Analytical technique for solving the quadratic nonlinear oscillator

Highlights

• A new modified harmonic balance method is introduced in this study.

• The proposed method reduces the algebraic complexity.

• All the related nonlinear algebraic equations are solved analytically.

• A quadratic nonlinear oscillatory problem is studied.

Abstract

Recently, an approximate solution of the quadratic nonlinear oscillator has been presented based on the harmonic balance method. According to this method a set of nonlinear algebraic equations appear among the unknown coefficients of the several harmonic terms. Moreover, all these algebraic equations have no analytic solutions and sometimes no real solution can be found. In this article, a simple form of harmonic balance solution is obtained where algebraic complexity is partially reduced and all the related nonlinear algebraic equations are solved analytically.