Abstract
This paper is a development of ref. [1]. Consider the following random equation:\(\ddot Z(t) + 2\beta \dot Z(t) + \omega _0^2 Z(t) = (a_0 + a_1 Z(t)).{\text{ }}I(t) + c\), in which excitation I(t) and response Z(t) are both random processes, and it is proposed that they are mutually independent. Suppose that I(t)=a(t)I·(t), a(t) is a known function of time and I·(t) is a stationary random process. In this paper, the spectral resolving form of the random equation stated above, the numerical solving method and the solutions in some special cases are considered.
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References
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Communicated by Chien Wei-zang.
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Wen-lu, J. A spectral resolving method for analyzing linear random vibrations with variable parameters. Appl Math Mech 5, 1091–1096 (1984). https://doi.org/10.1007/BF01875896
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DOI: https://doi.org/10.1007/BF01875896