层状弹性半空间轴对称动力问题的奇异解

本文利用Laplace-Hankel联合变换及传播矩阵技术导出了任意层数的层状弹性半空间轴对称动力问题时域奇异解的一般解析表达式,并给出了奇异解数值化实施的计算方法。文末的实例计算表明了本文给出解答的正确性以及数值化实施的可靠性,从而为进一步用边界元法直接解决由于层状介质而引起的非匀质动力问题开拓了一条潜在的途径。

SINGULAR SOLUTIONS OF AXISYMMETRIC ELASTODYNAMIC PROBLEM FOR MULTILAYERED HALFSPACE

In the paper, the singular solutions of axisymmetric elastodynamic problem for the multilayered halfspace due to unit dynamic load acting within layered media are derived in time domain with the aid of Laplace-Hankel mixed transforms and transfer matrix method. A numerical computation of these solurions is also proposed using a fast Hankel transform algorithm. Two examples show that the solutions can be readily evaluated and the numerical results have considerably high precision. The presented solutions can be directly applied to determine the transient waves caused by seismic sources and show the potential application to problems of elastodynamics solved by boundary integral method.