there is one degree of freedom that is perpendicular to the string axis and then there is a rotational degree of freedom perpendicular to dy/dt?
I don't see the equation for the string concatenation form is any where stated in the literature.  Am I missing it? 
Is there any way that dy/dt and dz/dt could have different frequencies so that the string radiates a complex sinusoidal function that is the sum of two frequencies?  I know that doesn't make sense, but there must be a simple explanation for tones and overtones that is easy to understand and that has been so far overlooked.
I am assuming that the deformation and concatenary forms are states of system and not modes.
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A mode of vibration in the string means a direction of vibration, e.g. x, y, and how many cycles of vibration there are along the string.
I expect Bernoulli's treatment started with a massless string with tension, with equally spaced point loading with masses (perhaps with half spacing at the ends), with vibration in one dimension.  This is a simple and probably good starting example.  In this case the number of modes is equal to the number of weights.  If you allow vibration in two dimensions this doubles the number of modes.  All the elliptical vibrations can be made by adding perpendicular modes.  If the string has a very large number of (almost infinitesimal) weights, as a real string has, then the number of modes is very high, and in the end is determined by exactly how many atoms there are in the string and their arrangement.  The infinite number of modes is only true for a string made out of continuous material, i.e. not atoms.
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The S1 circle is a boundary that classifies pitch in the Z/12Z system as the chromatic circle, which can also be a spiral.
The string concatenary is the shape the string returns to when plucked, which is a standing wave with the boundary condition for a standing wave d2y/dt2 = 0.
The string is closed by the octave into a chromatic circle and also open to union with any pitch by adjusting the frequency of the fundamental.
The fundamental of the string has only one degree of freedom and therefore it cannot have more than one mode of vibration.
The string in classic theory is defined on the interval (0, 1) which is an unordered pair but the musical string is on an ordered pair since the frets define the lower segment.
There are 3 sets: observed pitch, fret positions value, string pitch values.  The intersection of the pitch values and fret values on the string is a graph that is a restriction R x R onto R, which I think is the basis for both the S1 and d2y/dt2 = 0 boundary condition.
So I am wondering if the standing wave boundary is d2y/dt2 = (0, 1). 
There must be a theorem that say the string can only have one boundary condition if it has only one degree of freedom, right?
The string is the smallest set that contains an image of every set in music so long as the string is at least 12 in size.  There is the graph of pitch and position and then there are the tuning function f and the intonation function g.
The tuning function f maps the observed pitch to the string position and the intonation function g maps the string position to the observed pitch. f and g are composable functions that make an identity.  This makes the string a homomorphism that is an arrow with a 1 or just a 1.
Now my question concerns how the integration of the boundary condition can be determined.  It must be a simple sum if there is a smallest possible Lebesgue measure of 1 step that is countably additive so I think I can conclude the volume of the concatenary is 1. Since everything has to add up to 1, or at least a whole number. Then the boundary conditions are two ways to say the same thing.  "S12 = 1".
Please help me to formalize the string finite state model. Its a 300 year old puzzle not yet solved.
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I cannot see that these references go to the "corps sonore" which is the smallest possible set that contains every element, function, and relation in music.  The smallest unit is an integral domain that does not depend on the frequency level at which the system in intonated.
The problem I have is that you are assuming the sound wave emitted by the string is a model of the string itself.  But the frequency is merely the quantifier of the string and what we want to get at is the atomic structure.  You cannot assume the string is Fourier space where waves can be added together because the string is a restriction on R.
This may seem ridiculous to you because real analysis is absolutely compelling and as an approximation in R2 cannot be proven wrong in anyway.
However, your assumption that the space of music has the real number topology is not correct in general in projective space.
The classic idea that the musical string detained between two points is open neglects the fact that the string is closed by the octave.  In projective space the line is automatically closed in a circle.
There is no interest in modeling the timbre of notes, because the timbre is a secondary characteristic that is not a function of the string fundamental.
The problem is that if pitch is a real valued function then it cannot be written as a family of disjoint pairwise intervals using frequency.
