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The aim is to study the effect of flow velocity of a certain fluid in a pipe, on the vibrational behaviour of the pipe.
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why you only wnat Ansys, my thought is more good to you use "Fluent(CFD simulation program]"
is any reason you used the Ansys??
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Which is the most crack direction is studied in a metal cantilever beam? When the crack is vertical or horizontal? (I mean if the crack propagates vertically or horizontally?)
And how each type of excitation(Bending, Axial,..) is sensitive for each type of crack shape and orientation?
I am asking for test purposes .. So I can use the crack direction that is more sensitive for measurements in my experiment.
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I think it depend on the type of load applied.
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Is there any effect of damage shape on the damage severity? And which do you expect has more severity of damage the holes shape or longitudinal shape? And why?
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I think this article may be helpful
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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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How to represent natural frequencies and mode shapes in same matrix for many cases for damage detection purposes?
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As Christian Willberg already pointed out, a 2 DOF system can only have 2 eigenvalues and consequently 2 mode shapes. These mode shapes describe all possible movement/displacement fields of the system. That is to say, each system response is a linear combination of those 2 modes. Everything else is not possible. Thus, if you have 3 modes shapes you must have a 3 DOF system.
In the modal decomposition method, the modes can be used to decouple the equations of motion (provided that we fulfill certain assumptions with respect to the material damping).
Therefore, you must restate your question and provide more details on your system, if you expect a meaningful answer. At this point, the question you would like to be clarified is not physical. Please go back to your problem and think a bit about what you actually want/need to know.
Kind regards,
Sascha
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I have the following questions regarding vibration-based damage detection of a cantilever beam:
1-What is the purpose of discretizing the cantilever beam by finite element technique?
2-Do the number of discretized elements and their length affect the modal analysis( healthy and damaged natural frequency, mode shapes)?
3- Why do the biggest changes in natural frequency happened when the damage occurred near the fixed end and became smaller if the damage occurred far away from its fixed end?
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The reduction in stiffness will be high if the defect/crack is present in regions of high stress. In a cantilever beam, the maximum stress occurs at the fixed end. Therefore, if the defect/crack is near the free end you can expect a greater reduction in the natural frequency from that of an undamaged beam as compared to when the defect/crack is present elsewhere. You can find a discussion on the same in my research article. I have attached it below for your perusal.
Hope it helps.
Regards,
Jatin
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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 calculated the gear meshing frequency of planetary gearbox to be 786 Hz. However, when a FFT is performed on the data acquired for the same planetary gearbox I could see peak around 645 Hz and not at 786 Hz.
The calculated mesh frequency was done based on the speed and number of teeth. But the signals acquired during operation was under loaded condition.
Does external load change the natural frequency and meshing frequency of gear?
Is there any reference to calculate the theoretical gear mesh frequency in relationship with load.
Attached FFT plot.
Thanks in advance for sharing you knowledge.
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Gear meshing frequency is a kinematic (rotation speed-related) parameter. If you have another maximum in the spectrum under loading conditions, this effect can probably be related to another source (gear coupling or bearing). Of course, if you have reduced rotation speed under load (motor power drop), you will have shifted the frequency of gear meshing.
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I am analyzing the squeal of Disc Brake Assembly using Abaqus and I tried to find the unstable frequencies using complex frequency which caused the squealing noise: I am able to find the unstable modes but they are not forming a stable unstable pair. Also, the participation factor is coming for many modes. I am attaching the brake model for reference. Please help me to find unstable frequencies using Abaqus?
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Hi
For complex modal analysis, I fear we are all beginners.
Positive damping is conversion of vibration energy into heat, a nearly irreversible phenomenon, ie a power loss.
Negative damping implies power input, ie excitation.
Whether a mode get negative or positive damping depends on several factors. The cross product between transportation (rotation) and vibration matters, as does the mode inherent damping. Add to this effects from a spinning body where you get forward and backward rotating modes.
A well studied phenomenon that contain the same base physics is wind excitation of a circular elastically suspended body.
Anders advice wrt Jim Woodhouse is very good advice. In my mind, his work is sterling quality.
Hope this helps
Claes
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I have a simulation code for a Horizontal Washing Machine.
The code solves the equations of motions of the system by Matlab ode45 and plots the vibration response of the system at the transient state of performance.
In this code, the frequency (omega) is an exponential function of time, as it's stated below (and its diagram is attached to 'the question'):
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omega= (1-exp((-0.5)*t))*omega_0+(1-exp((-0.5)*heaviside(t-t1).*(t-t1)))*(omega_1-omega_0);
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ode command:
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[T,Y]=ode45(@snowa1,tspan1,initial_vector1);
plot(T,Y(:,1)-mean(Y(:,1)))
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The resulting displacement response is attached to the question.
It is desired to :
First, increase the frequency to omega_0 by exponential1
Then, increase it to omega_1 by exponential2
But 'the problem' is that:
the displacement response shows an unexpected increase in frequency at the beginning of the second exponential increase (it becomes 20 Hz, which is much larger than the maximum frequency in the simulation- 10 Hz).
Do you know what could be the reason for this response?
Any help would be gratefully appreciated.
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I understand that the 4DOF system for the washer can be quite lengthy. However, I'm unsure if your question is a control problem. If it is, and the 4DOF mathematical model can be expressed in such form:
x' = f(x) + g(xFc(ω)
where
  1. f(x) = [f1(x), f2(x), f3(x), f4(x)]T and g(x) are the nonlinear terms in column vector forms that you derived from the Lagrangian method,
  2. Fc(ω) is the control force that represents a function of ω in vector form, and
  3. ω (omega) is the control input,
then I think it is possible to design the spin speed profile for the control input, ω, so that the desired responses of x can be achieved. If you want to design the profile, you need to at least understand the mathematical equation for Fc(ω). Do you want to regulate the spin speed at 300 rpm, 600 rpm, or 1200 rpm? Because I see only the signal oscillates within the dimensionless amplitudes ± 4×10–3.
