一般各向异性单侧接触界面上波的反射和折射

研究简谐弹性波在一般各向异性介质单侧接触界面上的反射和折射问题．利用Fouier分析方法将非线性Coulomb摩擦接触边界波动问题化为一组代数方程．给出了确定局部分离、滑移和粘着区的思路和方法及各区域的解；讨论了出现界面局部分离和滑移的条件．对特定材料组合情况进行了详细数值计算，给出了界面力、相对滑移速度、张开位移、高频谐波的反射折射系数等特征参量；考察了平面和反平面波动的耦合及整体滑移等．其中关于高频谐波的结果可对已有实验结果给出很好的定性解释．在大多数情况下，即使对摩擦系数无穷大的粘滞接触界面，分离区端部也总是存在一个很小的滑移区。

REFLECTION AND REFRACTION OF ELASTIC WAVES AT A UNILATERAL CONTACT INTERFACE BETWEEN TWO GENERALLY ANISOTROPIC MEDIA

Reflection and refraction of harmonic elastic waves at a unilateral frictional contact interface is studied theoretically in this paper. The analysis is presented for generally anisotropic media but limited in the case of sub-critical angle incidence. The incident quasi-body wave is assumed strong enough such that the local separation and frictional slip may take place at the interface. Since the regions of the separation and slip are unknown as a part of the solution, the boundary value problem is indeed a nonlinear one. The displacements are expressed as Fourier series with all higher harmonics. Then Stroh formulism is used to derive the local relationship between interface tractions and relative velocities. Finally the considered nonlinear wave problem with unilateral Coulomb frictional boundaries is cast to a set of algebraic equations with simple form. Solutions in different zones are discussed. The conditions for the appearance of the local separation and slip on the interface are discussed. An iterative method is developed to determine the separation, slip and stick zones. Detailed computation is conducted for a particular material combination. The numerical results of the interface tractions, relative slip velocities, gap and reflection/refraction coefficients for lower- and higher-frequency wave modes are presented. The globe sliding and the coupling interaction between anti- and in-plane wave motions are examined. The results for harmonic generations can give qualitative explanation to some experiments. Moreover, it is found that there always exists a small slip zone connecting to the separation zone for most material combinations, even for the limiting case of unilateral adhesive contact interface with an infinite friction coefficient.