Transient dynamics of three-dimensional beam trusses using higher order kinematics

Abstract

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 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. A suitable HF transport model for beams is derived from the spectrum relations for Lamb waves in the HF range. At the interfaces between substructures, the energy flow is partly reflected and partly transmitted. The corresponding reflection/transmission coefficients are also derived in this study. Numerical simulations are performed by a spectral discountinuous Galerkin (DG) method for spatial ...