I have plotted the signal according to your suggestion, and compared it with Mahdi's original signal. Note that if t1 > 5/τ, then exp(–τ·θ(t – t1)·t) ≈ 0 after t1, because exp(–0.5·t) has decayed to almost zero.
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Can anyone suggest to me method to design fuzzy inference system (FIS) for MIMO structural damage detection (i.e. data distribution on the membership function, parameters of MF, Generate rules ... etc )
In my system there are 3 inputs and 2 outputs:
Inputs: Relative 1st Natural frequency , Relative 2nd Natural frequency , Relative 3rd Natural frequency
Outputs: Crack depth ratio , Crack Length
Note: I tried to use "genfis" By MATLAB it didn't give me reasonable results.
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Hi Murana Awad
Is it possible for you to share your data with me? I have some idea to solve your problem but I need your data.
I'm in touch by : ahmadi.v.1380@gmail.com
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I am doing vibrational analysis of mono-acetic acid after wavefunction and geometry optimisation. In the output file of vibrational analysis the following lines were present containing harmonic frequencies of mono-acetic acid.
****************************************************************
HARMONIC FREQUENCIES [cm**-1]:
-93.9446 -56.8345 -14.9036 79.1124
83.2432 123.7967 180.8622 415.9833
465.7580 564.8411 581.9038 795.9969
942.4123 1030.7040 1139.4888 1218.9753
1356.8784 1433.9457 1447.8727 1776.4078
2976.9823 3023.5483 3084.8354 3634.5117
PURIFICATION OF DYNAMICAL MATRIX
****************************************************************
HARMONIC FREQUENCIES [cm**-1]:
-55.0883 -0.0000 0.0000 0.0000
80.2766 101.0671 159.3476 415.9277
465.5977 564.8100 581.8316 795.9872
942.4062 1030.6968 1139.4801 1218.9731
1356.8769 1433.9456 1447.8725 1776.4022
2976.9823 3023.5483 3084.8354 3634.5117
ChkSum(FREQ) = 0.26286465E+05
Can some one help me understand what is meant by "Purification OF DYNAMICAL MATRIX" and interpret the above results CH3COOH should have 18 modes of vibrations (3N-6). but I am getting 20 modes of vibrations? Furthermore is -55.0883 cm-1 a false flag or is it because of incorrect optimisation of structure?
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Getting all zeros for the first 6 modes enforces the requirement of invariance of the PES with respect to translation/rotation. Harmonic frequencies obtained by finite differences may often lead, for lack of numerical precision, to non-zero values in these modes. The "purification" should consist (at least if it is the same as in GAMESS) in a procedure of transforming back and forth the matrix between cartesian and internal coordinates, which effectively helps zeroing the freqs and IR absorptions of the translational and rotational modes.
The fact that you still get those -55. and +88. cm-1 is a possible sign of your structure not being close enough to a true minimum, but I can't be sure on this. In some cases, a solution is met by simply repeating the optimisation with increased numerical precision in the DFT integration scheme and/or SCF convergence.
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In this picture an experiment analysis by Shaker . What is the conclusion from picture?
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Hi All,
I have two vibration signals taken from the same source using two difference sensors. Therefore, the frequency resolution for both the vibration signals is different (One is 1.5 Hz, other is 7 Hz). What methods or tools could be applied to compare both the signals?
Attached are the two signals obtained from the two sensors.
Note - acceleration is Y-axis is considered to comparison.
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I guess, first you need to know what you would like to compare.
And then understand, what kind of spectral data you have.
In addition, if you want to compare the magnitude of the signal for different frequency resolutions, you need to be aware of the difference of a spectrum versus a spectral density.
E.g., a power spectrum gives you the total power within the frequency bin, so for a broad band signal, the power changes with the width of that bin (i.e. frequency resolution). On the other side, a power spectral density gives you the normalized power per unit frequency, so it stays constant for white noise independent of the frequency resolution, but it changes with analysis bandwith for a narrowband signal (e.g. sine wave) due to the normalisation by the frequency resolution.
I hope this somehow covers what you are looking for as your original question is quite broad.
By the way, the frequency resolution of the spectra you have is not defined by the sensor, but by the analysis process applied to the signals. It might be helpful to understand the complete measurement and analysis process in more detail. Depending on your task, it might even be possible to use the 2 sensors with the same analysis process, making it easier to compare (not: understand) the results.
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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 have a project to do the vibration analysis of underwater pipeline hence i dont know from whee to start and how to do please help
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You should be aware of the widely used document in pipeline industry titled: "DNVGL-RP-F105 Free spanning pipelines". Then ANSYS can be used for a simple beam modal analysis if needed to determine the governing vibration frequencies and mode shapes which are used therein, with due account for the effective axial equilibrium force in the pipeline.
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while performing i'm encountering error , i'm attaching the mess file and APDL commands
*** WARNING ***                          Entity 3 is undefined.  The MPDELE command is ignored.                 
 *** ERROR ***                            Element type 2 is not the same shape as FLUID30.  Switching to a         different shape is not allowed while elements of type 2 exist.  
please help
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I am interested in the cooperation.
Is there a possibility of doing the research here in Tunisia?
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I am an undergraduate working on modelling generator noise through an aperture and writing my literature review has been a little extra difficult.
I have been trying to understand the methods of noise analysis in acoustic engineering. There are four of them which are mostly used. And I need to understand each of them to be able to choose the method I would be using in my modelling.
If you have any material, book or journal that could assist me with my research work please do send in, would be very much appreciated.
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see
1-Fundamentals of noise and vibration analysis for engineers
Cambridge University Press
M P Norton, D G Karczub
Year:
2003
2-Noise and Vibration Analysis: Signal Analysis and Experimental Procedures
Wiley
Anders Brandt
Year:
2011
3-Fundamentals of Noise and Vibration Analysis for Engineers
Cambridge University Press
Norton M.P., Karczub D.G.
Year:
2003
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I would like to ask teachers: many experts have done a lot of research on the vibration analysis of cylinder panel, what is the research background of cylinder panel ? Such as submarines, aircraft, missiles and so on ? Do you have any pictures of this cylindrical panels applied to an actual object ? For example, the cylindrical panels on airplanes and submarines. It is better to have photos of actual objects or paper containing photos of actual objects.
