An asymptotic method for periodic solution of nonlinear autonomous systems modeled by second order hyperbolic type partial differential equation

Abstract

In this article, a new perturbation is developed and used to find analytical solutions which describe the time response of nonlinear systems governed by second order hyperbolic type partial differential equations, based on the pioneer work of Krylov-Bogoliubov-Mitropolskii (KBM). In addition, a numerical code is also developed to test the accuracy of analytical solution. Finally, the method is applied to longitudinal vibration of a rod in which nonlinear behavior occurs. The analytical solution shows an excellence coincidence with numerical solution.