Modified Lindstedt-Poincare methods for some strongly non-linear oscillations Part I: expansion of a constant

In this paper, a modified Lindstedt-Poincare method is proposed. In this te chnique. a constant. rather than the non-linear frequency, is expanded in p owers of the expanding parameter to avoid the occurrence of secular terms i n the perturbation series solution. Some examples are given here to illustr ate its effectiveness and convenience. The results show that the obtained a pproximate solutions are uniformly valid on the whole solution domain, and they are suitable not only for weakly non-linear systems, but also for stro ngly non-linear systems. (C) 2001 Elsevier Science Ltd. All rights reserved .