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This chapter of the Marine Structural Design book might help you:
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This is the part of the input script. While running the simulation an error is showing
ERROR: Kspace style requires atom attribute q (src/KSPACE/pppm.cpp:208)
# vibration analysis simulation units  metal dimension 3 boundary p p f atom_style atomic neighbor 0.3 bin neigh_modify delay 2 every 1 newton on read_data vibration.data group Platinum type 1 group Argon type 2 group Carbon type 3 # force field pair_style hybrid/overlay lj/cut/coul/long 12.0 eam tersoff kspace_style pppm 1.0e-6 pair_coeff      1 1 eam Pt_u3.eam #Pt-Pt pair_coeff      * * tersoff BNC.tersoff NULL NULL C #C-C 3-3 pair_coeff      2 2 lj/cut/coul/long 0.0104 3.54 #Ar Ar Lj potential pair_coeff      1 1 lj/cut/coul/long 0.5650 1.066 pair_coeff      3 3 lj/cut/coul/long 0.0028 3.14 pair_coeff      1 2 lj/cut/coul/long 0.122 3.311 # Pt-Ar pair_coeff      1 3 lj/cut/coul/long 0.092 3.302 # Pt-C pair_coeff      2 3 lj/cut/coul/long 0.139 3.860 # Ar-C pair_modify       mix arithmetic #---------energy minimization------------------------------ minimize 1.0e-4 1.0e-6 100 1000 min_modify         dmax 0.4 min_style     cg
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Charges have to be set for each atom as the Kspace solver calculates long-range coulombic interactions and if you don't want to calculate these interactions, then remove the "Kspace" line.
Hope this helps
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i have vibration data of bridge and process the data with different possible techniques such as FFT, Wavelet decomposition, Empirical mode decomposition, Hilbert Transform, Frequency domain decomposition, spectrograms, etc. but still i am not able to locate exact or pin point frequency of the bridge structure. in the following techniques the results are in a specific range of frequency such as 2.6 to 3.1 Hz. The data showing this specific range and not providing the exact frequency. because in this range any number can be the natural frequency of the bridge structure. so the actual frequency lies in this specific range but i want to go further in depth to figure out the exact value of the frequency in Hz. but the problem is i am not able to find any technique that will give me answer of my curiosity. i recorded data from accelerometers considering normal traffic conditions. there is not closure of bridge. vehicles are passing normal situation.if anyone have any clue about it or still my question is not clear so i can explain further
i attached some of my results
i will be very grateful to anyone who let me find my answer
thanks
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Dear Ali,
the maximum response recorded by your accelerometers is mathematically the CONVOLUTION of the structural response of the bridge (with a peak expected at each natural frequency) and the excitation by the trucks (with a peak at their own suspension frequency) meaning the frequency of the maximum response is a mix of both! Of course the truck's primary suspension frequencies vary from a truck to the next, still in the same range.
In addition the natural frequency of the bridge is load dependant (weight and position of the heavy trucks at the time of the record), and temperature-dependant (meaning day/night, clear day/cloudy and seasonal fluctuations...)
Back to your precise question, you have just NO WAY to determine the exact bridge natural frequencies by this "natural response" method. As suggested, you must close the bridge (however with the same added load than the usual traffic) and use for example a dropped weight to generate a broadband shock (preferably located in consideration of the anticipated mode shape, which allows you to trigger distinctively the first flexural/torsional modes). And still the exact frequency will vary with the previously mentioned load and temperature conditions... Sorry for you, that's just the complexity of structural vibration physics!
Back to Vahid's remark, we could only appreciate the likely natural frequency range of your bridge by knowing its precise construction and span, but the natural frequency of very long bridge spans can even be below 1Hz (remember the ill-fated Tacoma bridge, destroyed by wind gusts at approx. 0.5Hz resonance https://www.youtube.com/watch?v=j-zczJXSxnw). Obviously short bridges have higher natural frequencies but you can interpret it as revealing over-designed structures! The Tacoma bridge example is also a good evidence of the 3D complexity of the mode shapes (something also well evidenced by Eric's study, which provide a very accurate in-situ modal analysis). My guess is that in your case the 2.6 to 3.1 band correspond effectively to the interaction of the trucks suspensions with one of the main natural frequencies of this bridge... in this global 2.8 +/- 0.3Hz band! But don't ask for more precision...
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I have been given samples for 'FTIR for vibrational analysis of compounds'.
What short of information i can get through this and how to read the FTIR spetra to right results for nano materials. Is there any specific spectra table for inorganic compounds.
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I am not sure about the spectra table. However, there are many videos on youtube that show how to analyze the FTIR results. You can search and watch some videos for more details
Regards,
K
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The various parameters taken are:
1. Radius
2. Span
3. Diaphragm arrangement
4. Number of Elements.
5. Boundary condition
6. Cross-section.
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Does this include spring-dashpot elements?
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Dear Mathias D, according to Abaqus manual, element damping is not available for the random response analysis (see tables 1 and 2 https://abaqus-docs.mit.edu/2017/English/SIMACAEANLRefMap/simaanl-c-dynamicproc.htm#simaanl-c-dynamicproc-linear__simaanl-c-alineardynamics-simdamping)
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I need some help, I have run block lanczos modal analysis in ansys APDL.It shows that the 'solution is done ' . However, there is no any result listed in result summary. How to overcome this problem?
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Hi
Check your boundry conditions. because they are very crucial for performing an analysis on ANSYS. I recommend you instead of adpl just go into workbench and select modal analysis
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I've run a few simple random vibration analysis such as cylindrical tube and cantilever beam in LS-Dyna. Now, I try to understand the output results in terms of PSD and RMS values.  For instance, if I input a flat acceleration PSD of 0.02 g^2/Hz over a frequency of 0.1Hz to 1000Hz, how can I use this input to hand calculate the RMS von mises stress? I don't mind the math if someone could explain. Thanks
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You can make an approximation using Miles' Equation for a Single DOF system. The parameters that you need are : (a) input PSD level (b) Natural Frequency (Fn) (c) Q, Transmissibility at fn
Grms = √ ( π *fn*Q*PSDi)
fn = natural frequency
Q =Transmissibility
PSDi = Maximum input psd level in g^2/Hz from PSD v Frequency Curve
NB: This formula gives you the maximum Grms level based on a "White-Noise" input. i.e. maximum input psd level from your input curve. You can make an 'approximation' at the maximum G level that the component will be exposed to and using that G level you will know the exposed G level of the unit. From that level you can run another analysis and evaluate your stresses.
