Path integration of the Duffing-Rayleigh oscillator subject to harmonic and stochastic excita\-tions

DOI10.1016/j.amc.2005.01.095zbMath1096.37029OpenAlexW2028630669MaRDI QIDQ2490984

Wei Xu, Li Cai, Wenxian Xie

Publication date: 18 May 2006

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2005.01.095

zbMATH Keywords

method of multiple scalesmethod of harmonic balancepath integrationharmonic and stochastic excitationDuffing-Rayleigh oscillator

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Random vibrations in mechanics of particles and systems (70L05) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Ordinary differential equations and systems with randomness (34F05) Generation, random and stochastic difference and differential equations (37H10) Stochastic analysis (60H99)

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Cites Work

• Response statistics of nonlinear systems to combined deterministic and random excitations
• The exact steady-state solution of a class of nonlinear stochastic systems
• A new path integration procedure based on Gauss-Legendre scheme
• Exact and approximate solutions for randomly excited MDOF nonlinear systems
• On the calculation of stationary solutions of multi-dimensional Fokker-Planck equations by orthogonal functions
• An exact solution to a certain nonlinear random vibration problem
• STOCHASTIC AVERAGING OF STRONGLY NON-LINEAR OSCILLATORS UNDER COMBINED HARMONIC AND WHITE-NOISE EXCITATIONS