Exact solution for the unforced Duffing oscillator with cubic and quintic nonlinearities

DOI10.1007/s11071-016-2986-8zbMath1371.34057OpenAlexW2487709139WikidataQ56907563 ScholiaQ56907563MaRDI QIDQ2407579

Enrique Arribas, Carolina Pascual, Tarsicio Beléndez, Augusto Beléndez, Mariela L. Álvarez, Francisco Martínez

Publication date: 6 October 2017

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

Full work available at URL: http://hdl.handle.net/10045/60667

zbMATH Keywords

nonlinear oscillatorsexact solutiondynamical systemssymbolic computationconservative systemsJacobian elliptic functionscubic-quintic nonlinear oscillator

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15)

Related Items

Approximate period for large-amplitude oscillations of a simple pendulum based on quintication of the restoring force ⋮ An improved Störmer-Verlet method based on exact discretization for nonlinear oscillators ⋮ Stable quasi-periodic orbits of a class of quintic Duffing systems ⋮ Exact time-integral inversion via Čebyšëv quintic approximations for nonlinear oscillators ⋮ Unnamed Item ⋮ Uniform global asymptotic stability for oscillators with nonlinear damping and nonlinear restoring terms ⋮ Effect of discrete breathers on the specific heat of a nonlinear chain ⋮ Closed-form exact solutions for the unforced quintic nonlinear oscillator ⋮ Homotopy perturbation method for strongly nonlinear oscillators ⋮ Performance analysis of a geometrically nonlinear isolation system subjected to high levels of excitation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• ``Quintication method to obtain approximate analytical solutions of non-linear oscillators
• Solution of the damped cubic-quintic Duffing oscillator by using Jacobi elliptic functions
• Exact solution of the cubic-quintic Duffing oscillator
• An accurate closed-form approximate solution for the quintic Duffing oscillator equation
• Newton-harmonic balancing approach for accurate solutions to nonlinear cubic-quintic duffing oscillators
• Nonlinear oscillator with power-form elastic-term: Fourier series expansion of the exact solution
• On Linstedt-Poincaré techniques for the quintic Duffing equation
• An analytical approximate technique for a class of strongly non-linear oscillators
• Duffing equations with cubic and quintic nonlinearities
• A new approach to Duffing equation with strong and high order nonlinearity
• Analytical approximate solutions for the cubic-quintic Duffing oscillator in terms of elementary functions
• Cubication of conservative nonlinear oscillators

This page was built for publication: Exact solution for the unforced Duffing oscillator with cubic and quintic nonlinearities