Three dimensional wave propagation in time-varying materials: A mathematical model based on the weak solutions of continuity in the moving property interface
Three dimensional wave propagation in time-varying materials: A mathematical model based on the weak solutions of continuity in the moving property interface
复制标题
时变材料中的三维波传播：基于运动属性界面连续性弱解的数学模型
DOI：
10.1016/j.apm.2017.03.052
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发表时间：
2017
影响因子：
5
通讯作者：
Chen Xi
中科院分区：
文献类型：
--
作者：
Shui Langquan;Liu Yilun;Chen Xi
本文研究了弹性波在时变材料中通过运动特性界面（MPI）的传播。首先，给出了时变材料中MPI的一般描述。然后，系统地研究了弹性波在MPI中的传播。一般情况下，通过MPI的波传播行为可以分为两种类型取决于MPI的移动速度和入射角。对于第一种情况，它具有类似于静态界面中的波传播特性，即反射波和折射波可以由MPI中的位移和应力连续性来确定。而对于第二种类型，它可以具有两个透射波，或者只有一个透射波或一个反射波。因此，由于过约束或欠约束问题，透射波或反射波不能用通常使用的连续条件，即MPI中的位移和应力连续性来求解。为了处理波在MPI中的传播，基于MPI中的弱连续形式，提出了一种新的数学模型。结果表明，波的传播系数不仅与波阻抗比和入射角有关，而且与MPI的运动速度有关。此外，MPI的移动速度对透射波和反射波的频率和波长也有显著的影响。当MPI赶上或超过反射波或透射波时，反射波或透射波的波长退化为零，从而在MPI中发现冲击波，MPI两侧的位移是不连续的。通过COMSOL Multiphysics软件进一步模拟了MPI中的波传播行为，结果与理论预测非常吻合。此外，还讨论了MPI中SH波的能量平衡。研究表明，本文提出的新的数学模型适用于高维动边界波动现象，能够研究复杂的波动方程，特别是动边界波动方程。
In this work, the elastic wave propagation through the moving property interface (MPI) in time-varying materials has been investigated. First, a general description of the MPI in time-varying materials has been given. Then, the elastic wave propagation through MPI has been systematically explored. In general, the wave propagation behaviors through MPI can be divided into two types depending on moving velocity of MPI and incident angle. For the first type, it has similar wave propagation behavior of that in static property interface, that is the reflection and refraction waves can be determined by the displacement and stress continuity in MPI. While, for the second type, it may have two transmitted waves, or only one transmitted wave or one reflected wave. Therefore, the transmitted waves or reflected wave cannot be solved by the commonly used continuous conditions, i.e. the displacement and stress continuities in MPI, due to the over constrained or under constrained problem. In order to deal with the wave propagation through MPI, a novel mathematical model is proposed based on the weak form of continuity in MPI. The results have shown that the wave propagation coefficients depend on not only the wave impedance radio and incident angle, but also the moving velocity of MPI. Besides, the transmitted and reflected wave frequencies and wavelengths are also significantly influenced by the moving velocity of MPI. When MPI catches up or exceeds the reflected or transmitted waves, the wavelength of the reflected or transmitted waves degenerates to zero, so that a shock wave is found in MPI and the displacements at the two sides of MPI are discontinuous. The wave propagation behaviors across MPI are further simulated via COMSOL Multiphysics software which shows very good agreement with the theoretical predictions. Moreover, the energy balance of SH waves in MPI is discussed. This work indicates that the novel mathematical model proposed in this paper is applicable to high dimensional wave phenomenon with moving boundaries, and is capable for studying complex wave equations, especially for wave equations with moving boundaries.