Steady-State Response of a Dynamical System Under Combined Parametric and Forcing Excitations

Abstract

A linear dynamical system subjected to combined parametric and forcing excitations of periodic nature is governed by a system of inhomogeneous differential equations with periodic coefficients. Presented here is an explicit expression for the steady-state periodic response of such a system, given in terms of the fundamental matrix of the homogeneous system. Based upon this expression, specific analytic formulas of the steady-state response can be derived for some physical systems. For a general system where such an analytical determination is not feasible, the derived expression allows us to devise a straightforward numerical procedure which is particularly suited for computer evaluation and which is equally suited for high-order systems.