First passage probability of overturning problem for the rocking motion of rigid block excited by the Poisson white noise

Precision instruments in spacecrafts may overturn under stochastic impulse excitation, leading to irreparable consequences. This phenomenon can be regarded as a reliability problem involving the rocking motion of rigid blocks. So, in this paper, the first passage time statistics and exit location distributions are discussed to characterize the overturning problem of the rigid block rocking motion subjected to the Poisson white noise. The proposed generalized cell mapping method is introduced to obtain key reliability indicators, including the mean first passage time, probability density function of the first passage time, reliability function, and exit location distributions. Monte Carlo simulations are used to validate the accuracy of the proposed method. Detailed numerical results indicate that increasing the impulse excitation intensity, restitution coefficient and slenderness ratio decreases the reliability of the rocking motion. For cases where overturning is inevitable, analysis of the exit velocity distribution, shows that the restitution coefficient does not influence the exit velocity at the onset of overturning. In contract, a larger slenderness ratio leads to higher a larger exit velocity, while stronger noise excitation broadens the distribution range of exit velocity.