I take your answer to be the string has n modes, not 1 or 2.  But I doubt the string can be divided into infinitely many parts.  In fact the size of the corps sonore is clearly 12, since any music in the 12-tone system can form an image in any string size 12 or more.
You see I need a system on Z2 while you are talking R2
Thank you for the references.
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Two time series data (1. Engine RPM wrt time and 2. Seat Acceleration wrt time) were analyzed using LMS Testlab and LMS AMESim post processing tools. It was observed that the order plot of acceleration wrt rpm obtained from both softwares using the same window type and trend removal option do not match. Further investigations reveals that using the same sampling frequency in AMESim and Testlab produced a result that have similar trends with Testlab result. However, the accelerations amplitudes have significant deviation from Testlab results.
What other parameters should be checked to obtain same results from Testlab and AMESim?
Best Regards,
David
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Hi David
Debugging software always is dog's work.
Suggestions on simple things to compare are
  • RMS (1s) values computed from raw time signals to ensure signals have similar energy content.
  • Autospectrum, verify that frequencies and amplitudes are identitical. Check Autospectrum with Amplitude shown as Peak, RMS, Pk-Pk etc.
  • A good overview of long time series often is to use Amplitude histograms and to look at Kurtosis.
Where possible, try and swap data between systems, i.e. get test data to act as simulation data and vice versa. If this works, use a simple calibrator signal of 1 g at fixed and known frequency as first signal to test AMESim.
If I should venture a guess, test systems use fixed sampling rates as the measurement HW uses fixed clock frequency. A simulation system may use different time steps because of numerical efficiency and this difference in time stepping may complicate post processing.
Have fun
Claes
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I'm carrying out an experimental modal analysis on the fixture of rotating beams. The rotary beams are attached to a D/C motor and I measured the vibrations at the fixture of the motor. I got peaks at very low frequencies before and after turning on the motor. 
Thanks in advance
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Dear Ahmed,
   This setup of fixture of rotating beams has a one per rev of 3.58 Hz. Are you getting low frequencies at 1/rev or still below? If its below 1/rev, then try to check for any play or looseness in the setup or sensor mounting itself. Also check the mounting base for its attachment rigidly to the ground. Hope it gives some clue..
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Bell plates are hand bells made from sheet material having a particular shape. When the plate is struck the resulting vibration and sound continues for a long period of time, even when held by hand. 
I am doing a project to investigate and understand the vibration characteristics of bell plates including the development of a computer model to predict the low level of damping achieved. Well anyone can help me out on a better understanding of the bell plate vibrations? Since the shape of my bell plate model is triangular kinda shape with a tang at the edge, any references on developing the FEA computer model by using ANSYS or COMSOL ?
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Hi
My guess is that the low level of damping is achieved by designing the bell such that the (hand held) support position has lots of nodes, i.e. minum vibration and thereby transmits very little energy as vibration into the hand. The modal equivalence is to design the structure for minimum modal response at the support position. In doing so, most of the damping is found from sound radiation.
See here for some ramblings on damping
On a more practical note - all you need is to compute modes and sum modal response at the support position. If you wish to be more specific, you can take into account also modal response where the clapper hits the bell when making sound.
You can use Ansys, Comsol or any other FE solver for this, e.g. freeware such as Code Aster (http://web-code-aster.org/V2/spip.php?rubrique18 ) or some other solver found here (https://www.simscale.com/ ).
To optimize, take a look at OpenMDAO (http://openmdao.org/)
You might get som ideas here as well
Sincerely
Claes
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Hello All,
I am simulating vibration of a cantilever in Abaqus using dynamics implicit in two cases; automatic time increment and fixed time increment. As far as I know, results obtained from automatic time increment should always be reliable/correct but surprisingly, in some cases, I can see that by reducing the time increment from the automatic one, I get different results. I am wondering if anybody has dealt with this problem. If this is the case, then we can not simply rely on the results of automatic time increment.
I appreciate your answers.
