Accurate analytical solution of the circular sector oscillation by the modified harmonic balance method

Abstract

This paper aims to solve the nonlinear differential equation of the circular sector oscillator analytically via the modified harmonic balance method (MHBM). To assess the reliability and the precision of the present method, we have compared the obtained results with the global residue harmonic balance method, Akbari–Ganji’s method, and numerical Runge–Kutta method which reveals that the MHBM is more reliable than others methods.

A simple modified harmonic balance method for strongly nonlinear oscillator with cubic non-linearity and harmonic restoring force

“…Many types of modification like the global residue harmonic balance method, [27][28][29][30][31] the modified energy balance method, 32,33 the modified harmonic balance method, [34][35][36] the modified homotopy perturbation method, [37][38][39][40] the modified Lindested-Poincare method, 41,42 the modified Laplace based variational iteration method 43 etc. were also used by many researchers to solve strong nonlinear problems.…”