A Novel Method to Improve the Multiple-Scales Solution of the Forced Nonlinear Oscillators

Abstract

We propose a novel procedure to improve the solutions obtained by perturbation methods for analyzing the solutions of strongly nonlinear systems in this paper. The proposed procedure is presented and then combined with the multiple-scales method for the optimum solutions of a class of forced oscillators with strong nonlinearity. The solutions obtained from conventional multiple-scales method and the proposed method are examined by the results from numerical continuation method. The results show that the proposed method is effective for the oscillators with nonlinear restoring force as well as nonlinear inertial force even if the nonlinearities are strong. Numerical results and comparison show that the proposed method can improve the solution a lot in comparison to the solution obtained by conventional multiple-scales method.