A Modified Lindstedt–Poincaré Method for a Strongly Nonlinear System with Quadratic and Cubic Nonlinearities

摘要

A modified Lindstedt–Poincaré method is presented for extending the range of the validity of perturbation expansion to strongly nonlinear oscillations of a system with quadratic and cubic nonlinearities. Different parameter transformations are introduced to deal with equations with different nonlinear characteristics. All examples show that the efficiency and accuracy of the present method are very good.