ABSTRACT
This paper deals with some recent developments for the modeling and numerical simulation of high-frequency (HF) vibrations of randomly heterogeneous slender structures. The mathematical model is derived from the semiclassical analysis of strongly oscillating (HF) solutions of quantum and classical wave systems, including acoustic, electromagnetic, or in the present case elastic waves. This theory shows that the associated phase-space energy density satisfies a radiative transfer equation in a random medium at length scales comparable to the small wavelength. The proposed model also considers energetic boundary and interface conditions consistent with the boundary and interface conditions imposed to the solutions of the wave system. They are given in the form of power flow reflection/transmission operators for the energy rays impinging on a boundary or an interface. Specular-like transverse boundary reflections, diffuse reflections, or fluid-structure coupling may be treated as a particular case of the proposed model. Nodal/spectral discontinuous `Galerkin' finite element methods and Monte-Carlo methods are implemented to integrate the radiative transfer equations with such boundary and interface conditions. Some numerical simulations are presented to illustrate the theory: the first one deals with an assembly of random thick beams, and the second one with an assembly of random thick shells. This research applies to the prediction of the linear transient responses of complex structures to impact loads or shocks, or the analysis of non-destructive evaluation techniques.
Keywords: High-frequency, Vibration, Radiative transfer, Discontinuous finite elements, Monte-Carlo method.