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Christian is absolutely right. Implicit time integration schemes are unconditionally stable. That is to say the time step can be chosen quite arbitrarily and should primarily depend on the highest frequency in the response signal. Therefore, if the time step computed by Abaqus (however they do it) is too large your results will not converge (unconditionally stable) but nonetheless can be arbitrarily wrong. Keep in mind, you always should try to balance the modelling error and the time-integration error. In the case of an explicit analysis Abaqus determines the time step according to the stability limit of the central difference method, which involves estimating the highest frequency in the system. You could also do this elementwise which would be a conservative estimate. To conclude, default settings in commercial programs are not always reliable and are also not necessarily the best choice for your analysis. Hence, you should be aware of what methods Abaqus uses
Hope that helps!
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One of the tests is using FRF(frequency response function),but besides FRF which else tests can be done to get the damping value?I want to perform structural vibration analysis of a washer and so i first have to find out the damping by testing and then use that value for simulation in ansys workbench.  
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If you model it by just 1 dof system, then free vibration oscillation can be approached with the logaritmic decrement method, in order to evaluate the overall damping. You have then to measure the oscillation in time domain, given the intial conditions, e.g. an imposed displacement. In frequency domain for forced oscillations you can approach it with the half-power frequency band method: you have to search for the frequencies at which the  response amplitude is that in resonance / sqrt(2), call them Freq1, Freq2; then the overall damping can be esitmated by (Freq2-Freq1)/(2*NatFreq),  where the natural frequency is undamped.
When instead you have a multi dof system, each mode shape can have its own damping ratio or modal damping coefficient, which is evaluated by means of a complete EMA.
Hope this was of help,
have a nice day,
Alessandro
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i have to do vibrational analysis of a washer from washing machine.i need damping values for it which i will get from frf(frequency response function) testing.but how do i find damping from frf?
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Hi, there are many methods to calculate damping coefficients via modal FRF testing. you may consult the book titled "Modal Testing" by "D. J. Ewins". One of the simple methods is peak-picking method.
with best regards.
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There are many studies for predicting the ground PPV (peak particle velocity) due to blast and its effect on structures. I wonder if there are empirical formulas for frequency distribution of the resulting vibration. I need the frequency distribution to build the time history for the vibration that will be used for more advanced structure analysis.
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I have interest in structural vibration especially stationary and moving loads on structures.
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Although your question is quite generic I will suggest the followings:
First you make sure that you have established a proper geometry that reflects your structure of interest (geometry and material properties)
Afterwards you should pay special attention to the boundary conditions
A very good intermediate step in modelling and simulation is to perform a modal analysis with the FE model and compare your outputs (frequencies, mode shapes) with the experimental ones (if available). The comparison can be done in terms of modal assurance criterion (MAC). By that means, you are gaining already insight on the match between your model and your actual structure
At a final step, you can apply different kind of loads (e.g moving loads or design spectra etc) and check the influences
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The pulse of the vibration within the ring itself is what I'm interested.  
My guess is that at least four wave formations occur, these being
(1) a sine curve which originates at the place where the hammer strikes (and its mirror image),
(2) A damping cosine curve of one half the period of the sine curve,
(3) four sub-sine curves at the nodes of the first sine curve space at 45 degrees off the place of the hammer striking in a square of equilibrium in the ring, and
(4) a combination of 1 and 2.  
Is there any material on this that presents the answer?
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The simplest scenario is a free ring in space. Then you have all the sinusoidal mode shapes (wave patterns) with a wave length corresponding to the length of the ring divided by any integer. That holds both for in-plane modes and modes normal to the ring plane. This is true for an pure impulse (Dirac) excitation: in practice, your excitation may not be so simple and some modes may be more or less excited that others (Shahab is right about this).
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Is there any experimental method to validate the numerical results that obtained from the simulation of rotating blade (flapwise and chordwise vibration) ?
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Building the blade deflection from strain signals is often called Strain Pattern Analysis, or "SPA". Practically, the way SPA is applied largely depends on the studied structure.
Briefly, it is not advised to integrate the strain to get the displacement. You should prefer calculating the blade deflection by combining several shapes. These shapes are obtained experimentally and actually form a vector basis. This basis can be either a set of static shapes, or modal shapes, or even a mix of the 2. The coefficients of the combination are obtained using the strain signals recorded during your main experiment and the strains obtained when recording the basis.
