A more accurate solution of nonlinear conservative oscillator by energy balance method

Abstract

Purpose

The purpose of this paper is to present an analytical approximate technique to solve nonlinear conservative oscillator based on the He’s energy balance method (improved version recently presented by Khan and Mirzabeigy). The method is illustrated by solving double well Duffing oscillator.

Design/methodology/approach

The Duffing equation with a double-well potential (with a negative linear stiffness) is an important model of a mass particle moving in a symmetric double well potential. This form of the equation also appears in the transverse vibrations of a beam when the transverse and longitudinal deflections are coupled (Thompsen, 2003).

Findings

The approximate solutions obtained by the present technique have good agreement with the numerical solution and also provide better results than other existing methods.

Originality/value

The results are more accurate than those obtained by other existing methods. The relative errors obtained by the present paper are less than those obtained by other existing methods. Therefore, the present technique is very effective and convenient for solving nonlinear conservative oscillator.

Citation

Molla, M.H.U., Razzak, M.A. and Alam, M.S. (2018), "A more accurate solution of nonlinear conservative oscillator by energy balance method", Multidiscipline Modeling in Materials and Structures, Vol. 14 No. 4, pp. 634-646. https://doi.org/10.1108/MMMS-10-2017-0130