Publisher DOI: 10.1016/j.jsv.2020.115284
Title: First passage time of nonlinear diffusion processes with singular boundary behavior
Authors: Dostal, Leo 
Namachchivaya, Navaratnam Sri 
Keywords: Duffing oscillator;First passage time;Mathieu oscillator;Random excitation;Stochastic dynamics
Issue Date: 23-Jun-2020
Source: Journal of Sound and Vibration (476): 115284 (2020-06-23)
Journal: Journal of sound and vibration 
Abstract (english): 
New 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.
ISSN: 0022-460X
Institute: Mechanik und Meerestechnik M-13 
Document Type: Article
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