2014-04-15

Generalized SDOF Systems

A procedure similar to the one used for rigid bodies systems can be applied to deformable bodies, assuming an instantaneous motion that satisfies external constraints and taking into account the internal virtual work in writing the equation of motion. Solving the equation of motion gives the amplitude of the assumed shape motion of the deformable body.

The procedure can be formalized to the so called "Rayleigh method" for computing an estimate of the first mode of vibration of, and we demonstrate that Rayleigh estimates have a lower bound in the true frequency of vibration of the system.

Good estimates require an assumed shape of vibration that's a good approximation of the true shape of vibration; we will see what discriminates a good from a bad shape, that is respect of the external constraints and a realistic distribution of internal stresses.

Starting from the above discussion of good shapes, we formalize an iterative method to obtain better and better estimates of the frequency of vibration.

Material available for this class:

Further material

I would like to remind you that a number of detailed solutions of the assignment of the previous years are available

Other solutions for even older problem sets are hidden in the site... well, hidden is not the right word!

Giacomo Boffi