Numerical and experimental study of first passage time of a steel strip subjected to forced and parametric excitations

The first passage time refers to the time required for a dynamical system to reach a target energy level for the first time, departing from a known initial state. Analytical studies of the first passage time of a linear Mathieu oscillator under stochastic forced and parametric excitations defined as Brownian white noises identified three behavioral regimes for the first passage time. The current work describes the design and use of an experimental set-up in order to validate the existence of the regimes. This paper successively describes the design and the finite element modeling of the set-up consisting in a pre-stressed steel strip, the reduction of the system to a single-degree-of-freedom system to match the framework of the theory, numerical studies on the influence of the frequency bands of the excitations on the first passage time and the experimental tests. Qualitatively, two of the three regimes are successfully observed in the experiment. Quantitatively, a good match is observed between the experimental and model results.