Summary
The method of generalized stationary potential is applied to obtain exact probability densities for multi-degree-of-freedom nonlinear Hamiltonian systems excited by Gaussian white noises. The excitations can be additive, or multiplicative, or both, and governing equations are more general than those previously reported in the literature. Further extension is made to a still more general class, which include the Hamiltonian systems as special cases.
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References
Cai, G. Q. and Lin Y. K., “On Exact Stationary Solutions of Equivalent Non-Linear Stochastic Systems,” International Journal of Non-Linear Mechanics, Vol. 23, No. 4, 1988, pp. 315–325.
Caughey, T. K. and Ma, F., “The Steady-State Response of a Class of Dynamic Systems to Stochastic Excitations,” Journal of Applied Mechanics, Vol. 49, 1982, pp. 629–632.
Caughey, T. K. and Ma, F., “The Exact Steady-State Solution of a Class of Nonlinear Stochastic Systems,” International Journal of Non-Linear Mechanics, Vol. 17, No. 3, 1983, pp. 137–142.
Dimentberg, M. F., “An Exact Solution to a Certain Nonlinear Random Vibration Problem,” International Journal of Non-Linear Mechanics, Vol. 17, 1982, pp. 231–236.
Ibrahim, R. A., Parametric Random Vibration, Research Studies Press, Letchworth, Hertfordshire, England, 1986.
Lin, Y. K. and Cai, G. Q., “Exact Stationary-Response Solution for Second-Order Nonlinear Systems Under Parametric and External White-Noise Excitations: Part II,” Journal of Applied Mechanics, ASME, Vol. 55, 1988, pp. 702–705.
Lin, Y. K. and Cai, G. Q., “Equivalent Stochstic Systems,” Journal of Applied Mechanics, ASME, Vol. 55, No. 4, 1988, pp. 918–922.
Scheurkogel, A. and Elishakoff, I., “Non-Linear Random Vibration of a two-degree-Of-Freedom System,” Non-Linear Stochastic Dynamic Engineering Systems, Edited by Ziegler, F. and Scheller, G. I., Spring-Verlag, Berlin, 1988, pp. 285–299.
Soize, C., “Steady-State Solution of Fokker-Planck Equation in High Dimension,” Probabilistic Engineering Mechanics, Vol. 3, No. 4, 1988, pp. 196–206.
Wong, E. and Zakai, M., “On the Relation between Ordinary and Stochastic Equations,” International Journal of Engineering Science, Vol. 3, 1965, pp. 213–229.
Yong, Y., and Lin, Y. K. “Exact Stationary-Response Solution for Second-Order Nonlinear Systems Under Parametric and External White-Noise Excitations,” Journal of Applied Mechanics, ASME, Vol. 54, 1987, pp. 414–418.
Zhu, W. Q., “The Exact Stationary Response Solution of Several Classes of Nonlinear Systems to White Noise Parametric and/or External Excitations,” Applied Mathematics and Mechanics, Vol. 11, No. 2, 1990, pp. 165–175.
Zhu, W. Q., Cai, G. Q. and Lin, Y. K., “On Exact Stationary Solutions of Stochastically Perturbed Hamiltonian Systems;” Probabilistic Engineering Mechanics, Vol. 5, No. 2, 1990, pp. 84–87.
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© 1992 Springer-Verlag Berlin Heidelberg
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Zhu, W.Q., Cai, G.Q., Lin, Y.K. (1992). Stochastic Excited Hamiltonian Systems. In: Bellomo, N., Casciati, F. (eds) Nonlinear Stochastic Mechanics. IUTAM Symposia. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84789-9_47
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DOI: https://doi.org/10.1007/978-3-642-84789-9_47
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