A Simple Frequency Response Function

The following article will attempt to explain the basic theory of the frequency response function. This basic theory will then be used to calculate the frequency response function between two points on a structure using an accelerometer to measure the response and a force gauge hammer to measure the excitation.

Fundamentally a frequency response function is a mathematical representation of the relationship between the input and the output of a system.

So for example the frequency response function between two points on a structure.  It would be possible to attach an accelerometer at a particular point and excite the structure at another point with a force gauge instrumented hammer. Then by measuring the excitation force and the response acceleration the resulting frequency response function would describe as a function of frequency the relationship between those two points on the structure.

The basic formula for a frequency response function is

H(f) = \frac{Y(f)}{X(f)}

Where H(f) is the frequency response function.

And Y(f) is the output of the system in the frequency domain.

And where X(f) is the input to the system in the frequency domain.

Frequency response functions are most commonly used for single input and single output analysis, normally for the calculation of the H1(f) or H2(f) frequency response functions. These are used extensively for hammer impact analysis or resonance analysis.

The H1(f) frequency response function is used in situations where the output to the system is expected to be noisy when compared to the input.

The H2(f) frequency response function is used in situations where the input to the system is expected to be noisy when compared to the output.

Additionally there are other possibilities, but they are outside of the scope of this article.

H1(f) or H2(f) can be used for resonance analysis or hammer impact analysis. H2(f) is most commonly used with random excitation.

The breakdown of H1(f) is as follows,

H1(f) = \frac{S_{xy}(f)}{S_{xx}(f)}

Where H1(f) is the frequency response function.

And S_{xy}(f) is the Cross Spectral Density in the frequency domain of X(t) and Y(t)

And where S_{xx}(f) is the Auto Spectral Density in the frequency domain of X(t).

In very basic terms the frequency response function can be described as

H1(f) = \frac{Cross\,Spectral\,Density\,of\,the\,Input\,and\,Output}{Auto\,Spectral\,Density\,of\,the\,Input}

The breakdown of H2(f) therefore is as follows,

H2(f) = \frac{S_{yy}(f)}{S_{yx}(f)}

Where H2(f) is the frequency response function.

And S_{yx}(f) is the Cross Spectral Density in the frequency domain of Y(t)and X(t)

And where S_{yy}(f) is the Auto Spectral Density in the frequency domain of Y(t)

In very basic terms the frequency response function can be described as

H2(f) = \frac{Auto\,Spectral\,Density\,of\,the\,Output}{Cross\,Spectral\,Density\,of\,the\,Output\,and\,Input}

In the following example we will discuss and show the calculation of the H1(f) frequency response function.

The excitation or input would be the force gauge instrumented hammer, as shown in Figure 1 as a time history.

Figure 1: X(t)

In this case the response or output would be the accelerometer, as shown in Figure 2.

Figure 2: Y(t)

However as discussed earlier the frequency response function is a frequency domain analysis, therefore the input and the output to the system must also be frequency spectra. So the force and acceleration must be first converted into spectra.

The first part of the analysis requires the Cross Spectral Density of the input and output, this is S_{xy}(f). This is calculated using the response as the first input and the excitation as the second input to the Cross Spectral Density Analysis in DATS the result is shown in Figure 3. Were S_{sy}(f) being calculated for use with H2(f) for example, then the excitation would be the first input and the response the second input to the Cross Spectral Density Analysis in DATS.

Figure 3: Sxy(f)

Next the Auto Spectral Density of the input, or excitation signal is required. This is calculated using the Auto Spectral Density Analysis in DATS, this analysis is sometimes known as Auto Power, the result of which is shown in Figure 4, this is S_{xx}(f).

Figure 4: Sxx(f)

The Cross Spectrum is then divided by the Auto Spectrum and the resulting frequency response function is shown in Figure 5.

Figure 5: H1(f)

The response function would normally be shown in modulus & phase form as shown in Figure 6.

