An efficient numerical procedure for calculating periodic vibrations of elastic mechanisms

Abstract

This paper proposes a numerical procedure based on the well-known Newmark integration method to determine initial conditions for the periodic solution of a system of linear differential equations with time-periodic coefficients. Based on this, steady-state periodic vibrations of mechanisms with elastic elements governed by linearized differential equations with time-periodic coefficients can be conveniently calculated. The proposed procedure is demonstrated by a dynamic model of a planar four-bar mechanism with the flexible coupler.