Abstract
Recently, an analytical solution of a quadratic nonlinear oscillator has been presented based on the harmonic balance method. By introducing a small parameter, a set of nonlinear algebraic equations have been solved which usually appear among unknown coefficients of several harmonic terms. But the method is not suitable for all quadratic oscillators. Earlier, introducing a small parameter to the frequency series, Cheung et al. modified the Lindstedt–Poincare method and used it to solve strong nonlinear oscillators including a quadratic oscillator. But due to some limitations of both parameters, a changed form of frequency-related parameter (introduced by Cheung et al.) has been presented for solving various quadratic oscillators.
Highlights
Classical perturbation techniques[1,2,3,4,5] are widely used tools for solving weak nonlinear problems in which the solutions are expanded in powers of small parameters
Cheung et al.[6] introduced a small parameter in the frequency series and solved some strong nonlinear oscillators which are the main concern of this article
A modified LP method developed by Cheung et al has been used to solve quadratic oscillators
Summary
Classical perturbation techniques[1,2,3,4,5] are widely used tools for solving weak nonlinear problems in which the solutions are expanded in powers of small parameters. Cheung et al.[6] introduced a small parameter in the frequency series and solved some strong nonlinear oscillators which are the main concern of this article. A set of nonlinear algebraic equations appear among unknown coefficients of several harmonic terms. In Hosen et al.[25] and Yeasmin et al.,[26] such nonlinear algebraic equations are solved introducing another small parameter (different from that of Cheung et al.[6]).
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