Dear Le

The damping ratio is a dimensionless measure describing how oscillations in a system decay after a disturbance. Many systems exhibit oscillatory behavior when they are disturbed from their position of static equilibrium.

The loss factor, which is the energy dissipation per radian to the peak potential energy in the cycle, is widely accepted as a basic measure of the damping.

 Please read the attached thesis.

Yes, Thank you so much. 

Hi

Rayleigh damping is hard to fit using modal methods. I suppose you could use a FE model and make a best fit towards measured FRFs, i.e. apply model updating, but this would be a costly procedure with limitations for success (i.e. the FE the model must be correct). 

Perhaps this prior discussion can be of use?

https://www.researchgate.net/post/Material_and_Structural_Damping_in_Abaqus?_tpcectx=search

SIncerely

Claes

If damping matrix is non proportional, which in fact is normally the case, you need to go with complex modal analysis. Eigenvalues and eigenvectors are no more real but rather complex. I would suggest to write the equations of motion in first order form (state space form). In this way you can obtain natural frequency and damping ratio of each complex mode.

 Yes, Claes Richard Fredö.

I will try to read. Thank you so much.

I just started study on modal analysis. i realized that it is difficult, actually. I needed reading on processing digital analysis, Fourier transform. And I make it alone without supervisor.

And, i remember that, I answered some my questions before.

Again. Thank you so much for everything.

Thank you so much. Filippo

Yes. Filippo.

I known about state space form when i read book on modal analysis by He.J, but without detailed knowledge. And I have not used it once yet. 

Do you mean is constitute a characteristic equation such form [K] - w^2*[M] = 0, and then solve it to obtain eigenvalues from this equation  and then is obtaining corressponding eigenvectors ?

Hi

Understanding is good. Avoiding reinventing the wheel is also good.

If you have Matlab - try this http://hosting.umons.ac.be/html/mecara/EasyMod/

Excel - try this http://www.noisestructure.com/products/MPE_SDOF.php

A new SW is this one in Python - https://github.com/openmodal

A good low cost commercial system with application examples - http://absignal.com/literature/index.php

If you are on your own - I believe it is worth reading this section as well.

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

Question - what is your intended application?

I looked at your profile and it seems to be bridges. If so, I imagine that Operational Modal Analysis (SSI and LSCE) are of interest?.

ModalView from AB Signal has both and can also make the measurements using NI measurement HW. http://absignal.com/literature/Bridge.php

/Claes

Yes. You are right, completely.  It is bridge structures. 

Links are attached above is so good. And, yes,  i have both Matlab and Excel. But, On Modal Parameter Estimation methods, I have not read them yet because as i commented above (with Filippo) , i just stared study on modal analysis. And now, i'm reading basic theory part (Chapter 2) of the book on modal analysis of D.J. Ewins. 

And, i know perhaps it is quite much. So sorry.

But i still tell you, i feel to appreciate you very much. 

Hi

Only happy to help someone get into the dark art of vibration. (Vibration as the child defined it - a motion not entirely sure of what it wants. )

My recommendation - read this material before doing the Ewins book. It will improve your understanding of the Ewins book which otherwise starts at too high level. The material is old but still the best in the business and, this is important, it was intended to be read by those starting from scratch.   http://qringtech.com/learnmore/recommended-reading/

Also, I may be wrong here as I read the Ewins book in the 90's - verify that Ewins handles Operational Modal Analysis as this is your primary interest.

Suggestion - if you want to deal with bridges and have at least some budget to back your project, consider using ModalView. It is good value for money and you can be up and running in no time. Also - for SSI - you need real time measurements, i.e. you need many synchronous measurement channels. For bridges, which is low frequency, you can use a simple datalogger and perhaps (=you need to check this), even cheap accelerometers (e.g. http://www.ebay.com/itm/Module-3-axis-GY-61-replacement-ADXL335-ADXL337-Analog-Output-Accelerometer-/232323964740?hash=item3617965f44:g:J9cAAOSwhvFZDBZt) to get what you need at moderate cost. Verify with AB Signal which HW they support before buing any hardware. http://sine.ni.com/nips/cds/view/p/lang/sv/nid/210054

/Claes

Yes. It is very kind of you.

Thank you so much.

Actually, I don't know how to start, what is needed for me that may be created deficiency on foundation (skills, detailed understanding) to me.

Start here

http://qringtech.com/learnmore/recommended-reading/

with the top links in the leftmost tab. Move on downward from there. Skip those obviously not of interest (but read them later as they are good to know).

