suppose you have a system(adsbygoogle = window.adsbygoogle || []).push({});

Ma + Kx = 0 for some nxn matricies M and K

assuming a harmonic solution of the form a = -w^2*x will, in principle, allow calculation of the natural frequencies based on the characteristic equation, and calculation of the corresponding mode shapes.

It's my understanding that to solve for the actual response of the system x(t) to some initial conditions, you have three options

1. Transfer Functions, which I don't really like frankly

2. State space x_dot = A*x, which is solvable by matrix exponentiation

3. "Modal coordinates", where the response of the system is written as a linear combination of the mode shapes

Could someone explain modal coordinates in detail? I can't find any decent online references that do a good job of explaining the concept and how you follow through with it and solve for x(t)

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# MDOF Vibrations Modal Coordinates

Can you offer guidance or do you also need help?

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