An analytical solution for the transient response of a semi-infinite elastic medium with a buried arbitrary cylindrical line source
An analytical solution for the transient response of a semi-infinite elastic medium with a buried arbitrary cylindrical line source
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DOI：
10.1016/j.ijsolstr.2016.09.012
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发表时间：
2016-12
影响因子：
3.6
通讯作者：
Zhendong Shan;D. Ling
中科院分区：
文献类型：
--
作者：
Zhendong Shan;D. Ling
本文应用拉普拉斯变换和Cagniard方法，给出了半无限介质在埋深一定的任意圆柱形线源作用下的瞬态响应的解析解。解析解以简单的封闭形式给出，每一项代表一个瞬态物理波。在求解过程中，首先将任意源脉冲分解为纵波（P）和切向波（S），然后分别导出P和S脉冲源在拉普拉斯域的解析解。应用Cagniard逆拉普拉斯变换方法和卷积定理，得到了时域解析解。最后，任意源脉冲的解析解可以表示为P和S脉冲源解的叠加。数值算例说明了柱面P波和S波在半无限自由面介质中传播的一些有趣的特征。在半无限介质中，由于S脉冲的作用，在一定区域内可以观察到首波，这是P脉冲问题中所没有的。
This study develops an analytical solution for the transient response of a semi-infinite medium subjected to an arbitrary cylindrical line source buried at a certain depth by using the Laplace transform and Cagniard's method. The analytical solution is presented in a simple closed form and each term represents a transient physical wave. During the solution procedure, the arbitrary source pulse is first decomposed into a compressional wave (P) and a tangential wave (S), and then analytical solutions in the Laplace domain for the P and S pulse sources are derived. By applying Cagniard's inverse Laplace transform method and the convolution theorem, analytical solutions in the time domain are obtained. Finally, the analytical solution for arbitrary source pulse can be expressed as the superposition of the solutions for the P and S pulse sources. Numerical examples are provided to illustrate some interesting features of the cylindrical P and S wave propagation in a semi-infinite media with a free surface. A head wave can be observed in a certain area of the semi-infinite media due to the S pulse, which is not found in the P pulse problem.