RESPONSE AND RELIABILITY OF POISSON-DRIVEN SYSTEMS BY PATH INTEGRATION

The paper deals with the stochastic response and the reliability of a nonlinear and nonhysteretic single-degree-of-freedom (SDOF) oscillator subject to a stationary Poisson-driven train of impulses. The state v ector made up of the displacement and the velocity components then bec omes a Markov process. The applied solution method is based on path in tegration, which essentially implies that a mesh of discrete states of the Markov vector process is initially defined with a suitable distri bution throughout the phase plane, next, the transition probability ma trix related to the Markov chain originating from this discretization is calculated, assuming the transition time interval to be sufficientl y small so that at most one impulse is likely to arrive during the int erval. Obviously, this assumption is best fulfilled for processes with low pulse arrival rates. Consequently, the method is the most effecti ve in such cases in contrast to all other approaches to the considered problems. The time-dependent joint probability density function (PDF) of the displacement and velocity is obtained by passing the system th rough a sequence of transient states. In the reliability problems, the probability mass is absorbed at the exit part of the boundary of the safe domain during transitions. The considered first passage time prob lem assumes time-invariant single or double barriers with deterministi c or stochastic start in the safe domain. The method has been applied to a Duffing oscillator with linear viscous damping, and the computed results have been compared with those obtained from extensive Monte Ca rlo simulations.