TRANSIENT DYNAMICS OF THREE-DIMENSIONAL BEAM TRUSSES USING HIGHER ORDER KINEMATICS

摘要

Spatial structures may be subjected to impulse loads whichrngive rise to the propagation of high-frequency (HF), strongly oscillatingrnwaves. Despite some recent researches, the characterizationrnof the transient response of engineering systems to suchrnloads remains an open problem. The objective of this researchrnis to develop a reliable model of the HF energy evolution withinrnthree-dimensional beam trusses in order to predict, for example,rntheir potential steady-state behavior at late times or the energyrnpaths. The theory of micro-local analysis of linear wave systemsrnshows that the energy density associated with their HF solutionsrnsatisfies a Liouville-type transport equation. A suitablerntransport model for beams is derived from Timoshenko kinematics,rnand subsequently illustrated by the dispersion relationsrnfor HF Rayleigh-Lamb waves in a waveguide. At the interfacesrnbetween substructures, the energy flow is partly reflectedrnand partly transmitted. The corresponding power flow reflection/rntransmission coefficients have also been derived. Numericalrnsimulations are performed by nodal or spectral discontinuousrnGalerkin (DG) methods for spatial discretization and a strongrnstability-preserving Runge-Kutta (RK) method for time integration.rnNumerical results using the RK-DG method are presentedrnfor the example of a three-dimensional beam truss that exhibits arndiffusive behavior at late times.