Nonlinear oscillator with power-form elastic-term: Fourier series expansion of the exact solution

DOI10.1016/j.cnsns.2014.10.012zbMath1333.34056OpenAlexW2078498480MaRDI QIDQ907604

Sergio Bleda, Augusto Beléndez, Jorge Francés, Enrique Arribas, Tarsicio Beléndez, Carolina Pascual

Publication date: 26 January 2016

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10045/43240

zbMATH Keywords

nonlinear oscillatorsdynamical systemsapproximate solutionssymbolic computationconservative systemsFourier series expansiontruly nonlinear oscillators

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Theoretical approximation of solutions to ordinary differential equations (34A45) Explicit solutions, first integrals of ordinary differential equations (34A05) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15)

Related Items

Exact solution for the unforced Duffing oscillator with cubic and quintic nonlinearities ⋮ Exact steady states of periodically forced and essentially nonlinear and damped oscillator

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Oscillator with a sum of noninteger-order nonlinearities
• Accurate solutions of conservative nonlinear oscillators by the enhanced cubication method
• A non-simultaneous variational approach for the oscillators with fractional-order power nonlinearities
• Higher accuracy analytical approximations to a nonlinear oscillator with discontinuity by He's homotopy perturbation method
• Oscillators with a fractional-order restoring force: higher-order approximations for motion via a modified Ritz method
• Oscillator with non-integer order nonlinearity and time variable parameters
• Application of He's homotopy perturbation method to conservative truly nonlinear oscillators
• Oscillators with a generalized power-form elastic term
• OSCILLATIONS IN AN x4/3POTENTIAL
• OSCILLATIONS IN AN x(2m+2)/(2n+1) POTENTIAL
• Frequencies of oscillators with fractional-power non-linearities
• GENERALIZED HARMONIC BALANCE/NUMERICAL METHOD FOR DETERMINING ANALYTICAL APPROXIMATIONS TO THE PERIODIC SOLUTIONS OF THE x4/3 POTENTIAL
• Iteration method solutions for conservative and limit-cycle force oscillators
• Theory of the Relativistic Oscillator
• The 𝐴𝑡𝑒𝑏(ℎ)-functions and their properties
• Analytical approximate solutions for conservative nonlinear oscillators by modified rational harmonic balance method