He–Laplace method for general nonlinear periodic solitary solution of vibration equations

Abstract

This paper suggests a universal approach to solve nonlinear periodic vibration equations by He–Laplace method, a coupling of He’s perturbation method and Laplace transform. The nonlinear periodic solitary solution of vibration equation is used as an example to elucidate the effectiveness and simplicity of the method, only few iterations are needed to obtain an extremely accurate solution.