Diffusion regime for high-frequency vibrations of randomly heterogeneous structures.
The evolution of the high-frequency vibrational energy density of slender heterogeneous structures such as Timoshenko beams or thick shells is depicted by transport equations or radiative transfer equations (RTEs) in the presence of random heterogeneities. A diffusive regime arises when their correlation lengths are comparable to the wavelength, among other possible situations, and waves are multiply scattered. The purpose of this paper is to expound how diffusion approximations of the RTEs for elastic structures can be derived and to discuss the relevance of the vibrational conductivity analogy invoked in the structural acoustics literature. Its main contribution is the consideration of a heterogeneous background medium with varying parameters and the effects of polarization of elastic waves. The paper also outlines some of the remarkable features of the diffusive regime: depolarization of waves, energy equipartition, and asymptotic Fick's law.
Savin
Eric
E
Aeroelasticity and Structural Dynamics Department, ONERA, Châtillon cedex, France.
D000162:Acoustics; D003198:Computer Simulation; D004058:Diffusion; D004548:Elasticity; D007700:Kinetics; D008962:Models, Theoretical; D009991:Oscillometry; D014732:Vibration