Rational harmonic balance-based approximate solutions to nonlinear single-degree-of-freedom oscillator equations

Abstract

The purpose of this paper is to extend the application of the modified, generalized, rational harmonic balance method to the determination of approximate analytical solutions to general single-degree-of-freedom oscillator equations. We propose a simple form of rational periodic function that depends on a parameter r such that 0<| r |<1 for the approximating solution. We show how one can determine this parameter analytically as a function of oscillation amplitude for a general nonlinear equation. Three examples are used to demonstrate the procedure and its accuracy.