1. The equations of the natural vibrations are simple - but they are in six
modes, two for each axis of the reference frame.
You live with young's modulus
2) in systems, anyone expert in vibration avoids designing systems with more
than a few parts. The parts talk to each other, the springs add up their
constants in the ugly series parallel equations, unless isolated, and the
fluids are the mass of the natural spring mass, one that changes with temp and
3) Control theory is helpful for systems theory- be ready to plot holes and
zeros in imaginary space, and a few other esoteric devices, to minimize systems
Laplace transforms help - the black box rings.
La grange transforms not so much, IMHO
4) If you are actually building something, know the test theory and open the
wallet, because you will be testing at different frequencies to see what shakes
off. Few, if any, can design a system of over four components to be without
vibrations at some particular frequency.
Fourier analysis works here, if you got the tiem and the bucks
5) The theory fails when the material moves into certain parts of the
6) The math ain't easy. Period.
7) Most college texts I have seen deal only in really rudimentary basics. Most
don't even address the various types of damping curves other than saying they
exist, and then not even that.
other than that, it's not too bad
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