Figure 6: H1(f) shown as modulus & phase

The entire analysis as used in DATS.toolbox is shown in Figure 7, the data flow from the original input and output, force and response, can be seen through to the frequency response function. The DATS software does, of course, provide a single step transfer function analysis. We have deliberately used the long-hand form below to illustrate the steps in this article.

DATS worksheet showing a simple transfer function
Figure 7: Complete DATS worksheet (Click to expand)

It is necessary to understand that for the purposes of understanding and clarity in this article some important steps have been glossed over, windowing of the input for example, to allow the basic understanding of what makes up the frequency response function.

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James Wren

Former Sales & Marketing Manager at Prosig
James Wren was Sales & Marketing Manager for Prosig Ltd until 2019. James graduated from Portsmouth University in 2001, with a Masters degree in Electronic Engineering. He is a Chartered Engineer and a registered Eur Ing. He has been involved with motorsport from a very early age with a special interest in data acquisition. James is a founder member of the Dalmeny Racing team.
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Ken
Ken
11 years ago

Hello,

Normally people don’t expect to see an Autospectrum, or Power Spectral Density on a linear scale, and it looks so noisy, that I suspect the impact was recorded using a Hanning weighting – a common mistake.
The end result, – the transfer function is also odd, to my eyes.
I would have expected a bode plot.
I am aware that linear display is useful for fatigue and stress purposes, but the frequency range is too high for this to be the application.

Samruddhi Katkar
Samruddhi Katkar
4 years ago
Reply to  Ken

Hello to get Natural frequency of any structure , if we are using modal Impact hammer and Accelerometer then FFT of Accelerometer signal
(as a response to impact of hammer)represents Natural frquency?

Khizar
Khizar
4 years ago
Reply to  James Wren

Dear Wren,

My question is related to the FRF (magnitude) vs frequency plot. I recently worked on the modal analysis of woven composites. Some of the FRF vs frequency plots don’t have very sharp peaks. The peaks are a little skewed for some of the plots. I was just wondering if I apply half power bandwidth on these plots, would it be validated?

Faithfully,
Khizar

Eapen
Eapen
11 years ago

what can be infered from figure 5,please explain..

kiran
kiran
11 years ago

how can v obtain auto spectral density of velocity from auto spectral density of the displacement

Paul
Paul
11 years ago

Hi

Just say you have several accelerometers on a complex vibrating structure. Each accelerometer has a slightly different frequency spectrum. Lets also pretend that you have a mic at some distance from this vibrating structure, and that you are trying to locate the particular component or part of the structure that is responsible for a radiating a particular tonal frequency. Would the cross spectrum be valuable in identifying which accelerometer is the culprit of this offending sound?

Many thanks

Andy
Andy
10 years ago

Going back to Paul’s hypothetical situation. Suppose that the accellerometers are measuring the start of an event that will be producing the noise that is being measured, but that there is no real reason to expect there to be any frequency correlation between them, would any conventional analysis work then?
For example, if you have 5 drums and a lightbeam sensor for each drum that triggered just before the drumstick hit each one, and that the drums are being hit in a regular sequence. How might one analyse the data (one mic channel and 5 drumstick sensors) to determine which drum was loudest/highest-pitch etc?

Andy
Andy
10 years ago

Sorry, perhaps I took my analagous situation too far. This is actually exactly the same question as Paul’s, but we have a slightly different conception of the nature of the data. I should perhaps have chosen a better analogy, as the trigger pulses occur at 20-150Hz which would be a pretty inhuman rate of drumstick operation.

Ashujc
Ashujc
10 years ago

I am looking for the information about the engine order, used for frequency response analysis.

We are working on frequency response Analysis for the exhaust systems, there we use different engine orders, i.e. 1st, 1.5, 2nd, 2.5 etc orders. Kindly let me know what is the actual meaning of this engine order. All I know is, its the disturbances created per rotation of the crank shaft. I need information.