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During parameter study for a project (signal processing applied in mechanical vibration), when I decrease the frequency to a very low value (less than 200 mHz, for a interested range of frequency of a few hundred Herz), the frequency response I have gets "squishy" (instead of a single line going up or down, I have a waveform going up or down).
Checking on some forums online yield me the connection to "dirac delta function", but I do not understand it fully. So I'd like to ask if there is any connection between dirac delta function and frequency resolution, with regards to FFT in vibration analysis. Thanks for your help.
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Roberto Ferretti Don't worry about that. I have a... strange explanation for it. Both in terms of "why the grey line is heavily smeared" and "why do we see peaks at 50 150 Hz and so on".
The first is a combination of very low frequency resolution plus window function. The second... noise. Probably noise. Or some equivalent "freak accident". More recently, I have repeated the experiment under the same conditions, the change is only "hitting different point" - but considering the graph above is the FFT of input force signal, there should be no change. Yet, the recent experiments show practically no such peaks at all.
Another answer (and a more technical one) is the influence of powerline (AC 50 Hz) and some internal harmonic of the measuring system under certain conditions...
Yeah, it is still quite fuzzy.
But still, thanks for your help.
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After taking the frequency spectrum of an impulse force (from a shaker, sampled from a vibration analysis test), there are noticeable peaks at 50 and 150 Hz (presumably due to some electrical/electronic artefacts or some mismatch impedance between the shaker's coil and its structure). This specific experiment aims to study the effect of frequency resolution on the spectrum.
When the frequency resolution is smaller (same bandwidth, or F_max - F_min, is used, and more spectral/FFT lines are used), these sudden peaks start to appear. It should be noted that the original input signal is the same. The question is why this happens?
Thanks for your help
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The graph shows the conversion of a "knocking force" (man-made impulse) from time to the frequency domain. Thus, the peaks should not be there in the first place. Time duration of the signal or the measurement time (defined by the software) is 1/delta f (inverse of the frequency resolution).
About the different heights, it can be contributed to the different coefficients in Fourier transform (this is made by having different frequency resolution)
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Dear all
I am working on dynamic vibration analysis of FGM plate with piezoelectric patch
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Hello folks,
i am doing a vibration experiments to analyze the transfer function. But, before that I want to see the effect of FFT-Lines (Band width kept constant) on my experiments. Higher the FFT-Lines will be, finer will be the frequency resolution, which is actually good to analyze the result (if measurement time is not a big factor). Now, I wanna know is there any limitation for frequency resolution? Does my frequency spectrum will not show any change after a certain frequency resolution factor?
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If you can get access to them, read the Keysight application notes on spectrum analysis. Many of the same principles apply when using an FFT, which is spectrum analysis. The old application notes are as good or better than the modern ones. They used to be Hewlett Packard and then Agilent. Their technical publications are excellent.
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Our research is turing to nonlinear vibrations of plates and solids of acosutic wave device strcutures. It is high frequency vibration, and associated phononmena can only be considered with nonlinear analysis.
Please share your experiences and publications on nonlinear Rayleigh-Ritz method with us.
Joint work on the problem is possible for co-authored publications.
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Dear professor Ji Wang
RR method can be used vastly when it is difficult to obtain analytical solution. One of the key benefits of this approach is its capability to be used for variety of boundary conditions.
For the nonlinear vibration it is used to transfer the space-time problem to the time problem. I mean, after applying this method the vibration problem converts to the a 1dof system, which is just time-dependent (mD[X,2]+cD[X,1]+kX=f). now you can implement a variety of methods for this current problem, namely, multiple scale, straight forward expansion, harmonic balance, etc.
Hope it helps
All the best
Mahdi
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I use a piezoelectric actuator for active control of a flexible structure, and measure the vibration amplitude at the same place using an accelerometer. When actuating the structure with a shaker, I see less noise, but when actuating with the piezoelectric actuator, there is too much periodic noise in the response, and it is not usable.
Any idea how I can reduce or remove it?
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I know there is an electric circuit especially for removing and attenuating the piezoelectric noise. although the software are able to attenuate some noise, but I have tried and I've seen that the hardware filters are much more effective.
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Dear researches
In general, the value of modal participating mass ratio (MPMR) for each vibration mode represents the participation of each mode in the structural responses.
when a structure equipped with TMD, a vibration mode is added to the others. MPMR value of the added vibration mode can be significant even when TMD mass is very small and as a result, TMD has no effect on the structural responses.
How can this contradiction be justified?
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I second Einar Strømmen & Pranoy Nair responses, also I would like to add a point that when we add a TMD we are introducing damping into the system. I am not really sure how you would define MPMR in such a system as modal analysis works only for undamped systems.
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I am conducting a project where underground blasting effects are analysed on soil and structures above the soil. I've currently only have a very basic Abaqus model of a soil block with an implicit dynamic step. A time history amplitude was induced on this basic block model of soil. It shows the stress wave propagations. It has parameters for the Mohr-Coloumb plasticity. I am looking for books or any literature to further understand how the vibration of the blast will effect the soil layer, and possibly different layers of soil (rocks, clay, silty, soil etc). Any help or advice is appreciated!
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ERT
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Dear friends
I'm working on the validation of an FIV case, which for making phase difference between force and displacement, I used an initial velocity in the structural, but after several coupling step, the drag force becomes constant, therefore the structure doesn't fluctuate, the drag force is more than the amount mentioned in the original case which shows vibration in the structure.
any suggestion will be appreciated
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dear Dr. Thomas Frank
thanks for spending your time and answering my question.i will check points you mentioned.
