Pragmatic Apparatus – The modified Lindstedt–Poincare method for solving quadratic nonlinear oscillators

Cited by Lee Sonogan

Oscillation - Wikipedia

Abstract by Ismot A Yeasmin, MS Rahman, MS Alam

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.

Publication: Journal of Low Frquency Noise, Vibration and Active Control (Peer-Reviewed Journal)

Pub Date: Dec 13, 2020 Doi:

Keywords: Harmonic balance, variational method, nonlinear oscillations, forced vibration (Plenty more sections and references in this research paper)

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