Nonlinear oscillations with parametric excitation solved by homotopy analysis method

Abstract

An analytical technique, namely the homotopy analysis method (HAM), is used to solve problems of nonlinear oscillations with parametric excitation. Unlike perturbation methods, HAM is not dependent on any small physical parameters at all, and thus valid for both weakly and strongly nonlinear problems. In addition, HAM is different from all other analytic techniques in providing a simple way to adjust and control convergence region of the series solution by means of an auxiliary parameter \({\hbar}\) . In the present paper, a periodic analytic approximations for nonlinear oscillations with parametric excitation are obtained by using HAM, and the results are validated by numerical simulations.