Caughey, Thomas K. (1963) Derivation and Application of the Fokker-Planck Equation to Discrete Nonlinear Dynamic Systems Subjected to White Random Excitation. Journal of the Acoustical Society of America, 35 (11). pp. 1683-1692. ISSN 0001-4966. doi:10.1121/1.1918788. https://resolver.caltech.edu/CaltechAUTHORS:CAUjasa63a
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Abstract
The Fokker-Planck equation is derived and applied to discrete nonlinear dynamic systems subjected to white random excitation. For the class of problems in which the nonlinearities involve only the displacements of the system, it is shown that exact solutions can be constructed for the stationary Fokker-Planck equation. It is further shown that if stationary solutions exist they are unique.
| Item Type: | Article | ||||||
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| Additional Information: | ©1963 Acoustical Society of America A. H. Gray, one of my students, is credited with the proof of the above Appendix. This work was supported in part by the Esso Educational Foundation. | ||||||
| Issue or Number: | 11 | ||||||
| DOI: | 10.1121/1.1918788 | ||||||
| Record Number: | CaltechAUTHORS:CAUjasa63a | ||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:CAUjasa63a | ||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
| ID Code: | 4087 | ||||||
| Collection: | CaltechAUTHORS | ||||||
| Deposited By: | Archive Administrator | ||||||
| Deposited On: | 26 Jul 2006 | ||||||
| Last Modified: | 29 Sep 2022 22:10 |
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