Exact, no-transform solution of multi-degree-of-freedom vibrations with non-harmonic, periodic excitation

Abstract

A procedure is proposed to obtain the steady state displacement solution to linear vibration problems with non-harmonic, periodic, continuous or discontinuous excitation for any finite number of degrees of freedom. The solution obtained is exact, in closed form and in a single equation. The procedure makes no use of any transform. Since the displacement solution is exact, it may be differentiated to obtain the exact velocity and the exact acceleration. An example of a quarter-vehicle suspension model is solved in detail.