My kids, 15 yrs, managed to read up to the HP signal analysis. They did not have all the maths to fully understand it but they managed to read it, so you should be fine.

One client managed to read all the material over the weekend. He phoned Monday and grilled me for 2 hrs, then had to reread part of the material overnight and then gave me a 2nd roasting the day after,

The message is - set your mind to it and you can cover all of it within a week's time even tough it will take time to let it all sink in.

Have fun

Claes

Yes. thank you so much.

Dear Dr. Claes Richard.

You told me that you read Ewin's book in the 90's. So, I'm so sorry but Could you show me how can we determinate natural frequency (wr) from Nyquist plot for receptance version of FRF in attached file (exactly, it is a figure that i took a photo from Ewin's book when i have read CIRCLE - FITTING METHOD (page 192 on that book)). Perhaps you remember still and understand it but to easily visualize i will note here such as: 

(i) is natural frequency of maximum response

(ii) is frequency of maximum imaginary receptance

(iii) is frequency of zero real receptance.

At here (in attached file), second and third lines, i understood how can we draw them. But, first line (i highlight it by a red narrow in that figure), i didn't know how can we draw it ?

In additional, I don't understand why first, second, third positions in Nyquist plot are frequency of maximum response, frequency of maximum imaginary receptance, frequency of zero real receptance, respectively. Because, for example, in third line you can see that value of Re (alphal) is non-zero.

Thank you so much.

Hi

I also used circle fit in the late 90's as it was one of the then viable methods for EMA with the current computer resources (at the time, using, automated analysis extracting 8 modes was an overnight calculation on a PDP11 fitted with vector processors and US export restrictions - a few years into the 90's you could fit much more complicated models using a work station in no time).

I believe that you would be well served from running some numbers for a sdof system to get to grips with the problem in hand. Use e.g. matlab, julia or python for this.

http://qringtech.com/TryMe/wp-content/uploads/2014/01/sdof.pdf

I suppose the concept is difficult because you have yet to see the FRF in 3D?

Calculate the sdof FRF and plot it in a variety of ways. If you use Matab, use the plot3(frequency,real(Y),imag(Y)), where Y(frequency). Running the numbers, you should end up  with something like the enclosed pdf.

Note that the data presented in the various views is exactly the same data and that the sdof natural frequency was set to 100 Hz.

As you can see, a sdof traces a circle in the Nyquist plane. The equation for a circle (i.e. with its radius and origin as unknown) can therefore be fitted to the FRF frequency points.

The phase angle change is the largest around resonance. Circle fit exploits this knowledge in the identification of the resonance frequency.

As modal summation simply is a summation of modes (sdof systems), we can fit multiple circles to extract modal data.

A real world FRF with lots of modes may look as shown in the below link. As you can see, the sdof has resonance at zero degree phase angle and this need not be the case when more and/or closely spaced modes are present as the circle then is offset by so called residual terms.This is where we exploit the knowledge of phase angle change, or the smallest FRF step on the circle to be the at resonance frequency. A further refinement is to make some extrapolation on this knowledge and interpolate the natural frequency.

In practice, in the days of old, one would look at at a frequency section of a few FRFs and pick a few frequency points to indicate where in frequency to fit a circle.

As suggested before - I strongly suggest that you read the B&K and the HP material found here before reading Ewin's book. The former is much easier to comprehend than the latter - as the latter goes into detail while the former provides an overview.

http://qringtech.com/learnmore/recommended-reading/

You will find the 3D FRF presentation in this material. For me, this was a major eye opener. (I noted that some of the HP links did not work - I have now updated them. )

Last - as the FRF is shifted by jw when going from displacement to velocity and by another jw multiplcation when going from velocity to acceleration, the real/imaginary parts will shift accordingly.

A good training is to do all these FRF variations for the sdof system to get one's bearings on the matter. After all, this knowledge very much is the nuts and bolts of dynamics and energy put into the subject therefore is time well spent.

Sincerely

Claes

http://vibrationacoustics.asmedigitalcollection.asme.org/data/journals/jvacek/28910/006003vaj2.jpeg

Yes. Thank you so much. 

I will obey you to read them before return with Ewin's book.

Perhaps i 'm too anxious to understand it without foundation knowledge.

Hi

Reading the B&K and HP material (start at the top and read downwards) is not suggested without reason.

For what is worth - this was also the road I once travelled.

Sincerely

Claes

Yes. You are right. I visualize this from incisive knowledge of you.