– Ashujc 🙂

Sania
Sania
4 years ago
Reply to  James Wren

Can I use the peak value of a frf curve as resonance frequency or I should convert it using any mathematical equation? If yes then which equation should be used?

Ya Huang
Ya Huang
9 years ago

James,

Thanks for a clear example.

Would be more useful if you could publish the parameters used by DATS.

e.g.

Sampling rate:
Anti-aliasing filter:
Number data in each FFT:
Windowing:

Ya

Steve
Steve
9 years ago

Hi James,

Your example is very instructive. However as a new comer in FRF, I could not figure out how you obtain the phase for FRF from the steps mentioned in figure 6. Obviously the division can only give a real number, which is the amplitude of FRF. Thanks.

Stuart
Stuart
9 years ago

I’m reading this because I’ve just been sent a newsletter that points to the page.

Are you sure you should really be advising use of H1 and H2 on single tap test recordings?

You see I agree with your first equation H(f)=Y(f)/X(f) but the subsequent equations are unhelpful if you end up using segment averaging (inherent in the calculation of the power and cross spectral densities) on a single tap. The windowed data for the force time history segments will all be zero except for the one window that contains the actual impact. Moreover the response in the subequent windows has nothing to do with the corresponding force window leading to potentially significant bias errors in the transfer function.

If you must use segment averaging to obtain transfer functions for tap test data then I think you need to make it very clear that this is for multiple taps and that the window length used must exactly correspond to each tap and response time history (i.e. there must be no segmentation within each time history pair) and the window length must be sufficient to capture the full decay of the vibration following the tap. Your readers should also know that the highlighted inappropriateness of segment avergaing for tap test data cannot be overcome by multiple taps at random intervals – that only compounds the errors introducing rippling in the estimated transfer functions because of the [Fourier transform properties of the] inherent similarity between one tap and the next.

Umar Butt
Umar Butt
9 years ago

Hi,
I have done FFT analysis on mild steel beam of 1 meter length and I was looking frequecy of mild steel on first three modes. After performing the test I have got auto spectrum input response graph and frequency response(response,force)input (magnitude) working graph. which graph is best to consider for the frequency?

Umar.

Umar Butt
Umar Butt
9 years ago

Hi,
Thanx for the reply, I just want to ask that what is the difference between Autospectrum response graph and Frequency response graph because they are giving same results.. and how can i find the length/breadth ratio against frequency plot, of a rectangular beam with the length= 1m and breadth= 0.039m.

Umar.

krishna
krishna
9 years ago

Hi,
Is there any way to estimate frf only from output data. Say, I have accelerometer output for vibration of a bridge under traffic etc over a period of time. Can I generate frf without knowing force.

Thanks a million,
Krishna

Nikk
Nikk
8 years ago

Hi James,
Let’s say I plan to perform a modal test on a quite complex test article. For this test, I will have 20 accelerometers scattering around the test article. Now, if I selected one location to hit with an instrumented hammer to excite the modes. Based on your explanation about the FRF, in this example, I would have 20 FRFs generated by DAT (each FRF represents the response relationship between the impact point with respect to one of 20 response points where the accelerometers are located). Now, my question is: “Can the resonance frequencies of the test article be identified by examining the modulus & phase plots of the FRFs?”. If yes, then how to identify those resonance frequencies?. Thanks.

Nikk
Nikk
8 years ago
Reply to  James Wren

James,

Thanks for the response. I have 2 more questions for you:

1) You said: “as a rough rule, a resonance will show itself as a peak in the Modulus plot and as a flip of the angle in the Phase plot”. According to this sentence and after looking at the sample Modulus/Phase Angle plots in Figure 6 posted on your blog above, the Modulus plot has many peaks and the Phase Angle plot has many flipped points (0 to 180 degrees), so how do I know which peak in the Modulus plot associated with a flip of the what angle in the Phase plot is a correct resonant frequency?

