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- W2029489025 abstract "Structures excited by random vibrations can often be modelled as time-independent, lumped-parameter systems with white noise excitation. In the non-linear case, moments and probability densities of higher order than the first cannot usually be obtained exactly. However, these quantities can be expressed as expansions of the eigenfunctions of the corresponding Fokker-Planck-Kolmogorov operator. Some exact solutions are given for systems governed by first-order differential equations. For higher order systems a variational method can be used to obtain approximate solutions. This is applied to obtain the autocorrelation and spectral density functions of three severely non-linear one-degree-of-freedom oscillators. The results are compared with those obtained by direct digital simulation of the system equations." @default.
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- W2029489025 date "1973-09-01" @default.
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- W2029489025 title "Eigenfunction expansions for randomly excited non-linear systems" @default.
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- W2029489025 doi "https://doi.org/10.1016/s0022-460x(73)80110-5" @default.
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