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In ABAQUS help I read the applications of direct solution in steady state dynamic analysis as follows , what are the examples of applications and where I can NOT use this method ? I would appreciate a comprehensive answer , thank youhttp://ivt-abaqusdoc.ivt.ntnu.no:2080/v6.11/books/usb/default.htm?startat=pt03ch06s03at09.htmlThe direct-solution steady-state analysis procedure can be used in the following cases for which the eigenvalues cannot be extracted (and, thus, the mode-based steady-state dynamics procedures are not applicable):
  • for nonsymmetric stiffness;
  • when any form of damping other than modal damping must be included; and
  • when viscoelastic material properties must be taken into account.
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Aha, I see.
Well, even with zero damping, you will get finite response as long as you do not hit exactly the resonance frequency.
To better understand, take a look here - the sdof system is key to all linear dynamics
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Damping of oscillation by interstitial atom movement through lattice shows a damping peak. Why the damping is frequency dependent, while interstitials transit from site to site, and restoring forces are not strictly hookean? An article claims, such fitting of damping data with mechanical impedance models have no theoretical justification, ( , , )why?
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Dear Sumit,
I think snoek effect is related with hydrostatic relaxation and orientation.
relaxation.
Interstitial atoms in ternary b.c.c. alloys exhibit hydrostatic relaxation, if an applied stress has a dilatational stress component. The effect is absent in binary alloys. Hydrostatic relaxation, in contrast to orientation relaxation effect, involves long-range diffusion; in order to understand various aspects of the process. The Snoek relaxation is associated with the redistribution of interstitial atoms in the bcc lattice under the application of the oscillatory stress. Addition of substitutional solutes introduces new peaks or broadening of the normal snoek peak. The relaxation due to interstitial solutes in bcc metals is often affected markedly by the presence of a small amount of substitutional solute atoms. This effect may be originated from the interaction between the substitutional and interstitial solute atoms, or the s-i interaction.
Example, damping of steel tuning forks goes through a maximum as a function of temperature and that the location of this maximum is dependent upon the frequency of the fork.
Ashish
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Hello,
I want to analyze a wheel-tire system. In order to do that I need Young's Modulus, Shear Modulus, Loss Factor and Poisson's Ratio. I have already checked some articles but I need a specific TPE or rubber. Because I will produce this system after my analyses. How can I find these properties?
Thank you.
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Dear sir,
Rubber properties vary from each and every blend based on each constituents added per 100 parts of rubber, their process, shelf life, etc. Better to obtain properties from RMA or original manufacturer.
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I am trying to regenerate the Natural Frequencies of a clamped-clamped viscoelastic core via. ACM (Approached Complex Eigenmodes) method as is in the article : "Linear and nonlinear vibrations analysis of viscoelastic sandwich beams" (DOI: 10.1016/j.jsv.2010.06.012).I am trying to use semi analytical Galerkin method in order to do so. the problem with the use of ACM method for modeling the core my answers are close but when I increase the number of modes to solve the problem in more precise way my answer get worse! and also there is no convergence happening with increasing the number of the modes. what the problem could be? and would it be a better approach to solve the frequency dependent problems which wouldn't be highly costed in solving?
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Hi. There are two ways. the first one is to construct a mechanical model to describe the viscoelastic behaviour (in frequency domain) and include it in the stiffness matrix of the model (In this case, the Kglobal matrix will depend of the frequency and you will need use a recursive algorithm to compute the modal parameters). the second way is to express your model in a time domain and use the FFT.
I describe the fist way in my reseach
Uncertainty propagation analysis in laminated structures with viscoelastic core
WP Hernández, DA Castello, TG Ritto - Computers & Structures, 2016
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I have been doing research on extracting information like acceleration, distance, etc. from an analogue signal by performing analogue signal processing on any type of signal. I haven't found any certain techniques which would help me in providing a formula or any sort of information which would lead to extracting information by analogue signal processing. If anyone is aware of analogue signal processing, could you please enlighten me if it is even possible to do this?
After spending hours, I am at a stage where I feel like it's not even possible to do this.
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I think so. The most acceptable method is to convert the measured non-electric quantity (acceleration, distance, etc.) into an electrical quantity (voltage, current, resistance). After receiving the analog electrical signal corresponding to the measured value, you can further work on the processing of this signal. First of all, it will be necessary to choose the appropriate type of sensor (accelerometer, piezo sensor, displacement sensor, etc.). The analog signal received from the sensor will most likely have to be amplified, and then it can be processed using an analog-to-digital converter. But the easiest way is to convert the signal from the sensor into electrical voltage with a value proportional to this value and then using the capabilities of a conventional multimeter, you can control this value. If the received DC signal, then using a multimeter you can easily control the voltage in the range of 1 mV - 1000V. If the AC voltage is less than 200mV, then it must be amplified so that it can be measured with a multimeter.
I wish you success
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Hi All
How can I define frequency dependent damping in Ansys ?
it seems to be Damping frequency, but I am told that the value I input here, is used only to calculate the stiffness matrix coefficient, so If I input multiple values for damping , they will get overwritten
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Number you change according t o your requirement
sample
TB,SDAMP,1,,1 TBFIELD,FREQ,30 TBDATA,1,0.02 TBFIELD,FREQ,70 TBDATA,1,0.018 TBFIELD,FREQ,120 TBDATA,1,0.016 TBFIELD,FREQ,200 TBDATA,1,0.014 TBFIELD,FREQ,240 TBDATA,1,0.012 TBFIELD,FREQ,308 TBDATA,1,0.01
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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 looking for ways to do vibrational analysis for the molecule I studied. But I found very little about how to self-define coordinates. And I don't know the meaning of 's' or 'k' in the first column of automatically generated .dd2 file.
Does anyone know the logical way to do it?
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I am using FFT(Matlab) to convert time domain curve in frequency domain but it is showing me the number of samples in X-axis instead of frequency. How to obtain the frequency in X axis in frequency domain curve obtained from time domain using FFT?
