Vibration Testing - Science topic

1. How measured vibration response, i.e. with 3D-accelerometer?

2. You must separate residual vibrations of a structure ones from structure-on-fixture construction. Thus, you must check an vibration response for a fixture itself for this purpose.

Some things to check:

How does coherence look like? If close to 1, then there is a nearly linear relation between input an output, if closer to 0 then maybe something wrong with your measurement setup (bad SNR?) since

SNR = gamma²/(1-gamma²), with gamma being the coherence.

Bad SNR can be due to the fact that the eigenmode (at a certain eigenfrequency) is not "excitable", i.e. you hit it at a node, not at a point of maximum amplitude, or your acceleration sensor has bad "observation", i.e. it likewise sits at a node of this mode and not at a point of maximum amplitude.

You might also want to check the APS (Autopowerspectrum) of the hammer pulse. Depending on the hammer tip you are using, you will be able to excite a different distribution of energy, i.e. more energy at lower frequencies for low stiffness tips (like rubber) or higher energy at higher frequencies for higher stiffness tips (like hard resin or metal). The shape of the APS of the hammer pulse will show you the details.

Regarding windowing you should also be careful to choose rectangular or exponential for the hammer pulse (and the response). Do not use Hanning or Hamming windows, since they will "fade-in and out" the time signal and you loose too much energy of the hammer pulse (which sits at the start of the window).

There are some good commercial programs available like Head Acoustics Artemis, LMS, etc. that support you in doing it right.

Hope this helps (or is it all known?)

You could perform a transient vibration recording during the start (or shut-down) of the compressor until it reaches its nominal speed and visualise (waterfall display) the dominant harmonics (maybe the unbalance is not the predominant one?) and if they evolve smoothly with the square RPM (if they trigger some structural resonance you will see bumps in the waterfall)

Sorry Amiaan, Physics dictate that any sensor will measure the local level of vibration whatever the origin, so environment-induced vibration will equally be recorded by the LV. And you have to be further cautious to protect the LV device and mirrors from this environment-induced vibration...

As previously commented, if you use an accelerometer, its mass will also alter the vibration reading, which is not the case of LV - this is the main difference!

you need to ensure that the mode shapes being compared are in the same format. Here's a suggested approach:

Once you have both mode shapes in the same format (real-valued), you can calculate the MAC using the standard formula. The MAC formula involves comparing corresponding displacement values at each node between the two mode shapes.

Remember to normalize the mode shapes before applying the MAC formula. Normalization helps in removing any scaling effects and ensures a fair comparison between the mode shapes.

I hope this explanation helps you resolve the issue and accurately calculate the MAC between your experimental and FEM mode shapes. If you have any further questions or need additional assistance, please feel free to ask.

Does the accelerometer sit truly fixed or is it possible that it rattles?

How about the cable?

Interference in some sort can give results of dips and peaks like this. But they are very dense. Might be related to something slow in the time history?

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

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"

@https://vru.vibrationresearch.com/lesson/calculating-psd-time-history/

I hope it will be helpful ...

Best regards ...

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?

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.

Thank you so much for your reply, and have a nice day. Best regard.

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

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

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.

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

Dear Muhammmad Fayrus ,

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

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.

Thank you so much for providing me with useful information.

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

The followings are good sources for ground vibration test (GVT):

http://www.garteur.org/Technical%20Reports/SM_AG-19_TP-115_OPEN.pdf

https://apps.dtic.mil/dtic/tr/fulltext/u2/a108262.pdf

I hope it is helpful for you.

All the best.

Dear Marina,

You may find the following links useful

It is a very interested question

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.

Hi ,Everybody

I agree with all the above answer.

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.

Hi Sameer,

I have reported several works using sound of the engine.

I recommend you to check them up.

The latest is:

Good luck

Peyman

Hi

This is a classic problem & a nuisance. 

Try these steps. 

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

This is a very interesting question with a number of possible answers.

A thorough approach to guitar tuning is given in

This paper is quite good, since it gives basic definitions for music that includes both sound and silence and for a musical instrument (see the Abstract).

Here is a remarkable approach to guitar tuning by modern cochlear implant (CI) users:

See, also:

Hi

I believe that you find all your questions answered in the book written by M.L. Munjal, Acoustics of Ducts and Mufflers

https://www.amazon.com/Acoustics-Ducts-Mufflers-M-Munjal/dp/1118443128 

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

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. 

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.

 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

Hi Timi

You might like this link for basic understanding

http://qringtech.com/2014/05/27/piping-vibration-fatigue-risk-assessment/ 

(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

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

http://qringtech.com/learnmore/why-simulate-measure-correlate-automate/ 

Hope this helps

Claes

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

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

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

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.

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.

Hi David

Debugging software always is dog's work.

Suggestions on simple things to compare are

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

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..

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

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!

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

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.

Please see the attached file

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

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).

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.

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.

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. 

It is difficult to aviod the lossing of some bits since it is lossy techniques

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

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.

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.

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. 

   

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)."

http://www.sandv.com/downloads/0308alle.pdf is a good starting point.

If you send me your cdb file (CDWRITE, ALL) and the experimental mode shapes I will try to send you the corresponding MAC matrix.

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)

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.

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..

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).  

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.

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.

Take a look to pdf file tirled:"experimental validation of a novel structural health monitoring

strategy for bolted pipeline joints"

Herewith I've attached the hpf file.Just try it out. Thank you in advance.

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.

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.

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).

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.

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

It will affect the phase, but not the amplitude of the frequency response (given that you captured the entire signal +/-)

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

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