A perturbation-incremental method for strongly non-linear oscillators

Abstract

A perturbation-incremental method is presented for the analysis of strongly non-linear oscillators of the form x ̈ + g(x) = λf(x, .x).x , where g( x) and f( x, . x) are arbitrary non-linear functions of their arguments. The method is an extension of the perturbation-iterative method to the case where λ is not necessarily small. It incorporates salient features from both the perturbation method and the incremental method. Limit cycles of the oscillators can be calculated to any desired degree of accuracy. The stability of the limit cycle is also discussed.