Natural frequency of frame structure with general mass sitiffness and viscous dumpinig (M DOF) 2

[aouiche]

I m a new user of matlab and i have a question about how to obtain natural frequency and mode shape corresponding in the general case of system mass,sitiffness and viscous dumpinig (MDOF)

Example:

m=[40000 4000 0;0 30000 0;50000 0 20000];

c=[330 0 0;0 -8000 8000;0 -8000 8000];

k=[30000 -10000 0;-10000 20000 -10000;0 -10000 10000];

Thanks

 

[amanuensis]

Draw the reader's attention on a vocabulary issue is not to GL's credit.
Natural or Eigen frequency, it's not the point.

As an engineer or researcher, the only important thing is the relationship between mathematics (here linear algebra, matrix calculation and complex numbers) and physics or nature.

Why complex numbers are so well suitable for defining damping ?
Why the fact of diagonalizing a matrix is so well suitable for finding the natural frequencies of a structure ?

This is very mysterious and reflects all the strength (and so the beauty) of mathematics for describing vibration.

 

[GregLocock]

Not too sure what you are getting at, my point is that there is not just one frequency of maximum amplitude in a fully coupled damped system for a given approximate mode shape.

In practice it is worse than that, the frequency of maximum response is not only affected by the location(s) of the forces exciting it but also their amplitudes.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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[FeX32]

Negative stiffness many times cause unstable differential equations.


"Simplicity is the ultimate sophistication." L. da Vinci
- Gian