2) Looking at Figures 3 and 5 posted on your blog above, there were 2 different colored curves (red and blue), and I wonder what did red and blue curve represent?

rummy
rummy
8 years ago

Hi James:

This is great! I actually need to calculate the FRF for an experiment. I have the excitation acceleration signal and an acceleration response singnal in time domain. I am new to signal processing and would like to know in detail about the meaning and numerical computation of auto and cross spectrum in order to compute the FRF. I hope you could guide me to something useful for understanding the underlying concepts. Any insights into computing the FRF for my case would be great!

Thanks.

Rummy

rummy
rummy
8 years ago

hey thanks James. I think I have some good initial idea now to build upon. Cheers!

David Van Aelst
8 years ago

I am new to signal processing and french speaking; so I hope that these two drawbacks will not make my questions become too stupid.
My problem is about structures on which à kind of wind tunnel test has been made. In the case were a single excitation point is used, say A, then at each frequency w, a transfer function from the input towards an output quantity B exists, Hab(w) .
Then the power spectral density of the ouput quantity B is said to be Sb(w)=|Hab(w)|².Sa(w)
(Sa being the power spectral density of the input quantity A)

Now what if the input is divided in four points ?

If Saiaj(w) is a cross spectral density of
input j versus input i, can I consider |Sa1a1(w) Sa2a1(w) |
an input cross spestral matrix, being that : [SIN]=|Sa1a2(w) Sa2a2(w) |
and then how can I use it | a4a4 |
to obtain the output responses ? And How ?

Thank’s a lot to explain me these basic things,
David

Adrian Lincoln
8 years ago

Hi David,
First of all can I ask if you are measuring forces or just responses? Also do you know if the input signals(forces) are independent from one another? (If they are independent then the coherence spectrum between any pair of signals will be approximately zero.) If the input forces are indeed independent then the output will be a simple summation of the responses to the individual inputs. However, if the inputs are not completely independent then the predicted response is not so easy to calculate as it requires the computation of the partial coherences between the inputs. If you can tell me a little more about your test situation then I can give you more appropriate advice.

Adrian

dva2tlse
dva2tlse
8 years ago

Hi Adrian,

thank’s a lot for having spent some time with my question. As an answer to your first question, please take in account that I am stress analyst, thus the data I’m interested in is neither forces nor displacement responses, but stresses. But our stress analysis software knows how to convert displacement responses towards stresses.

Secondly, the sources acting on my structure are not completely independent; they are aerodynamic noises on different parts of a same structure. It is an aircraft component which size is slightly smaller than a meter, and six micros have been fixed on it during the wind tunnel tests, in order to measure the input PSD’s.

If I call Sa(w) the input PSD (in Pa²/Hz since it is that of an acoustic pressure),

and Sj(w) the output PSD, (in MPa²/Hz since it is that of a mechanical stress),

and Hja(w) the transfer function from the pressure towards the stress at rotating frequency w :

Then for each w, Sj(w)=|Hja(w)|².Sa(w)

And I am interested in the RMS value of that stress over a certain frequency band of the aerodynamic noise.

Now let’s see what happens when there are, say just two input zones, a and b.

There is an input direct PSD over zone a, say Saa(w),

there is another input direct PSD over zone b, say Sbb(w),

there are two input cross PSD’s, say Sab(w) and Sba(w) which should be its complex conjugate. (Tell me please if it is true)

Then for each w, the output PSD is Sout(w)= ?j=a,b ?i=a,b ( hi(w).hj(w)*.Sij(w) )

And I am still interested in the RMS value of that stress over a certain frequency band of the aerodynamic noise.

Now let’s see what happens when there is only one input zone, but two distinct PSD’s acting on it. For simplicity I input within the stress analysis program that I use, that the cross PSD’s are almost zero, say 1.E-12 or 1.E-18 times the product of the two input direct PSD’s.

That is the point that I want to know; is it possible to “add” two PSD’s acting on the same area, with almost zero cross PSD’s.

It seems to me that I could.

