7. Experimental and Numerical Study of the Second Order Moment of the First Passage Time of a Steel Strip Subjected to Forced and Parametric Excitations

The first passage time is the time required for a stochastic process to leave a subdomain of the state space for the first time when starting from a given initial state in this subdomain. Analytical studies of the first passage time of a linear Mathieu oscillator subjected to forced and parametric excitations defined as δ-correlated Brownian noises highlighted the existence of three behavioral regimes for the average first passage time. The current work describes the design and outcomes of an experimental study demonstrating the practical existence of these regimes for the second order moment of the first passage time. On the one hand, tests are carried out on an experimental set-up consisting in a pre-stressed strip subjected to forced and parametric stochastic excitations. On the other hand, a finite element model of the structure is built, updated and used to address the same problem using a numerical approach. Both the experimental tests and the numerical simulations produce mean square first passage time maps that provide evidence for the existence of the three foreseen behavioral regimes. The good match of the first passage time maps confirms the accuracy of the finite element model updating as well as the relevance of the theoretical model for this type of problem.