An exact solution of the first-exit time problem for a class of structural systems |
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Authors: | Agnessa Kovaleva |
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Affiliation: | Space Research Institute, Russian Academy of Sciences, Moscow 117997, Russia |
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Abstract: | The mean time to escape from a region of desired operations is one the basic reliability measures in stochastic dynamics. In general, a precise solution of the first-exit time problem is unavailable. This paper demonstrates an exact solution of the mean exit time problem for a multidimensional non-dissipative Lagrangian system excited by additive Gaussian white noise. We identify the Fokker–Planck equation whose solution characterizes the mean time needed to reach a critical energy and explicitly construct the solution. For illustration, we apply the developed theory to engineering examples. We calculate the mean time of the standard operation for a flexural nanotube with likely noise-induced buckling and analyze the mean time of the stable functioning for a gyroscope subjected to random and dissipation torques. It is demonstrated that the solution of the first-exit time problem for a non-dissipative system gives a quite good approximation to a numerical solution of a similar problem for a system with small dissipation. |
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Keywords: | Nonlinear stochastic systems Exit time problem |
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