Dostal, LeoLeoDostalNamachchivaya, Navaratnam SriNavaratnam SriNamachchivaya2020-03-192020-03-192020-06-23Journal of Sound and Vibration (476): 115284 (2020-06-23)http://hdl.handle.net/11420/5430New theorems for moments of the first passage time of one dimensional nonlinear stochastic processes with an entrance boundary xe are formulated. This important class of one dimensional stochastic processes results among others from approximations of the energy or amplitude of second order nonlinear stochastic differential equations. Since the diffusion of a stochastic process vanishes at an entrance boundary, xe is called a singular point of the stochastic process. The theorems for the moments of the first passage times are validated based on existing analytical results. In addition, the first passage times of a forced and damped Mathieu oscillator, as well as a nonlinear stochastic differential equation, which is important for the determination of dangerous ship roll dynamics, are calculated. The proposed analytical expressions for the moments of the first passage times can be calculated very fast using standard quadrature formulas.0022-460X2020Duffing oscillatorFirst passage timeMathieu oscillatorRandom excitationStochastic dynamicsJournal Article10.1016/j.jsv.2020.115284Other