Why are we only considering the first eigenfrequencies?

[snejburg]

Hey,

I have a question concerning eigenfrequencies:

Let us assume we examine a beam that is fixed at one end and free at the other end. It is possible to get an analytical solution in form of a unlimtied series: sum_i=1..infinity eigenfunction(i)*exp(i*eigenfrequencie(i)*t). (something close to that).

My question is first: Why do usually the first eigenfunctions have the highest amplitudes?
and second: Why is it in technical devices most important to supress the first eigenfrequencies?

I know that it has something to do with the higher energy of the higher modes but why do they have higher energy? And why is it apparently not dangerous to excite higher eigenfrequencies?

Thanks a lot for your help

 

[FactChecker]

I disagree with your conclusion that the lowest frequency is always the most important, highest amplitude, one. You may be looking at examples that have already been ordered so that the "first" frequency is the highest amplitude frequency.

Often the lowest frequency is so slow that it doesn't require design changes. An operator may correct for a low frequency oscillation without even thinking about it -- even if the uncontrolled amplitude is large.
One criteria that is often used is "time to double". That tells you how quickly a behavior needs to be corrected. That can be more significant than simple amplitude.