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- W2007111550 abstract "Abstract The present investigation focuses on the determination of the statistical properties, transition probability function, mean, and variance, of the response v(t) of the first-order system governed by the non-linear stochastic differential equation dv dt +ƒ(v)=D(t)W(t) , where ƒ(v) is a piecewise constant. D(t) is an arbitrary deterministic modulation function and W(t) is a stationary Gaussian white noise. An exact solution of the Fokker-Plank equation associated with the process v(t) is first derived in terms of a set of unknown boundary conditions. It is then shown that these functions of time satisfy a system of linear Voltera integral equations of the second kind, which are readily solved numerically and sometimes analytically. Finally, these concepts are applied to the seismic sliding of rigid structures and examples of application are presented." @default.
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- W2007111550 date "1993-07-01" @default.
- W2007111550 modified "2023-09-23" @default.
- W2007111550 title "Non-stationary response of some first-order non-linear systems associated with the seismic sliding of rigid structures" @default.
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- W2007111550 doi "https://doi.org/10.1016/0020-7462(93)90015-d" @default.
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