二维垂向梯度非均匀介质中弹性波传播特性

研究了二维弹性波在宏观非均匀介质中传播的问题。由于介质物理性质的非均匀性，弹性波在该介质中的传播需用包含介质物理性质的空间导数的非均匀介质波动方程来描述。采用有限元法求解波动方程，重点研究和讨论了物理性质垂向梯度渐变的非均匀介质中弹性波的传播特点。结果显示：波速在垂向上的对称的递增或递减引起平面弹性波的会聚或发散；若波速在垂向上满足双曲余割分布，则弹性波可以在对称轴上周期性聚焦。
The propagation problem of two-dimensional elastic wave in macroscopical inhomogeneous medium was analyzed. As the physical properties of medium are variable with space, the elastic wave propagation in this medium should be described by a set of inhomogeneous wave equations which conclude the space derivatives of the medium properties. By solving the inhomogeneous wave equations with finite element method, the elastic wave propagation characteristics in inhomogeneous medium whose physical properties vary with vertical gradients were studied and discussed. Results show that the planar elastic wave converges or diverges respectively when the wave velocity ascends or descends symmetrically in the vertical direction. Moreover, when the profile of the wave velocity is arc-hyperbolic secant, the planar elastic wave focuses periodically on the symmetric axis.