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For example, if you have N data in a range of T seconds, then the steplength in frequency domain is 1/T Hz. Keep in mind, FFT will also return N data in frequency domain.
Thus, what you get is exactly [0:(N-1)] * 1/T Hz in frequency domain.
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I have frequency domain result for pressure. After converting it to time domain by applying inverse Fourier transform it's amplitude is changing. It is not matching with the respective (1/frequency) values in time domain curve. Is there any normalization applied while converting by inverse Fourier transform?
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Yes, there is often a constant scaling factor, such as a 1/(2*Pi), or square root of that, as I vaguely recall. Each FFT package seems to use its own favorite scaling.
You must look up the detailed description of the inverse FFT package that you are using. It should place the equations for the forward and the inverse FFT side by side in the description, from which you can see exactly how the scaling is being handled. You generally have to check for every different FFT routine you use (MatLab, MathCad, R, Numerical Recipes, etc...)
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Hi all
in an HCF analysis for a Shell body, how do I use probability in Stress level in wohler curve ?
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Hi Farzad, could we consider bootstap fir this problem? Let s try
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We know that IRF for an SDoF is:
h(t-ta) = ( 1/m*wd ) * e- kesi * wn * (t-ta) * sin( wd * (t-ta))
what is the form of an MDoF function, with this in mind that we do not want to use modal analysis to decouple the equations?
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Hello Mohammad Maldar
The Impulse response function for a MDoF will be given by the same expression as for a SDOF system with the exception that the terms in the formula will now be matrices and vectors.
That is h(t-ta) = (M*wd )-1 * ekesi * wn * (t-ta) * sin( wd* (t-ta))
where M is the mass matrix ; K is the stiffness matrix
wn = sqrt(KM-1) wd = wn*sqrt(I -D2)
I = unit matrix ; D = damping matrix
The user should know how to compute a function of matrix A: f(A). This involves the diagonalization of A by determining its eigen values and eigen vectors.
Note that K = [ k11 k12.......k1,n ; k21 k22..............k2,n; ..................; Kn,1 kn,2 ........................kn,n]
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I want to do a free vibration analysis for a plate. In this research, I want to use the Ritz method. For Ritz-shape functions, which are the best polynomial functions that give the most accurate answer?
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you can find one of them in the link below
fenix.tecnico.ulisboa.pt/.../Shape_functions.pdf
and the other one in my derivation for static deflection of simple (beam/plate)under uniform load
Load = w
Shear = w (x - a/2)
Moment = w/2 (x^2 - ax), Moment = 0 at x=0, so integration constant =0
slope = w/2 (x^3/3 -ax^2/2 + a^3/12) slope = 0 at x = a/2
deflection = w/2 (x^4/12 - ax^3/6 + a^3 x/12 ) , def. = 0 at x=0, constant =0
deflection = w/24 ( x^4 -2 a x^3 + a^3 x)
shape function = ( x^4 -2 a x^3 + a^3 x) x ^m
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Hello everyone!!!
I am very curious to know about the real life applications of various elastic foundations such as Winkler elastic foundation, Pasternak elastic foundation etc.
Thank you in advance
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Dear Subrat,
The Winkler elastic foundation concept is valid for both the shallow (strip footing, individual footing & raft foundation etc and deep foundation.) The applied load on these foundations are always lesser than the ultimate loqad by considering higher factor of safety so Winkler model concept is valid. However, these models have its own limitation, the main limitation is the predicted settlement will be considered only at the point, it does not consider the continuity effect..The application of these model for predicting the response for sheet pile wall or the pile subjected to only lateral load or combination of vertical and lateral load is questionable. Also, Winkler model theory is not very much useful in case of ground movement predictions due to earthquake. But, still Winkler model based analysis is valid for shallow foundation subjected to pure vertical load..Ok all the best in your research..
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Hello everyone,
I want to simulate SKF bearing 6308 in ANSYS Workbench explicit dynamic. I created the model as below, but for simplifying the model, I used 3 balls for the bearing. 
The inner race of the bearing has a local fault. As it clear on the outline, I used frictional contact (coef=0.005), an angular velocity of 1000 RPM for the inner ring, fixed support of the outer surface of the outer ring, and end time 0.018 (for one complete revolution). I did not consider any radial load. After solving the problem, I realized that only the inner ring rotates and the cage and balls slip a little (3-5 mm). For this problem, I changed the frictional coef from 0.005 to 0.1 and even no separation. But, still, I did not see any rotation in balls. They just slip a bit with the inner ring. One more time, I assigned clearance between balls, races, and the cage. Again, it did not work (clearance 0.01 mm).
It was weird why balls do not follow the rotation of the inner ring. As a result, I created a simple model similar to bearing the cross section with a ball between them. As shown in the picture below. 
By moving the upper part to the right, again the ball remains constant without any rotation. It just has a bit displacement (slipping). 
I really appreciate if anyone can help me step by step to solve this problem. 
Thank you. 
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Hi
i thin you must attention to connection and interaction type between bodies
suggest test different connection type and select better of that
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I'm trying to solve motion equations of one degree of system with tuned mass damper. the principal mass is subject to withe noise excitation. how can i have obtained the frequency response and the temporal response??
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Hello Aymen, if your system is linear, you can use Frequency Response Functions (FRF) analytically derived from differential equations to calculate system response by the simple formula: Sij(jω)=|Wij(jω)|^2 x S0(jω), Sij - response spectrum, S0 - input spectrum, Wij - FRF. White noise excites all natural modes.
Good source here:
If you solve equations numerically, just apply at input a white noise signal and see response.
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Hello,
A structure is tested for a Random Vibration (say Z axis, 0.1PSD, 20-3000Hz), where I obtained response acceleration from measurement system. Now I wanted to obtain same output(amplitude of modes) by giving Harmonic(sine) sweep as input(in Frequency domain) to Shaker machine. I read some on-line papers explaining conversion/equivalence from PSD to harmonic but none of them are actually working. Can someone please refer some good source?
