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# Complex Mode Shapes

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## Complex Mode Shapes

(OP)
Hello,

So I have a set of measured FRFs gathered from the vibration laboratory. I am using a peak picking method to reconstruct the magnitude of the FRF and get the natural frequencies, damping coefficient and modal constant (two mode shapes components multiplying each other). Knowing the driving point, I can reescalate the rest of the modes. But i need the modes to be complex, because in the case of study viscous damping is assumed.

So I was wondering how could I get these complex mode shapes using the pick peaking method (i would like to avoid circle fit). I don't know if looking at the real or imaginary parts of the FRF I could get this information. Help would be appreciated.

Thank you.

### RE: Complex Mode Shapes

You can calculate the dynamic response with damping, the 'mode shapes', however, are inherently real and lossless.

Evaluate your system response with varying degrees of damping to answer your question.

### RE: Complex Mode Shapes

(OP)
The mode shapes are not inherently real in a viscous system. It is not proportional damping so I do not understand your answer

### RE: Complex Mode Shapes

You are correct with viscous damping losses, so calculate your mode shapes with viscous damping as a parameter, and explore how your damping affects you measured parameters.

### RE: Complex Mode Shapes

(OP)
But why should I use viscous damiping as a paramater when I have well determined its value? The problem I have is how to get from the magnitude of the modal constant to a complex number so i can get complex mode shapes and not just real ones.

### RE: Complex Mode Shapes

If your system is relatively lightly damped and the modes are uncoupled you may be able to use the phase from the frequencies you got from peak picking. Your mode shape for each frequency and response point is then defined by R=peak_magnitude *cos(phase_at_peak), and I=peak_magnitude*sin(phase_at_peak).

Then resynthesise your FRF for each response point using your damping and the complex mode shape and modal frequency for each mode and see if the magnitude and phase of the FRF is accurate.

It won't be, peak picking is not a robust method. So you'll fiddle about with your estimate phase and amplitude for each mode until you get a good resynthesized FRF. By the time you've done that you've actually done an MDOF fit, perhaps not in an efficient manner. I used to do this automagically when we did modals of whole cars, which have too many non linearities and local and coupled modes for circle fitting to work well.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

### RE: Complex Mode Shapes

(OP)
Thank you a lot for the explanation Greg. Do you have any reference on a good MDOF fit and maybe with some MATLAB info that can help me to program it if I decide to go with one of those?

My teacher suggested me to go simple with peak picking since currently I am undergraduate, but for this task I am encountering many issues and given that I have no real background in modal analysis other than what I am reading here and there, a little help would be appreciated.

Thank you

### RE: Complex Mode Shapes

I stand corrected, the viscous damping does yield complex mode shapes, appologies there.

Greg has the best approach for the phase correction.

### RE: Complex Mode Shapes

(OP)
Hello,

I have one more doubt about what you said earlier Greg. The phase you are referring to is the phase of the FRF at each natural frequency? And if so, could you link me some theorical background for that because I do not see the correlation between that phase and the mode shapes one.

Thank you a lot

### RE: Complex Mode Shapes

Let's try again.

Peak picking is not a robust method. I have never used it except as a quick and dirty method for getting approximate values as a basis for a more accurate MDOF fit. So I wouldn't expect anyone to waste time trying to prove (or disprove) that the phase angle from a peak pick is much use as a mode shape. It does work, to some extent, on lightly damped simple structures, where basically it is just giving you the sign of the imaginary response.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

### RE: Complex Mode Shapes

(OP)
I have been trying to implement an MDOF fit with MATLAB but I am having a hard time.

The problem is that you do not give estimated values to MATLAB, so when you use commands like 'modalfit' it does not replicate the initial FRF in a good way.

I tried also to create a continuous-time FRF by using 'tfest' and then extract the modal parameters from there, but not with great results.

MATLAB seems to use these algorithms ( like least squares rational fraction ) ignoring the residues because I have see narticles from people using them and getting much better reconstructions. I know my data is tricky because it is a beam with 23 points of measurement but I can not figure how to extract the complex mode shapes with good results.

If you could get me to some code or reference featuring these problems will be so much helpful for me.

Thank you.

### RE: Complex Mode Shapes

Well, I've never used Matlab for modal work. One trick is to synthesise a set of data, and then see if you can analyse that successfully. If not then you don't stand much chance with real data.

Before I actually type this into my favorite search engine I hazard a guess that searching 'modal analysis matlab' will get me more than 20 tutorials, lecture notes and how tos. Significant underestimate as it turns out.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

### RE: Complex Mode Shapes

For modal analysis using Matlab, take a look at http://abravibe.com/toolbox.html

Haven't used it myself, but it seems really useful.

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