A simple approach to nonlinear oscillators

DOI10.1016/j.physleta.2009.08.033zbMath1233.70009OpenAlexW2949840325MaRDI QIDQ665424

Zhong-Fu Ren, Ji-Huan He

Publication date: 5 March 2012

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physleta.2009.08.033

zbMATH Keywords

nonlinear oscillatoramplitude-frequency relationshipperiod solution

Mathematics Subject Classification ID

Nonlinear resonances for nonlinear problems in mechanics (70K30)

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Ren-He's method for solving dropping shock response of nonlinear packaging system ⋮ Analytical approximations to the solutions for a generalized oscillator with strong nonlinear terms ⋮ An optimal iteration method for strongly nonlinear oscillators ⋮ Hamiltonian approach to nonlinear oscillators ⋮ Approximate periodic solutions for the Helmholtz-Duffing equation ⋮ Periodic solution for nonlinear vibration of a fluid-conveying carbon nanotube, based on the nonlocal continuum theory by energy balance method ⋮ A new modification of the variational iteration method ⋮ Multiple-parameter Hamiltonian approach for higher accurate approximations of a nonlinear oscillator with discontinuity ⋮ On the variational homotopy perturbation method for nonlinear oscillators

Cites Work

• Application of He's parameter-expansion method for oscillators with smooth odd nonlinearities
• Application of a modified rational harmonic balance method for a class of strongly nonlinear oscillators
• Variational iteration method -- a kind of non-linear analytical technique: Some examples
• Solution for an anti-symmetric quadratic nonlinear oscillator by a modified He's homotopy perturbation method
• Approximate period of nonlinear oscillators with discontinuities by modified Lindstedt--Poincaré method
• He's frequency formulation for nonlinear oscillators
• SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS

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