Experimental and numerical study of first passage time

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 single-degree-of-freedom systems governed by the linear Mathieu equation and subjected to broadband forced and parametric excitations have revealed the existence of different regimes for the first passage time. This Master thesis aims at the experimental validation of the existence of these regimes for a real structure consisting in a strip pre-stressed by a mass. The complete process, from the structure design to the experimental validation, is conducted in this work.
A finite element model of the structure is built in Matlab and updated with various state-of-the-art techniques from the field of experimental modal analysis. A model reduction of the full multi-degree-of-freedom system is introduced to match the conditions of the analytical results. It is shown that the dynamics of the structure can be approached by a single-degree-of-freedom reduced model only when both the forced and parametric excitations are narrow-band processes. The influence of narrow-band excitations on the first passage time is therefore studied numerically. The results of this numerical preparatory study are used to define the conditions of the experimental tests. First passage time maps are reproduced experimentally in the framework of the linear single-degree-of-freedom Mathieu equation.
This work provides the first physical evidence that the first passage time of real multi-degree-of-freedom systems can be characterized with the physical properties of the structure. It also addresses for the first time the influence of narrow-band excitations. Therefore, it opens the way to broadening the scope of the first passage time theory beyond the context of one-degree-of-freedom linear systems subjected to broadband excitations considered so far.