Application of a modified rational harmonic balance method for a class of strongly nonlinear oscillators

DOI10.1016/j.physleta.2008.08.024zbMath1223.34055OpenAlexW2167838058MaRDI QIDQ641493

Juan-Miguel Gracia

Publication date: 21 October 2011

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

Full work available at URL: http://hdl.handle.net/10045/9205

zbMATH Keywords

nonlinear oscillatorsapproximate solutionsrational harmonic balance method

Mathematics Subject Classification ID

Stability for nonlinear problems in mechanics (70K20) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15)

Related Items (12)

Approximate Analytical Solutions of A Nonlinear Oscillator Equation Modeling A Constrained Mechanical System ⋮ On the solution of strong nonlinear oscillators by applying a rational elliptic balance method ⋮ Periodic solutions for Hamiltonian equation associated with Gaussian potential ⋮ Notes on ``Application of the Hamiltonian approach to nonlinear oscillators with rational and irrational elastic terms ⋮ Analysis of the nonlinear structural-acoustic resonant frequencies of a rectangular tube with a flexible end using harmonic balance and homotopy perturbation methods ⋮ Approximate analytical solutions to a conservative oscillator using global residue harmonic balance method ⋮ Approximate periodic solutions for the Helmholtz-Duffing equation ⋮ Approximate solution for the Duffing-harmonic oscillator by the enhanced cubication method ⋮ Application of the Hamiltonian approach to nonlinear oscillators with rational and irrational elastic terms ⋮ A simple approach to nonlinear oscillators ⋮ Global residue harmonic balance method for Helmholtz-Duffing oscillator ⋮ HARMONIC BALANCE FOR NON-PERIODIC HYPERBOLIC SOLUTIONS OF NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS

Cites Work

• Application of He's parameter-expansion method for oscillators with smooth odd nonlinearities
• Modified Lindstedt-Poincaré methods for some strongly nonlinear oscillations. I: Expansion of a constant
• Homotopy perturbation method for bifurcation of nonlinear problems
• A new analytical approach to the Duffing-harmonic oscillator
• Nonlinear oscillator with discontinuity by parameter-expansion method
• Construction of solitary solution and compacton-like solution by variational iteration method
• Variational approach for nonlinear oscillators
• Solution of a Duffing-harmonic oscillator by the method of harmonic balance
• FOURIER ANALYSIS OF A RATIONAL HARMONIC BALANCE APPROXIMATION FOR PERIODIC SOLUTIONS
• Application of the homotopy perturbation method to the nonlinear pendulum
• Accurate approximate solution to nonlinear oscillators in which the restoring force is inversely proportional to the dependent variable
• SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS
• Alternative perturbation approaches in classical mechanics
• Letter to the Editor

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