Path integration of the Duffing–Rayleigh oscillator subject to harmonic and stochastic excitations

• Published in: Applied mathematics and computation Vol. 171; no. 2; pp. 870 - 884
• Main Authors: Xie, W.X., Xu, W., Cai, L.
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 15.12.2005; Elsevier
• Subjects: Duffing–Rayleigh oscillator; Exact sciences and technology; Global analysis, analysis on manifolds; Harmonic and stochastic excitation; Mathematical analysis; Mathematics; Measure and integration; Method of harmonic balance; Method of multiple scales; Ordinary differential equations; Path integration; Sciences and techniques of general use; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Harmonic and stochastic excitation; Path integration; Method of multiple scales; Duffing–Rayleigh oscillator; Method of harmonic balance; Density of states; Stability; Path integral; Probability distribution; Duffing-Rayleigh oscillator; Harmonic balance; Probability density; Stochastic excitation; Applied mathematics; Duffing Rayleigh oscillator; Multiple scale; Sinusoidal excitation; Steady state solution; Harmonic oscillator
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2005.01.095

This paper is focused on the Duffing–Rayleigh oscillator subject to harmonic and stochastic excitations using path integration based on the Gauss–Legendre integration scheme. First applying methods of harmonic balance and multiple scales to the deterministic case, the stabilities of the responses can be analyzed. Then the steady state periodic solution of probability density can be captured via path integration. At the same time, the changes of probability density induced by the intensities of harmonic and stochastic excitations are discussed in three cases.