I am very glad to be able to write such a text as above, as I feel a bit more “clever” about signal processing. Please continue telling me if what I wrote above is plenty of sense or not, and feel free to ask anything if you feel that some questions or answers may make me progress in that domain.

Thank’s again,

David

JayW
JayW
8 years ago

My structure (steel) in question is small, thin and light. I cannot physically attach any accelerometers, as the mass and cable tensions would alter the frequency response. So I use non-contact displacement measurements (like Laser or Capacitance Probe or EC probe). Also – I cannot use the typical impact hammer as well – I might brake the structure. I can may be drop a small steel ball on the structure to provide excitation.

Two questions.

1. Since direct excitation measurement (impact hammer) is not possible, can I measure the impact force by dropping the same ball on top of the accelerometer or load cell on a separate run?

2. If Q1 is possible, then I’d have input data in accelleration, and output data in displacement. What should I do from here?

Thank you very much for your time.

JayW
JayW
8 years ago
Reply to  James Wren

James thank you for reply.

Sorry for the confusion. What I meant by “dropping a ball on the accelerometer” was, to setup an accelerometer on a flat table (not on the thin structure in question), and drop a ball on it to see how much impact the “ball dropping” can deliver.

Originally, I was thinking of shooting the ball using a BB air gun to deliver the impact. If I shoot the ball on an accelerometer (provided distance and airpressure would be consistent), I would know how much impact there is, and assume that the same amount of impact will occur when I shoot it to my thin structure in question.

I hope this makes sense.

rummy
rummy
7 years ago

Hi James:
I have a question related to FRF computation for transient input-output signals. Would it be OK to compute the FRF of a system by only considering a certain transient region, instead of the entire time-history (i.e, before the signals die out) ?

Thanks and regards

Prasad
Prasad
7 years ago

Hi James,

I,m new to signal processing. I would like to know how you calculate the dynamic stiffness,Kd from this curve. How would you calculate the Kd at any random point on this curve other than peak responses.

Suppose I’m plotting an FRF graph taking magnitude(0-120db) on Y-axis and frequency(0-600Hz) on X-axis. I would like to calculate dynamic stiffness,Kd using this graph using least square method, rms method, average method.

Also how it differs if it is undamped,underdamped,critical damped,overdamped structure. How to change the spring/bush stiffness values using damping values.

It will be of much help if you can explain this in a simple way with the formula used for calculating the above.

Thanks and regards

Prasad
Prasad
7 years ago

Hi James,

I have forget to say that I’m interested in acceleration as output response and accelerance(acceleration/force) as the magnitude on the Y-axis.

Prosig
Admin
6 years ago

Thank you James for answering my question earlier today , I hope I am not taking lots of your time .

First of all I would like to congratulate your company to have an outstanding intelligent person like yourself . From the nature of your answer I can see that given the fact I am student at Aberdeen university ,

You will note that some of the facts I studied in the past I only understood it from theoretical point of view with no physical understanding , I am finding your comments are EXTREMELY useful .

It would be greatly appreciated if you could possibly make useful comment or answering the questions in simple way .

In the embedded figure you attached Nik , I can see that there are three peaks , two of them are for the Zeros of the systems and one of them for the Pole where is the resonant peak occur .In your answer to the question I found in determining the peak ,, the phase will be inverted .
Question 1) To what extend the phase shift is required for peak resonant is occurred , is it necessarily to -180 or depend on the order of the system , for example the phase inverted by -90 ? Also would the sign make difference if it is +180 or +90.

Question 2) Looking at the zero peaks in my system they are below 0 decibel different than the one on the figure . Do you have any physical comment about those peaks occurring in the frequency response for the zeros ? I can also see phase shift inversion at those peak ?

Question 3 ) In my system The Bode diagram shows a 180° phase lag at every resonant frequency and a 180° phase lead at every anti-resonant frequency. This is a characteristic of collocated systems.? I do not understand this clearly as you have excellent skills in showing the material in more physical understanding .

