基于表面阻抗张量的界面滑移波动态失稳分析

Analysis of Dynamic Instability of Interfacial SlipWaves Based on the Surface Impedance Tensor

基于Stroh公式和表面阻抗张量理论,提出了研究界面滑移波动态失稳问题的一种新的方法· 该方法将表面阻抗张量概念推广到复波速域,并将摩擦接触界面上的边界条件以表面阻抗张量表示· 最终将边值问题化归为求解一个复多项式在单位圆内的根· 以弹性半空间与刚体平面相对稳态摩擦滑移为例进行了详细的分析,导出了一个4次复特征方程并讨论了方程在单位圆内解的特性。

A new method relying on the Stroh formulism and the theory of the surface impedance tensor was developed to investigate the dynamic instability of interfacial slip waves.The concept of the surface impedance tensor was extended to the case where the wave speed is of a complex value,and the boundary conditions at the frictionally contacting interface were expressed by the surface impedance tensor.Then the boundary value problem was transformed to searching for zeroes of a complex polynomial in the unit circle.As an example,the steady frictional sliding of an elastic half-space in contact with a rigid flat surface was considered in details.A quartic complex characteristic equation was derived and its solution behavior in the unit circle was discussed.An explicit expression for the instabilility condition of the interfacial slip waves was presented.