运动振源作用下各向异性弹性介质平面问题的基本解
Fundamental Solutions in Plane Problem for Anisotropic Elastic Medium Under Moving Oscillating Source
摘要：
本文研究了在无界均匀各向异性弹性二维介质中作匀速运动并以周期频率振荡的集中点力问题。本文描述了二维问题在运动坐标系中平面波的性质及其相位、慢度、射线速度曲线和群速度曲线。利用Fourier积分变换技术，建立了平面波的性质，得到了各种源运动的弹性动力学Green张量在有限区间上的积分之和的显式表达式。提取了格林张量的动态分量。应用稳相法导出了远场波场的渐近近似。给出了运动观测器和固定观测器的坡印亭能流矢量的简单公式。值得注意的是，在远区中，柱面波在运动学和能量下被分离。结果表明，运动会引起远场特性的变化。它们是波传播带及其数目的改变，在跨震和超震运动下出现的快波和慢波等。
英文摘要：
In present article we consider the problems of concentrated point force which is moving with constant velocity and oscillating with cyclic frequency in unbounded homogeneous anisotropic elastic two-dimensional medium. The properties of plane waves and their phase, slowness and ray or group velocity curves for 2D problem in moving coordinate system are described. By using the Fourier integral transform techniques and established the properties of the plane waves, the explicit representation of the elastodynamic Green's tensor is obtained for all types of source motion as a sum of the integrals over the finite interval. The dynamic components of the Green's tensor are extracted. The stationary phase method is applied to derive an asymptotic approximation of the far wave field. The simple formulae for Poynting energy flux vectors for moving and fixed observers are presented too. It is noted that in the far zones the cylindrical waves are separated under kinematics and energy. It is shown that the motion bring some differences in the far field properties. They are modification of the wave propagation zones and their number, fast and slow waves appearance under trans- and superseismic motion and so on.
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