Question four )
The in-bandwidth zeros of the system are highly dependent on the out-of-bandwidth poles ? what does that mean if you have more clarity it would be greatly appreciated

question five )
if I want modify system from containing resonant poles followed by interlaced zeros, to zeros followed by interlaced poles ? in terms of stability what does that mean , can you please clarify things for me clearly.

Dhruvit
Dhruvit
6 years ago

Hello James,
I am new to practical testing & signal processing.
I have few question about selecting excitation and response points.

1) How do we select excitation and response points for practical component FRF testing? I mean if I hit structure with hammer in X direction do I need to take response only in X direction or response in Y,Z directions as well? or Do I need to hit separately in each direction (Y,Z) and take response in (Y & Z respectively)?

2) Do I need to select input point near mounting point of component while doing component FRF or at free end of component?

3) Different response points give different amplitude values but peak frequency could be same (Correct me if I am wrong). How do we make sure which response point gives us proper frequency and amplitude values?

What is your suggestion?

Thank you,
Dhruvit

Sudeep Joshi
Sudeep Joshi
5 years ago

Dear Mr.James

I have a question…i have tried harmonic analysis of the Cantilever beam in ANSYS. i got FRF but i need to find the mode shapes through FRF so that i am able to compare the experimental results….cab you help me in any way…
i also have another question, can you throw light on the real and imaginary part of an FRF

nguyen hoang quan
4 years ago
Reply to  Sudeep Joshi

Dear Mr.James & Mr.Sudeep,

I have the same simulate in Ansys for the harmonic analysis of the Cantilever beam.
All data based on this article “A frequency response function-based structural
damage identification method, Usik Lee *, Jinho Shin” (I can not paste the chart at this comment). But I can not have the peak of FRF the same with my reference.

So can you share with me some reference about how to create FRFs chart on Ansys? I am a PhD student at the Vietnam university. It is a pleasure for me if you reply me on my email: “nguyenhoangquan72@gmail.com”.

Thanks & Best Regards,
Quan

Salman
Salman
5 years ago

Hi Mr. Wren,

I noticed that in the impact signal there is a negative part to the amplitude right after impact, resulting from some kind of recoil in the hammer load cell (I guess). Is it normal to get this considering this is a negative force? I am getting similar results but the negative amplitude is almost equal to the positive part. Can you please elaborate on this and how to take care of this in FRF calculation.

Thanks,
Salman

Lee
Lee
5 years ago

Hello James,
Great article and blog. I just have a few questions:

1. You mentioned that you windowed the input signal, but not the output. Under what circumstances would you also window the output?

2. Are there any differences to calculating the FRF using the ratio of FFT’s vs. CSD/ASD? Which do you prefer and why?

3. I’m a little confused about using the FRF (e.g., accel/force) vs. the transmissibility (accel/accel) to calculate structural properties such as damping, etc. In other words, if I do an impact test and get an FRF in units of (m/s^2)/N, then do a base excitation on the same structure to get a dimensionless transfer function (dB or gain), will the half-power method give me the same result for the damping ratio for both tests? If this is outside the scope of this article, could you point me to a reference that might answer this? Thanks!

jason
jason
5 years ago

Suppose for each accelerometer, there are three axes, X, Y and Z, and I’m using an excitation of both X and Y direction. Should I compute the FRF separately for each axis, or these three axes need to be integrated before computing the FRF (If so, how to combine them together?)

Jamie Kim
Jamie Kim
5 years ago

I am trying to formulate a frequency response function for a pipe resonance
analysis. The input is a continuous signal input of a single frequency (say
100 Hz) which is injected down a water-filled pipeline for over 5 minutes.
The output is given as the pressure reading at a chosen point along the
pipeline in a time domain. (i.e. pressure vs time where time is the
recording time).
The question is, what would be a sensible approach in figuring out the
cross spectral density of the input and output, and power spectral density
of the input?
Thanks for your time.
Jamie

rajesh
rajesh
5 years ago

Hi James,

I have conducted impact hammer test on a structure to find out natural frequency of the structure with a 2-channel analyser. I have the time series data anf FFT spectrum from the software given. However i cannot progress futher. I actually need to calculate the FRF for an experiment.I hope you could guide me to something useful for understanding the underlying concepts. How would I will identify natural frequency from these graphs and spectrum.
Thanks.

