Analytic approximations to nonlinear oscillatory systems

Abstract

This paper deals with nonlinear oscillations of a conservative, nonnatural, single-degree-of-freedom system with odd nonlinearity. By combining the linearization of the governing equation with the method of harmonic balance, we establish approximate analytic solutions for the nonlinear oscillations of the system.Unlike the classical harmonic balance method linearizaion is performed prior to proceeding with harmonic balancing thus resulting in linear algebraic equations instead of nonlinear algebraic equations. Hence,we are able to establish these approximate analytic formulas for the exact solution. These approximate solutions are valid for small as well as large amplitudes of oscillation.