Path integration of the Duffing–Rayleigh oscillator subject to harmonic and stochastic excitations
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 ca...
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| Published in | Applied mathematics and computation Vol. 171; no. 2; pp. 870 - 884 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
New York, NY
Elsevier Inc
15.12.2005
Elsevier |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0096-3003 1873-5649 |
| DOI | 10.1016/j.amc.2005.01.095 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Xie, W.X. Cai, L. Xu, W. |
| Author_xml | – sequence: 1 givenname: W.X. surname: Xie fullname: Xie, W.X. email: xiewy8899@eyou.com organization: Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, PR China – sequence: 2 givenname: W. surname: Xu fullname: Xu, W. email: weixu@nwpu.edu.cn organization: Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, PR China – sequence: 3 givenname: L. surname: Cai fullname: Cai, L. organization: College of Astronautics, Northwestern Polytechnical University, Xi’an, Shaanaxi 710072, PR China |
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| Cites_doi | 10.1016/S0266-8920(02)00034-6 10.1016/0020-7462(82)90023-3 10.1016/0020-7462(82)90013-0 10.1016/S0020-7462(96)00096-0 10.1006/jsvi.2000.3083 10.1016/0020-7462(90)90014-Z 10.1016/0020-7462(96)00053-4 10.1016/S0266-8920(99)00031-4 10.1023/A:1008389909132 |
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| Keywords | 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 |
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| References | Von Wagner, Wedig (bib6) 2000; 21 Lin, Cai (bib4) 1995 Dimentberg (bib3) 1982; 17 Zhou, Zhu (bib13) 1998 Di Paola, Sofi (bib7) 2002; 17 Yu, Lin (bib11) 2003 Cai, Lin (bib5) 1996; 31 Caughey (bib1) 1971 Caughey, Ma (bib2) 1982; 17 Naess, Moe (bib8) 2000; 15 Huang, Zhu, Suzuki (bib9) 2000; 238 Nayfeh, Serhan (bib12) 1990; 25 Yu, Cai, Lin (bib10) 1997; 32 Lin (10.1016/j.amc.2005.01.095_bib4) 1995 Von Wagner (10.1016/j.amc.2005.01.095_bib6) 2000; 21 Zhou (10.1016/j.amc.2005.01.095_bib13) 1998 Huang (10.1016/j.amc.2005.01.095_bib9) 2000; 238 Caughey (10.1016/j.amc.2005.01.095_bib1) 1971 Dimentberg (10.1016/j.amc.2005.01.095_bib3) 1982; 17 Yu (10.1016/j.amc.2005.01.095_bib11) 2003 Caughey (10.1016/j.amc.2005.01.095_bib2) 1982; 17 Yu (10.1016/j.amc.2005.01.095_bib10) 1997; 32 Nayfeh (10.1016/j.amc.2005.01.095_bib12) 1990; 25 Di Paola (10.1016/j.amc.2005.01.095_bib7) 2002; 17 Naess (10.1016/j.amc.2005.01.095_bib8) 2000; 15 Cai (10.1016/j.amc.2005.01.095_bib5) 1996; 31 |
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| SubjectTerms | 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 |
| Title | Path integration of the Duffing–Rayleigh oscillator subject to harmonic and stochastic excitations |
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