Abstract
The response to Gaussian white noise excitation of a hinged elastic shallow arch is studied. The steady state solutions are obtained by means of the Fokker-Planck equation. A class of transient solutions, viz. the first-passage time probability for snap-through of a sinusoidal shallow arch, is studied numerically by the generalized cell mapping method and direct Monte Carlo simulation. In obtaining the global information of first-passage time probability of the system, there are large computational advantages of the generalized cell mapping method over direct Monte Carlo simulation.
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