Abstract
The reliability problem of a SDOF non-linear and non-hysteretic oscillator subject to a stationary Poisson driven train of impulses is considered. In the first passage time problem of the oscillator, time-invariant double barriers with a deterministic start in the safe domain are assumed. Initially, the Kolmogorov-Feller backwards equation for the reliability function along with associated initial and boundary conditions is specified. Next, a Petrov-Galerkin approach with shape and weighting functions matching all differentiability and continuity requirements of the weak formulation is applied to solve the consequent partial differential equation. As an example, a Duffing oscillator with linear damping is considered.
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