Thank you,
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The basic assumption of the random vibration is that you can't predict the actual time realisation of the process, only the statistical measures, which assuming a Gaussian process is the standard deviation. So you can only compare a harmonic and random it in an average sense, which is to have the same input power. And that is what the PSD gives you. PSD is usually approximated as the square of the signal's Fourier Transform. So if you know what PSD value your random process has in a fequency bin, then you can work out what amplitude of sine wave would give similar power. But the only way you can relate the two are through the PSD, comparing actual time histories is irrelevant
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Hi All
For an ndof vibration system of mass and dampers, we know the equation of motion for imposed force.
but in finite element codes, it is also possible to apply a constant displacement and calculate the reaction force in the fixed end of the system as the response function .
Anyone could help with how to write the equation of motion for such a vibrating system ?
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What are the advantages and disadvantages of performing numerical integration from acceleration to displacement in the time domain and frequency domain, respectively?
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When you deal with high frequencies, time domain integration such as trapezoidal method may give incorrect results. One thing to remember in frequency domain integration is that waveform needs to be demeaned and padded for DFT to avoid aliasing (caused by cyclic convolution property of the inverse Fourier transform)
I suggest the following paper, which nicely covers the topic:
Brandt, A. and Brincker, R. (2014). “Integrating time signals in frequency domain – Comparison with time domain integration,” Measurement, 58: 511-519.
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I use Ansys to perform random vibration analysis. But I have a doubt about the input load spectrum. Is the amplitude of the input load spectrum force fitted in the normal distribution model such that the maximum load recorded ( from road load data acquired) equal to the 3-sigma load?
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For normal distribution, about 99.7% are within three standard deviations, hence, some values may be greater with 0.3% probability. Even +/- 6 sigma will not give 100% of probability.
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doing a project related to a plate and its vibrational analysis in the presence of fluid surround itself.
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Dear/Safiq SONAL
The next step is to do the following:
In a two-way FSI modeling, the results of the CFD analysis are transferred to the mechanical model whereas the subsequently calculated displacements at the interface are transferred back to the CFD analysis. The coupling capability that is currently available enables CFX to work with the ANSYS Mechanical solver within an ANSYS Multi-field simulation. During coupled simulations, the ANSYS CFX and Mechanical solvers execute the simulation through a sequence of multi-field time steps, each of which consists of one or more coupling iterations. Coupled simulations begin with the execution of the ANSYS Mechanical and CFX field solvers. The Mechanical solver acts as a coupling master process to which the CFX-Solver connects. Once the connection is established, the solvers advance through a sequence of six pre-defined synchronization points . At each of these points, each field solver gathers the required data from the other solver in order to advance to the next point. The iterations are repeated until a maximum number of iterations are reached or until the data transferred between solvers and all field equations have converged.
For complete details on performing a full transient dynamic analysis can be found in ANSYS Mechanical APDL Structural Analysis Guide. The modeling process starts in ANSYS-WORKBENCH multi-field when the simulation is performed between transient structural (ANSYS-MECHANICAL) and fluid flow (CFX-Pre). Both models are developed independently. Each model requires independent mesh, boundary conditions, analysis options and output options. The ANSYS-STRUTURE works as a master code. It reads all commands including interface meshes from the CFX, maps and communicates time, and stagger loop controls to the CFX code.
You consider the followings:
Influence of force application to investigate the effects of considering different forces (step force, periodic force, increasing force),
- Influence of mesh
- Influence of time step
- Influence of fluid velocities .
One of the most important issues in creating the appropriate meshes for the fluid and structural domain in a fluid-structure problem is to prevent any misalignment in the meshes for the common interface of the structure and the fluid.
To avoid any mesh alignment error in the model, the values of “Non-Matching Area Fraction” and “Number of Un-Mapped Nodes” are kept to less than 0.1% and equal to zero, respectively
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I've found several iPhone accelerometer and Android accelerometer apps (for example http://www.iseismometer.com and http://www.now-instruments.com/products/3-vibsensor ).  Are these useful for doing quantitative vibration analysis in the lab, and if not, what are their deficiencies?
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In addition to that you can measure the vibration by idynamics. it's a new kind vibrometer for android phones.
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I am currently studying the behaviour of a cantilever beam and I need to obtain the damping factor of each mode of the beam. Does anybody know how to do this?
I have the time-response of my beam that I have obtained with an accelerometer but in this time response all modes are together.
I need the different damping factors in order to be able to obtain the rayleigh coefficients of my beam and simulate it in Abaqus.
I have read that I can obtain these dampings factor with the bode diagram, but I dont know how to obtain bode's diagram out of my time-response graph.
Or even how to isolate one mode and that the accelerometer only registers that mode.
Thank you very much!!
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I guess this would help:
Regards
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Is there a way to find the Eigenvectors and Eigenvalues when there is unknown values in a complex damping matrix , using theoretical methods ?
Is it also possible to be done in MATLAB ?
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Hi Farzad
I assume you are referring to FE of a bounded region?
There are two kinds of modes that can be computed, Real modes and Complex modes. The former is standing waves that conserve energy, i.e. with node position (=minimum response) that stand still. The latter uses damping information and describes energy transport across the system and, hence, has node positions that move.
As indicated by their names, real modes have real valued response while complex modes have complex values response.
Real modes can be computed without any damping information.
As indicated by Giuseppe Pennisi damping can be added afterwards with the tacit assumption that it is evenly distributed and light. Other common damping models are viscous modal damping and hysteretic material damping.
The former (viscous) is a weak approximation of sound radiation, the latter (hysteretic) a weak appoximation of internal material friction. The Raleigh damping model mentioned above is used for mathematical convenience and does not originate from any physical damping mechanism.
In real life, damping can be many things. Some ramblings of mine on this topic can be found here https://qringtech.com/2014/06/22/designed-damping-types-mechanisms-application-limitation/
Sincerely
Claes
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Hi all!!!
I am trying to obtain frequency parameters of one dimensional nano-structure which is placed on an elastic foundation by using MATLAB code. But I am getting complex numbers (purely imaginary) and complex conjugates for frequency parameters . What do those imaginary values mean and why am I getting this?
Thank you in advance.
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complex frequency means frequency with phase information.
