KINETIC MODELS OF ELASTIC WAVES IN BOUNDED MEDIA WITH APPLICATIONS IN ENGINEERING MECHANICS

In this talk we will present some recent developments concerning the mathematical modeling and numerical simulations of the transient dynamics of engineering structures, based on the semiclassical analysis of high-frequency (HF) solutions of wave systems. The transport and/or radiative transfer models we consider are constructed adopting a kinetic point of view of wave propagation phenomena in heterogeneous and/or random media excited by impulse loads. They describe the asymptotic evolution properties of the underlying kinetic and strain energy densities in the HF limit usually adopted in ray methods. We have extended the existing results for isotropic elastic media to fully anisotropic elastic media, as well as to slender structures with due consideration of the boundary conditions pertaining to the energy ?uxes at the interfaces. Numerical simulations of the HF regime are performed using Monte-Carlo methods and higher order nodal/spectral discontinuous ”Galerkin” ?nite element methods. The concurrence of the proposed framework with the classical engineering approach will be illustrated by several examples.