Improved accuracy of He's energy balance method for analysis of conservative nonlinear oscillator

摘要

In this paper, the accuracy of He's energy balance method for the analysis of conservative nonlinear oscillator is improved based on combining features of collocation method and Galerkin-Petrov method. In order to demonstrate the effectiveness of proposed method, Duffing oscillator with cubic nonlinearity, double-well Duffing oscillator, and non-linear oscillation of pendulum attached to a rotating support are considered. Comparison of results with ones achieved utilizing other techniques shows improved energy balance method can very effectively reduce the error of simple energy balance method. Also, results show in large amplitude of oscillation, and improved energy balance method yields better accuracy rather than second-order energy balance method based on collocation and second-order energy balance method based on Galerkin method. Improved energy balance method can be successfully used for accurate analytical solution of other conservative nonlinear oscillator.