FIRST PASSAGE OF A RIGID STRUCTURE ON A SLIDING FOUNDATION.

The first passage problem for a sliding rigid block on a frictional foundation, subjected to Gaussian white noise through the foundation, is studied. Two related methods are used to obtain estimates of system reliability versus time. In the first, the Pontriagin-Vitt equation is formulated and solved by the finite element method to obtain the first two moments of first passage time, over a range of parameters. Maximum entropy distributions are used to obtain the system reliability, given the first two moments. In the second, an initial-boundary value problem related to the backward Kolmogorov equation is solved directly for the system reliability. Results of both are compared with those obtained by Monte-Carlo simulation, for several systems of interest.