Self Excited Vibrations

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 pressure 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 oscillation 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 stress-strain curves. 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

Thank You. What about the recommended sites. Ismail

6 vibration modes would be a minimum for a 6 degree od freedom (DOF) body. A continuos body has an infinite number of modes; one for each DOF.

Chapter 7 in "Mechanical Vibrations" by Den Hartog. A good very readable practical book. Cheap, since it was re-popped by Dover, and even available in many technical and non-technical libraries