Savin Eric
Aeroelasticity and Structural Dynamics Department, ONERA, Châtillon cedex, France.
J Acoust Soc Am. 2008 Dec;124(6):3507-20. doi: 10.1121/1.3003088.
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.
在存在随机不均匀性的情况下，诸如铁木辛柯梁或厚壳等细长非均匀结构的高频振动能量密度的演化由输运方程或辐射传输方程（RTE）描述。在其相关长度与波长可比等其他可能情况中，当波发生多次散射时，就会出现扩散 regime。本文的目的是阐述如何推导弹性结构RTE的扩散近似，并讨论结构声学文献中所引用的振动电导率类比的相关性。其主要贡献在于考虑了具有变化参数的非均匀背景介质以及弹性波的极化效应。本文还概述了扩散 regime的一些显著特征：波的去极化、能量均分和渐近菲克定律。
