Sound and Vibration

Hi All,

I'm from Electronics Engineering background. My company assign me to incharge on acoustic measurement and failure analysis. My counterpart from San Jose,CA recomended me a book title Vibration Spectrum Analysis for beginers.

Do you have anyone have any recomendation on books or website

Thanks

 

[GregLocock]

I wonder if this Question gets Asked Frequently?



Cheers

Greg Locock

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[electricpete]

Of course in Greg's humorous way he is referring you to the FAQ section where you will find some good on-line references.

Since you recommended them Greg I took a look.

B&K's "Structural Testing Part 1" on page 10 or 11 (depending on which page number you look at) has the following:

"An important property of modes is that any forced or free
dynamic response of a structure can be reduced to a discrete
set of modes."

I get the free part. The forced part was a surprise to me. If a system has two modes at frequencies f1 and f2 and I provide sinusoidal excitation at frequency f3, in my mind I cannot be exciting either of those modes. Or am I mistaken?

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[GregLocock]

Wot me, sarcastic?

ep - Welcome to the wonderful world of modal superposition. I'll give you the hand-waving version, because the details are a blur.

If you look at the FRF between the two natural frequencies you'll see that there is still a phase and a magnitude, and if you animate that response you'll see it is a mixture of the two modes.

Now, rather more strangely, at frequencies below the lowest mode /even down to DC/ the residual of the high frequency modes still affects the response, in fact the static stiffness of the system is the sum of the 0 Hz residuals of all the higher modes. Likewise at high frequencies, but that is less useful. One practical consequence of this is that the response EVEN AT THE RESONANT FREQUENCY is partly controlled by the residuals from the surrounding modes. This is more obvious to anyone who has ever extracted mode shapes by circle fitting in the Nyquist plane.

The useful upshot of this is that a good dynamic modal model of a system implicitly gives the 0 Hz stiffness of the system, which is a very hard thing to measure.

So, for my suspension models I don't use an FEA model of the arms, say, I can just use the residuals of say the first 6-50 flexural modes of each arm. That may seem crazy, but that abstracted level of data solves very quickly, unlike an FEA model.

To go out on a limb, slightly, I think this is the frequency domain equivalent of the time domain result that when you 'start' a system at some arbitrary state - then the subsequent behaviour is the weighted sum of the mode shapes that match the start condition (and if you think that's why you have as many modes as there are DOFs you'd be dead right).

This seems to me to be a very 'deep' behaviour of dynamic systems.

Cheers

Greg Locock

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[wes616]

Greg,

Why don't you write a book! I'd read it (or buy it at least :

Wes C.
------------------------------
When they broke open molecules, they found they were only stuffed with atoms. But when they broke open atoms, they found them stuffed with explosions...

 

[GregLocock]

Haven't got the patience!



Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[electricpete]

I know what you are saying about predicting the forced response from the modes.

If we take space out of the picture and just look at time variation, any linear time invariant system can be expressed as a ratio of polynomials in Laplace transform variable s. If we factor the numerator and denominator we know the poles (modal frequencies) and zero's. From those poles and zero's, we can compute the amplitude and phase of the transfer function at any other frequency. So the poles and zero's have a very distinct relationship to the response at all other (non-pole, non-zero) frequencies. BUT, that doesn't mean that if I excite the system at another frequency, I am exciting a natural frequency.

Modal shapes and frequencies are a property of the system independent of the excitation. Free response will be a superposition of modes (mode shapes varying at their modal frequencies). Forced response at a general non-modal frequency is not a superposition of modes (not a superposition of mode shapes varying at their modal frequencies), by virtue fo the fact that the forcing function and all system response is at the non-modal frequency.

At least thats' the way I see it. Please let me know if I am mistaken.

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[GregLocock]

"If we take space out of the picture and just look at time variation,... BUT, that doesn't mean that if I excite the system at another frequency, I am exciting a natural frequency.

Modal shapes and frequencies are a property of the system independent of the excitation. Free response will be a superposition of modes "

Absolutely true. In a linear system it is not possible to excite a different frequency to the driving frequency.

" Forced response at a general non-modal frequency is not a superposition of modes "

Well, I'm not so sure I agree, but I think it's just terminology. The response at an arbitrary frequency is the vector sum of the SDOF responses of each and every mode, at that frequency.

To make it easy, going back to a system with two modes, with resonant frequencies F1 and F2, damping c1 and c2, correctly defined model masses m1 and m2. From this we can work out the associated modal stiffnesses k1 and k2.

Now excite the system at F3

Taken by itself the first system, m1 k1 c1, will respond at a certain level x1 (complex) at frequency F3, governed by the usual SDOF equation.

Similarly m2 k2 c2 will have a response x2 to forcing at frequency F3

The total system response at F3 will be the vector sum of the responses of the two separate single degree of freedom systems represented by k1, m1 c1 and k2 m2 c2, at F3, ie x1+x2

Now, is that more confusing? Hope not.

Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[electricpete]

I reveiwed my textbook and I see what you are saying now. Thx.

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