Wave chaos in acoustics and elasticity
Wave chaos in acoustics and elasticity
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DOI：
10.1088/1751-8113/40/50/r01
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发表时间：
2007-11
期刊：
影响因子：
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通讯作者：
G. Tanner;N. Søndergaard
中科院分区：
文献类型：
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作者：
G. Tanner;N. Søndergaard
根据潜在的射线动力学解释波动现象为线性波动方程的分析增加了新的维度。一方面在光谱和波函数之间形成明确的联系，另一方面在相关射线动力学的性质之间形成明确的联系是一个相对较新的研究领域，特别是在弹性和声学领域。该理论确实主要是在量子背景下发展起来的。然而，越来越明显的是，重要的应用在于机械振动和声学领域。我们概述了这个新兴的波动混沌领域的基本概念。其范围从格林函数的射线近似到周期性轨道轨迹公式和随机矩阵理论，并总结了在声学中应用这些思想的最新技术——无论是从实验还是从理论/数值的角度。
Interpreting wave phenomena in terms of an underlying ray dynamics adds a new dimension to the analysis of linear wave equations. Forming explicit connections between spectra and wavefunctions on the one hand and the properties of a related ray dynamics on the other hand is a comparatively new research area, especially in elasticity and acoustics. The theory has indeed been developed primarily in a quantum context; it is increasingly becoming clear, however, that important applications lie in the field of mechanical vibrations and acoustics. We provide an overview over basic concepts in this emerging field of wave chaos. This ranges from ray approximations of the Green function to periodic orbit trace formulae and random matrix theory and summarizes the state of the art in applying these ideas in acoustics—both experimentally and from a theoretical/numerical point of view.