As any other measurement mean, SPA has its advantages & limitations. You should find on the web without too much difficulties some information about it.
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I think that it's related to the geometry of the specimen under test and the frequency of the impact hammer?
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1. What you measure depends on the frequency you stimulate by your method. You will measure sound waves and eigenforms if you excite your structure with a broad band signal (impact hammer). However, in the amplitudes of the eigenforms are dominant.
2. Sound waves and eigenforms are both waves. The difference is, that the wavelength of an eigenform is the multiple of the length of the structure, its. called standing wave. For a beam this is very easy to understand and to visualize.
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I have a cantilever beam with cracks, I found out natural frequencies experimentally. 
The natural frequencies of intact cantilever are less than that of same cantilever with cracks. 
I made literature and I found some papers show that cracks caused increase in the natural frequencies and other papers show reduction in them ...
I'm confused ,because logically the cracks should reduce the stiffness of the beam. 
What is the physical meaning of that increase in the natural frequencies?
Thank you in advance 
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Hi Ahmed,  I concur with other colleagues.  If you consider a simple model of the cantilever beam, given that w= sqrt (k/m), once k, the stiffness, is decreased the natural frequency should increase.  However, generation of cracks increase the damping in the system due to higher energy dissipation.  Thus, what you might have been measuring has not been the natural frequent but the frequency of a damped system (which is sometimes is referred to as damped frequency).  As you know the relationship between damped frequency and natural frequency is  damped freq= sqrt(1-zeta squared)gnat freq.   As zeta increases (damping) due to cracks, obviously the new damped frequency will increase, that is not the increase in the natural frequency but in the damped frequency.  So, I am afraid you have been measuring the damped frequency instead of natural frequency, which as I said due to cracks (more energy dissipation) that will increase.  Please check your results to make sure what you are measuring. 
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vibration analysis enveloping and demodulation
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It is difficult to aviod the lossing of some bits since it is lossy techniques
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I want establish FE model for the disc brake to calculate the vibration responses...
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When a coarse set of SIMO FRF is available, the driving point is just one. But when the FRF are estimated very close to each other in spatial domain, and might be very similar and all with PI-constrained phase or one sided imaginary part (apart from little measurement errors), how can we discriminate the best/true driving point FRF?
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Hi Allesandro
I believe I must complicate your world a bit more. :)
You measure mobility (receptance or accelerance) rather than impedance.This is a common mistake, in fact the Impedance standardization group had to switch name to mobility standardization. 
Why? Well, if you set up the impedance matrix, i.e. forced displacement input, you must block motion at all other positions and there measure blocked force. This can only be done in special test stands and with some limitations at that.
See Figures 3 & 4 here & try the same for mobility and the difference is obvious
Next, I used to be a big fan of impedance heads until I learned that impedance heads are riddled with measurement errors. The reason lies in the force cell being situated in between your measurement object and the accelerometer.
If the measurement object stiffness is higher than that of the force cell, the accelerometer response will not move in phase with the measurement object and your FRF is in error. As most FRFs have anti.resonances, and stiffness if very high at anti-resonance, this error in your drive point FRF will be notable.
Incidentally, this is a unique way to identify the difference, ;), between the FRFs where the FRF with the accelerometer placed close to the drive point will be the correct one.
When checking things, I find that it is very useful to rely on a no-excuses-accepted case. One such is a rectangular, say 10mm thick, 40 mm wide and 1+ m long steel beam. You can simulate this case using simple Euler Bernoulli beam theory and make very accurate free-free measurements on this case. In any case, this is what Mike and I did when we were working on 6 dof mobility measurements a while back in time. https://www.researchgate.net/publication/256801180_Direct_measurement_of_moment_mobility_Part_I_A_theoretical_study?ev=prf_pub
Over2Jo
Claes
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Can anyone answer me the simplest way to do it.....
