Averaging Method Using Generalized Harmonic Functions For Strongly Non-Linear Oscillators

Abstract

An averaging method in which generalized harmonic functions are used is applied to study the approximate solutions of the strongly non-linear oscillators ẍ + g(x) = εf{hook}(x, ẋ) and ẍ + g(x) = εF(x, ẋ, Ωt), where g(x) is an arbitrary non-linear function. The method gives the approximate solutions in terms of generalized harmonic functions. These functions are also periodic and are exact solutions of strongly non-linear differential equations. Some phenomena considered include limit cycles of strongly non-linear autonomous oscillators and steady state response of strongly non-linear oscillators subject to weak harmonic excitation. The procedure is simple and easy to apply. © 1994 Academic Press. All rights reserved.