曲面曲率对Rayleigh波传播特性的影响

INFLUENCE OF CURVATURE ON THE PROPAGATION PROPERTIES OF RAYLEIGH WAVES ON CURVED SURFACES OF ARBITRARY FORM

对任意形状的均匀各向同性线弹性曲面物体,用 WKB～（1）方法求解了沿曲面传播的Rayleigh表面波的运动微分方程,同时考虑了波传播方向及其垂直方向曲面曲率对波的穿透性的影, 所获波动方程的势函数解答表明,在一般情况下垂直波传播方向的曲面曲率对波的穿透深度的影响是不容忽视的.进而以同种介质平面表面情况下的Rayleigh面波的传播特性为基准,给出了曲面曲率引起波数或波速变化的解析表达式.通过理论分析和数值算例,描述了曲面上Rayleigh面波传播行为的一些基本特征.

Surface waves possess the important practical property of propagating around a sufficiently smooth curved obstacle almost unhindered. This fact allows surface waves are applied to check industrial products of complicated shape while the usage of bulk waves give undesirable reflection that strongly distort the legitimate signals. Thus, the surface waves are commonly utilized to detect the surface cracks, surface hardness, thickness of the coatings and residual stress distribution etc. Meanwhile, the delay effect of surface wave propagation along curved surfaces can be applied do design delay lines in electro-acoustic devices. Properties of surface waves, mainly the Rayleigh waves, propagation along curved surfaces play important roles in seismology, acousto-electronics and other scientific fields. For the homogeneous isotropic linear elastic structures with curved surfaces of arbitrary form, the WKB method is applied to solve the motion differential equation of Rayleigh surface wave propagation along curved surfaces. Both the effects of the curvatures of curved surfaces which along and perpendicular to the propagation direction on the penetration property of waves are taken into account. The potential function solution of the wave equation obtained by our method indicate that the influence of the curvature perpendicular to the propagation direction of waves is not neglected in general case. The analytical expression of Rayleigh wave number or wave velocity vs. curvature of curved surfaces are obtained by setting the propagation properties of Rayleigh waves on plane surface as basis. Some basic characteristics of the Rayleigh surface wave propagation behavior along curved surfaces are described through theoretical analysis and numerical examples. The results obtained in our research also indicate the potential practical application of these properties in engineering.