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In Civil Engineering, the peak particle velocity is used for assessment of traffic vibration effects on structures. Measure vertical and horizontal vibrations at the foundations and the upper floor or the roof. Use ISO 4866-1990 or its U.S counterpart ANSI S2.47-1990: Vibration of Buildings - Guidelines for the Measurement of Vibrations and Evaluation of Their Effects on Buildings.
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My recent perception experiments (The Tension Theory of Pitch Production and Perception) show that the physical dimension (length of a string or diameter of a membrane) is an inherent source of force for the vibrating body. I am now trying to see how tension meters measure the tension of a string since they do not seem to take all the physical dimensions of the string (or other bodies) into account.
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Thank you very much Pooya. I was told the same thing by the Department of Astronomy, but my investigations came up with very different results. I looked at your list of publications and noted that you must be in really advanced physics and mathematics (if I'm not wrong). I am looking at the tension issue from the standpoint of auditory psychophysics and not in terms of pure physics. The document I'm referring to is my paper The Tension Theory of Pitch Production and Perception. This is the work that led to all the questions I am asking.  if you are not in hearing research, the paper  may bot be relevant to you area of expertise...
Thank you once again for your help on the matter.
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Say I hit the free end of cantilever beam hinged at other end with a hammer and find the frf of middle point on the beam.
In the second case I put the shaker at the free end of the same hinged cantilever beam and calculate the frf at the middle point on the beam.
So what differences I may find between the two frfs?
I suppose that both will be same only difference I feel is the impluse excitation by hammer will consists of all the frequencies while the shaker test will contain only the frequencies that the shaker is configured for.
Please correct me If I am wrong.
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It was already mentioned that with shaker you can apply energy to the structure for a long time so you can get more samples. Sometimes you need big number of samples to estimate reliable modal parameters. Bu there are also cases that the the record time must be long due to the frequency (low frequencies). Application of the shaker could be crucial in such a case, while with impact testing the response time is limited. Moreover, shakers are often used for modal testing of big structures not only because the low frequency.  You use multiple synchronized shakers and thanks to that approach you apply the energy to the structure in uniform way. Of course you cover, already mentioned, long time excitation of low frequencies. Having only hammer impact you can have problems to excite whole structure uniformly. You could use multiple hammers but synchronization can be the problem. 
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How do you calculate vibrational frequencies at different temperatures? This can not be done on Gaussian.
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Dear V. P. Gupta.
Your question is not clear for me, If you want to obtain temperature-dependent natural frequency such as problems in high temperature, it is essential to take into consideration temperature dependency thermoelastic materials and express effective materials properties as a function of temperature, like "Reddy, J. N. and Chin, C. D. Thermoelastical analysis of functionally graded cylinders and plates, Journal of Thermal Stresses, 21, 593-626, (1998)."
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I have some problems in understanding criteria of computing MAC.
This my second question on the same topic. 
I have an accelerometer on the tip of a wind turbine blade and after exciting it with white noise I got the mode shapes. 
I made modal analysis on the ansys apdl and got the mode shapes.
I want to check the pair of modes (experimental and analytic) 
What is the simple way to get MAC for both?
How to extract the data?!
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If you send me your cdb file (CDWRITE, ALL) and the experimental mode shapes I will try to send you the corresponding MAC matrix.
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As every one knew that mufflers are place in a automobile to reduce the noise of the engine and car body currently I'm working on exhaust mufflers and specially on exhaust absolute mufflers but I couldn't find required theory for it.
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I would recommend looking into:
Acoustics of Ducts and Mufflers With Application to Exhaust and Ventilation System Design, M. L. Munjal
or papers by M. L. Munjal, H. Bodén, M. Åbom, T. Elnady that are talking about two port networks or related topics.
There is a lot of details if you want to learn about exhaust system design from the acoustic point view but I think two port network analysis (and transfer matrix approach) of mufflers gives a lot of insight and also has the practical advantage of being a simpler model to use and implement on software (this is why muffler design software packages use it)
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I performed modal analysis using Ansys and experimental modal analysis on a wind turbine blade. 
