Computation Method for Forced Vibration Response of a Multiple DOF Parametric System

In this paper, a mathematical approach is presented for the forced vibration analysis of a multiple DOF system that is governed by ordinary differential equations with both time-periodic stiffness and external force that have different periods. Based on an equivalent dynamic system, a closed-form solution, i.e. a special trigonometric series, is presented for the forced vibration response of the system. Computation is realized by applying the harmonic balance operation, and the parametric vibration equation is converted into a set of infinite-order linear algebraic equations. Based on the physical property of the forced vibration response, all the coefficient vectors of the forced response are solved by the use of inverse matrix. The present approach can be used to predict the forced vibration response and its spectrum with better computation performance. It can help reveal some nonlinear phenomena in the parametric system. Therefore, it proves to be a useful tool for future research and engineering applications of parametric systems.