On the harmonic balance with linearization for asymmetric single degree of freedom non-linear oscillators

DOI10.1007/s11071-012-0326-1zbMath1258.34075OpenAlexW2023531145MaRDI QIDQ1928983

Serge Bruno Yamgoué

Publication date: 4 January 2013

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11071-012-0326-1

zbMATH Keywords

linearizationsingle degree of freedomconservative systemasymmetric oscillatorharmonic balance

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Theoretical approximation of solutions to ordinary differential equations (34A45) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Perturbations, asymptotics of solutions to ordinary differential equations (34E10)

Related Items

Approximate Analytical Solutions of A Nonlinear Oscillator Equation Modeling A Constrained Mechanical System ⋮ Multimode analysis of the dynamics and integrity of electrically actuated MEMS resonators ⋮ Asymptotic analysis and accurate approximate solutions for strongly nonlinear conservative symmetric oscillators ⋮ Analytical approximations to primary resonance response of harmonically forced oscillators with strongly general nonlinearity ⋮ Periodic solution of the strongly nonlinear asymmetry system with the dynamic frequency method

Cites Work

• Unnamed Item
• Application of the Krylov-Bogoliubov-Mitropolsky method to weakly damped strongly non-linear planar Hamiltonian systems
• An iteration approach to nonlinear oscillations of conservative single-degree-of-freedom systems
• The simplest resonance capture problem, using harmonic balance based averaging
• Modified Lindstedt-Poincaré methods for some strongly nonlinear oscillations. I: Expansion of a constant
• Large amplitude non-linear oscillations of a general conservative system
• An analytical approximate technique for a class of strongly non-linear oscillators
• On the analytical approximation of damped oscillations of autonomous single degree of freedom oscillators
• Presenting a new method for the solution of nonlinear problems
• Multiple scales via Galerkin projections: Approximate asymptotics for strongly nonlinear oscillations
• A new analytical approach to the Duffing-harmonic oscillator
• Comparison of alternative improved perturbative methods for nonlinear oscillations
• Quadratic non-linear oscillators
• Solution of a quadratic nonlinear oscillator by the method of harmonic balance
• Exact solution of a quadratic nonlinear oscillator
• Higher accuracy analytical approximations to the Duffing-harmonic oscillator
• Solutions of a quadratic nonlinear oscillator: Iteration procedure
• Some Remarks on the Harmonic Balance Method for Mixed-Parity Non-Linear Oscillations
• THE SUBHARMONIC MELNIKOV THEORY FOR DAMPED AND DRIVEN OSCILLATORS REVISITED
• A Generalization of the Mixing-Length Theory of Turbulent Convection.
• A method for obtaining approximate analytic periods for a class of nonlinear oscillators