The deviation between FE and experimental measurement for higher modes (third mode shape) is so big 
274 Hz from ansys and 306 Hz from experiment.
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If you define error as the difference between an exact analytical solution and your finite element solution, then error is larger for higher modes because the element shape functions provide a better basis (approximation) of the shape of low modes and a relatively poorer basis for higher modes.
However, you are comparing results from a finite element model and an experiment. In this case, there are several sources of discrepancy. The usual suspects are (1) boundary conditions that you are using in the model do not accurately reflect the real conditions of the experiment and (2) the model is missing non-structural mass. In your case, these sources of error would probably lead to a higher (rather than lower) frequency. Note, a comparison of mode shapes can be useful to help identify the spatial location in the model that needs to be improved.
Finally, you should at least consider the numerical precision and potential for error in the data analysis performed on experimental data to identify the frequencies.
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I am familiar with the theory, it's well documented in the manual. What I am looking for is some sort of pdf/links etc. that has some tutorial examples.
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An explanation about degrees of freedom and a shape for each connector provided in ABAQUS. you can see that as a comment when using them .
Good Luck..
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I am hoping to analyse vibrations occurring in a MEMS device, and calculations indicate I will need to measure frequency and amplitude between 1 - 150 kHz range. The sensors I have looked at (e.g., accelerometer) top out around 20 kHz. What might one suggest?
-Ryan
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I understand that you are interested in finding the frequency response (frequency vs. amplitude plot) of a MEMS device. Instead of using a separate sensor, you may go for a characterization equipment called Laser Doppler vibrometer (LDV). It can detect out-of-plane vibrations up to 24 MHz. In case you are interested in in-plane vibrations, stroboscopic video microscopy may be used. It can support frequencies up to 1 MHz. Both these features are available in Polytec Micro System Analyzer (MSA-500).  
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I want to use Buckinghum Pi Theorem to relate a similitude of the blade to the prototype blade. 
I began as stating the natural frequency is function of ( Young's Modulus, Length of the blade, Cross Section area,Moment of inertia,Density) 
Fn (fn,E,L,A,I,Rho) ,then I got the dimensionless pi groups that relate natural frequency of similitude to the prototype !!!
Is this correct procedure or should I derive the natural frequencies equations first ?
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Ahmed,
You do not need to derive the natural frequencies if you are just scaling them between a prototype and full-scaled model. Please also check the attached files. Check page 16 of "6-scaleeffects.pdf"; the other two files give helpful tips as well. I hope these help.
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I would like to build a shaker running at variable frequencies between 50Hz to 1kHz at 20 micron displacement with a load of 20 gram using PZT piezo stack actuator.  I am trying to decide whether to go for a close loop voltage driven or an open loop charge driven system.  Which system is preferable in such a situation.
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If you REALLY want to preserve amplitude of oscillation across this frequency range, you may use a charge feedback loop as amplitude is directly coupled to charge fed into piezo.   No voltage or current feedback or no feedback would do amplitude stable.
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In exhaust pipe lines at the clamps, because of vibrations, the clamps welds fails. Can I replace the clamps by rubber dampers near the chase portion? What kind of rubber material can I use?
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Take a look to pdf file tirled:"experimental validation of a novel structural health monitoring
strategy for bolted pipeline joints"
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I have data which is in .hpf format that I am trying to convert .xlsx file. Can any one help me out?
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Herewith I've attached the hpf file.Just try it out. Thank you in advance.
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Basically, I am trying to detect damage on beam structures for a cantilever support. Suppose, I am measuring first natural frequencies from the experiments at several times of undamaged state of structure. I will get different first natural frequencies value in each trial with slight variation. Now how do I take single value of natural frequency ? Which method should I use to get mean value?
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If you are using Bayesian method to obtain the frequency from each test, you will also obtain the variance of each estimate. Then, you can do a weighted average with the weighting being the reciprocal of the variance.
Otherwise, assuming that each test is associated with same duration, same sampling rate and similar noise level, then you can approximate it using the simple average.
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If anyone can help me by telling me the source of vibrations (may be low or high frequency) except engine vibrations in aerospace structures?