Anders H
Anders H
5 years ago

Hello!
I found you blong in search of a small problem I have.

I have performed a modal analysis of a structure, computed my FRF and now I want to adjust my input PSD spectrum specified at the point of the modal test insertion point.

From what I understand I must then multiply each PSD value by the power of the corresponding FRF value at that specific frequency to obtain my “new” PSD at the measurement location, is ths correct?

Adrian
5 years ago

Hi Anders,

After you have computed your Frequency Response Function, H(f), then you are able to predict what the "spectrum", Y(f) of the output response will be when excited by a known "spectrum" X(f) at the input (assuming that the input and output locations are the same as those used for the FRF calculation). In the case where the "spectrum" Y(f) is a simple Fourier Spectrum which is often the case for short, transient signals, then the response spectrum is given by

Y(f) = H(f).X(f)

In the case where the input and output response spectra are both spectral densities, Sxx(f) and [latex]Syy(f)[/latex], and remembering that the transfer function [latex]H(f)[/latex] can be calculated using either the cross spectral density S_{xy}(f) in the case of an H_1(f) calculation, or S_{yx}(f) in the case of an H_2(f) calculation, then the required response spectrum that you are trying to calculate is found from

S_{yy}(f) = H_2(f).S_{yx}(f) = H_2(f).S_{xy}*(f) = H_2(f).H_1*(f).S_{xx}(f) = |H(f)|^2.S_{xx}(f)

where H1*(f) is the complex conjugate of H_1(f), and H_1(f) = H_2(f),
Syx(f) is the cross spectral density between the output and the input
Sxy(f) is the cross spectral density between the input and the output,
and Sxx(f) is the input spectral density.

Sudipto
Sudipto
5 years ago

Hello

I am a newcomer in this field. I have a very simple question. Since FRF=Y(f)/X(f), why don’t we calculate it as FFT(y(t))/FFT(x(t)) instead of crosspower/autopwer?

Micaela Wurm
Micaela Wurm
4 years ago

Thought-provoking discussion – I was enlightened by the insight . Does someone know where I would be able to access a sample a form version to complete ?

Ahmed Alzubaidi
Ahmed Alzubaidi
4 years ago

Hi Dear
Could you send me the code into python how to find the Cross and Auto spectral density for experimental data?
Sincerely,

Aida T
Aida T
4 years ago

Hello ,I am doing some modal analyses on a free-free shaft. My FEA shoes one of the modes as torsional and to my surprise the impact test, with one accel ,has captured it. My assumption has been I can not capture a torsional vibration with the just one accel as I need at least 2 accel in opposite direction to be able to see the torsional mode while the bending is cancelling. Is there any explanation for it? Thanks

danny
danny
4 years ago

hello, your blog is really helpful, i would like to ask a few question, ive already produce an frf by using fft(Y)/fft(X) and have obtain a phase angle figure. 1) how do i analyse and obtain the mode shape from the frf or phase angle figure ? 2) apart from natural frequency, damping ratio, mode shape, what other details can be analyse and can i get from the frf? 3)my frf, seems to show noises, what are the cause of this and how do you explain the noise from the figure? note that im doing a simple hammer test, thansk!

Reem
Reem
4 years ago

hello!
when i get the mode shapes, 2 curves are displayed blue and red, and sometimes they are different, which one should i take for an actual mode shape presentation?

reem
reem
4 years ago
Reply to  James Wren

hello James,
how could i change them to modulus and phase?
thank you in advance.

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