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

Abstract : Spatial structures may be subjected to impulse loads which give rise to the propagation of high-frequency (HF), strongly oscillating waves. Despite some recent researches, the characterization of the transient response of engineering systems 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 linear wave systems shows that the energy density associated with their HF solutions satisfies a Liouville-type transport equation. A suitable transport model for beams is derived from Timoshenko kine-matics, and subsequently illustrated by the dispersion relations for HF Rayleigh-Lamb waves in a waveguide. At the interfaces between substructures, the energy flow is partly reflected and partly transmitted. The corresponding power flow reflec-tion/transmission coefficients have also been derived. Numerical simulations are performed by nodal or spectral discontinuous Galerkin (DG) methods 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.
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Yves Le Guennec, Eric Savin. TRANSIENT DYNAMICS OF THREE-DIMENSIONAL BEAM TRUSSES USING HIGHER ORDER KINEMATICS. Internoise 2012/ASME NCAD meeting, Aug 2012, NYC, United States. pp.3232, ⟨10.1121/1.4708056⟩. ⟨hal-01450649⟩

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