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In the atmospheric flight, flow separation and reattachment at all Mach numbers; shock boundary layer interactions in transonic, supersonic and hypersonic speeds are some of the main sources for generating structural vibrations.
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I recorded the raw response signal and repeated the set of experiments to reduce uncertainty in the measurement by averaging process.
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So you are doing Impact modal test :)
The standard way is to average in frequency domain. So after each measurement, convert your raw time data to frequency domain by using FFT, calculate auto and cross spectrum and average them. Typically, 5 averages should be sufficient (in other words, you need to repeat each measurement 5 times).
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In modal analysis , most of the researchers are following the average of 'n' FRF measurements to reduce the noise. Is this correct?
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I am not sure if I understand your question completely. I suppose your question is in general about averaging technique used for calculating FRFs so that they have free of random noise errors.
It is correct that averaging is done to reduce the noise such that the averaged FRFs are smoother and more importantly free of random noise. However, there can be other kind of errors, which are not taken care of by the averaging procedure and require other signal processing techniques.
Please refer any standard modal analysis text for more details on averaging and other signal processing techniques used for reducing the effect of noise on the FRFs.
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Modal parameters that need to be extracted from experimental modal analysis. So I want to use RFP method because it deals with multi FRF signal which suited for SIMO and MIMO method. If any of you having good material, kindly share with me.
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Hi Prakash
You can find the details of RFP algorithm in the following paper
Richardson, M., Formenti, D.; “Parameter estimation from frequency response measurements using rational fraction polynomials”, Proceedings of the 1st IMAC, Orlando (FL), USA, 1982.
I will also suggest you to read following two papers on Unified matrix polynomial approach, which is a framework that helps in understanding and explaining most modal parameter estimation algorithms including RFP.
Allemang, R.J., Brown, D.L.,; “A unified matrix polynomial approach to modal identification”, Journal of Sound and Vibration, Volume 211, Number 3, pp. 301-322, April 1998.
Allemang, R.J., Phillips, A.W.; “The unified matrix polynomial approach to understanding modal parameter estimation: an update”, Proceedings of ISMA International Conference on Noise and Vibration Engineering, Katholieke Universiteit Leuven, Belgium, 2004.
Further, unless you have some specific condition that require you to use RFP, I would suggest that you start with Polyreference Time Domain algorithm as that is comparatively easier to understand and code. You can find detail of PTD in UMPA papers listed above.
BR
Shashank
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The signals acquired from both accelerometer and impact hammer through DT9837 DAQ Card using MATLAB. Will it affect the frequency of the structure if data starts to capture after nth sample?
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It will affect the phase, but not the amplitude of the frequency response (given that you captured the entire signal +/-)
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Can anyone tell me that which method of balancing is being used in overhung fans? For rotors, single plane and double plane balancing can be selected by seeing their D/W ratio where "D" is diameter of the rotor and "W" is the width of the rotor. What will be the width of the of Fan or Blower if the same is the method used to select type of balancing?
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I am not so sure about what you are asking. of course, the length-to-diameter ratio will influence your balancing operation. But this ratio has nothing to do with the balancing method . The influence coefficient method can perfectly balance the overhung rotor. I have used this method in field balancing of several overhung gas turbines. Both single plane and double planes can be used, which depends on the rotor being balancd
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Is there anybody performing random vibration analysis? Random vibration analysis results do not include phase data, so stress invariants such as von mises equivalent stress can not be directly calculated. Is there any method or tool which you use to estimate Von Mises Equivalent Stress in random vibration analysis?
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Dear Fatih Aruk,
first of all, what is the geometry of the structure you want to analyze and how to you measure the vibration (scanning optically or other)? For simple geometries like cantilevers it is sufficient to know the amplitude, e.g. as measured by AFM and thermal-noise excitation (check out papers by JE Sader), to reconstruct the vibration using eigenmode decomposition. For complex geometries you would need to measure the amplitude on each point of the surface. Then you can use FEM eigenmode analysis to find a matching modeshape.
Please provide more details on your subject.
Regards, Erwin