A time-reversal process for beam trusses subjected to impulse loads

Abstract

Spatial structures are often subjected to impulse loads which give rise to high-frequency (HF) waves. The objectives of the research outlined in this paper are twofold: (i) develop a reliable direct model of the transient dynamic response of built-up structures subjected to such impulse loads and (ii) use this model in a time-reversal inverse process in order to possibly detect the location of the shocks. The present study is more particularly focused on beam assemblies, as typically encountered in aerospace applications. At first, a transport model describing the evolution of the HF vibrational energy density in a three-dimensional beam truss is outlined, with an emphasis on the consideration of the reflection/transmission phenomena at the beam junctions. The latter contribute to spread HF waves within the entire structure, yielding a diffuse (noisy) vibrational energy field amenable to be efficiently time-reversed for the purpose of locating the source which has generated it. The time-reversal process itself is presented in a subsequent part. Its originality lies in the consideration of quadratic observables (energy densities) as the processed data. The approach is illustrated by a numerical simulation performed on a three-dimensional beam truss.