This occurs when the matrix we solve to get frequency is asymmetric. It happens when we solve coupling of fluid-structure interaction problem or when damping is significant i.e. very high.
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I want to start working on the generalized differential quadrature (GDQ) method to solve the problem of the mechanical behavior of beams, plates and shells.
Dear colleagues, I hope to give some suggestions (papers, books, etc.) and simple examples for work on this method.
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I want to start working on the generalized differential quadrature (GDQ) method to solve the problem of the mechanical behavior of the beams, the plates and the shells.
Dear colleagues , I hope to give some suggestions (papers, books, etc.) and simple examples for work on this method.
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I am trying to find the nonlinear frequency of plate. I have just started working on "Nonlinear analysis of plates and shells". Can anyone suggest the better iterative scheme for finding the nonlinear frequency of plate?
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Check my researches articles...
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As is well-known, there may exist some paradoxes when one uses the nonlocal differential type constitutive equations. For example, the fundamental frequencies of the structures increase with increasing nonlocal parameters, and when the nonlocal parameters exceed to some values, the higher mode frequencies vanish [1-3]. Obviously, this paradox does not agree with the fact that the inclusion of nonlocal parameter makes the structures softening. Therefore, it is of great necessity to develop a method to overcome this paradox. Luckily, the variational-consistent boundary value problems (BVPs) have been developed recently [4, 5]. The numerical results clearly show that the modified BVPs can result in the expected softening effects for structures with clamped-free boundary conditions. Additionally, the BVPs for other constrains can also yield the same results compared with Lu et al. [6] and Wang et al. [2]. Therefore, the present method is effective for solving the paradox for the dynamic cases. However, this method is not applicable for the static case. Hence, I recommend the authors use the corresponding integral type constitutive equations, although it is reported that the common integral type nonlocal constitutive equations may induce the inconsistence [7, 8].
Analogously, the present method can also found to be effective for solving the inconsistences encountered [9]. I think, form this point, that building the relationships between the nonlocal strain gradient theory and its corresponding integral type are going to be an interesting topic.
References
[1] P. Lu, H.P. Lee, C. Lu, P.Q. Zhang, Application of nonlocal beam models for carbon nanotubes, Int. J. Solids Struct., 44 (2007) 5289-5300.
[2] C.M. Wang, Y.Y. Zhang, X.Q. He, Vibration of nonlocal Timoshenko beams Nanotechnology, 18 (2007) 105401.
[3] X.-F. Li, B.-L. Wang, Vibrational modes of Timoshenko beams at small scales, Appl. Phys. Lett., 94 (2009) 101903.
[4] X.-J. Xu, Z.-C. Deng, K. Zhang, W. Xu, Observations of the softening phenomena in the nonlocal cantilever beams, Compos. Struct., 145 (2016) 43-57.
[5] X.-J. Xu, M.-L. Zheng, X.-C. Wang, On vibrations of nonlocal rods: Boundary conditions, exact solutions and their asymptotics, Int. J. Eng. Sci., 119 (2017) 217-231.
[6] P. Lu, H.P. Lee, C. Lu, P.Q. Zhang, Dynamic properties of flexural beams using a nonlocal elasticity model, J. Appl. Phys., 99 (2006) 073510.
[7] G. Romano, R. Barretta, M. Diaco, F.M.d. Sciarra, Constitutive boundary conditions and paradoxes in nonlocal elastic nanobeams, Int. J. Mech. Sci., 121 (2017) 151-156.
[8] X. Zhu, L. Li, Closed form solution for a nonlocal strain gradient rod in tension, Int. J. Eng. Sci., 119 (2017) 16-28.
[9] X.-J. Xu, B. Zhou, M.-L. Zheng, Comment on “Free vibration analysis of nonlocal strain gradient beams made of functionally graded material” [Int. J. Eng. Sci. 102 (2016) 77‒92], Int. J. Eng. Sci., 119 (2017) 189-191.
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I realize that differential formulation gives paradoxical results for cantilever bending analysis. However, it should also be recognised that the nonlocal model in integral form is unable to model detailed local effects at boundaries, and hence there are always likely to be discrepancies between the actual and simulated bending moment at the boundary.
About a solution for solving the paradoxical results, recently Romano and Raffaele Barretta proposed a stress-driven model to solve the issue.
[Romano, G. and Barretta, R., 2017. Nonlocal elasticity in nanobeams: the stress-driven integral model. International Journal of Engineering Science, 115, pp.14-27].
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Currently I'm doing a project to analyse vibration data of Induction Motors to identify different kinds of faults that they can have. For that I would like to get more samples with various inductions motors having different faults (ex: Mechanically Loosed, Bent Shafts, Bearing Faults, Unbalanced etc.) in order to have a more accurate analysis. If someone have such data, I would like to collect them.
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  1. Is there any alternative of Mode Superposition approach for linear dynamics?
  2. What are the methods for nonlinear dynamics as mode superposition is for linear dynamics?
  • Please suggest me some good literature which I can refer to get better understanding of mode superposition and other alternative approaches for linear and nonlinear dynamic analysis.
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The mode superposition method applied to non linear systems of equations can not be accurate like the other methods because it uses a combination (i.e superposition) of the modal solutions which are ideal solutions and for many reasons it can not reflect the exact response solution. If you do not have the possibility or do not need to compute all the necessary frequencies you will convergence will be lost.
The other method is the general transient dynamic solution method called full solution. In practical cases, this method uses the newmark difference scheme and is not numerically very expensive and it is widely used by finite element sotwares. The programmer can use alternatively another finite difference scheme for the numerical stability purposes.
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In the article titled "NURBS-based isogeometric vibration analysis of generally laminated deep curved beams with variable curvature" have been presented non-dimensional natural frequencies for layups [45/45/45/45] and [30/30/60/60]. Therefore the problem's formulation still stands for these layups. I have 2 questions:
1. Why the D16 and D26 stiffness coefficients for these layups have been considered to be zero, and in other words, there is no coupling between bending and torsion?
2. For which other layups it is not anticipated to there will be a coupling between bending and torsion?