Transient dynamics of three-dimensional beam trusses under impulse loads
Résumé
Spatial structures are often subjected to impulse loads which induce high-frequency (HF) wave propagations. Despite some recent researches, the characterization of the transient response to such loads remains an open problem. The objective of this research is to develop a reliable model of the HF energy evolution within three-dimensional Timoshenko beam trusses in order to predict, for example, their potential steady-state behavior at late times or the energy paths. The theory of micro-local analysis of wave systems shows that the energy density associated with their HF solutions satisfies a Liouville-type transport equation. At the interfaces between substructures, the energy flow is partly reflected and partly transmitted. The corresponding power flow reflection/transmission coefficients are also derived in this study. Numerical simulations are performed by a spectral Discontinuous "Galerkin" (DG) method for spatial discretization and a strong stability-preserving Runge-Kutta (RK) method for time integration. Numerical results using the RK-DG method are presented for the example of a three-dimensional beam truss that exhibits a diffusive behavior at late times.