- #1

Trying2Learn

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- TL;DR Summary
- Modal analysis

Consider this system, above.

If I studied the mechanics of this system, I get this system of equations.

At that point, I choose to study a free vibration problem and drop the damping, and conduct a modal analysis.

I understand the process:vvI assume a solution such that each mass moves with the same frequency, expressed as a complex exponential.

Then, I assume a singular matrix to avoid the null solution, work out the determinant, get the characteristic equation and find the modes.

**OK, so, with that in mind, what IS a modal analysis?**

What I am hoping to learn, is a self-contained explanation that links the assumptions of the solution approach, to what a modal analysis is

in a simple way, without a discussion of resonance or eigenvalues, etc.

I look up on quora or wiki and other sites and get this:

__Modal analysis____is the study of the dynamic properties of systems in the frequency domain.__

So, yes, I get that. I see that. But I feel (and I am sorry) I am still bereft of explanation of what a modal analysis is, that is stripped of any mathematical analysis.

Yes, I understand the explanation of pushing a child on a swing, at a certain frequency, or the Mexico city earthquake. I understand the resonance. But I am hoping for an explanation that links the steps of the analysis to the desire of what we are trying to obtain?

Or is it as simple as this (in my words)?

"We assume all mass elements in the system are activated by the same natural frequency and we study the tendency of the behavior (the modes) under that common frequency"

Is it that simple?

Note that for an eigenvalue analysis, we assume we can separate the mode shapes (SPACE) from the frequency response (TIME). So, could another explanation of modal analysis be:

"The assumption that one can readily separate the spatial displacements of all constituent mass elements, from a common frequency response."

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