含衬砌孔洞的凸起的垂直入射SH波的动力分析

采用复变函数法，求解半无限空间中含圆形衬砌孔洞的半圆形凸起对稳态SH波的散射问题，给出在一定边界条件下的SH波散射的动力分析的解析方法．利用介质与衬砌结构在交界处应力、位移的连续性，构造一个可以自动满足凸起边界上应力边界条件的圆域对SH波散射的波函数．再利用波函数将圆域与半圆形凹陷半空间的“公共边界”进行“契合”，并对该问题进行求解．给出了当稳态SH波垂直入射时2种无量纲参数下的算例分析，讨论了波数与衬砌厚度变化对动应力集中的影响．介质和衬砌内动应力集中系数随孔径、衬砌厚度、波数变化而变化，且与衬砌性质有关．

Dynamic Analysis of Upright Incidence of SH-Waves at Semi-Cylindrical Interface with a Circular Lining Structure

The scattering of harmonic SH-waves at semi-cylindrical interface with a circular lining structure is studied. Complex function method is employed to find out the expressions of dynamic analysis under certain boundary conditions. The coefficients depend on the continuity of stress and displacement between medium and lining structure. A wave function of SH-waves can be constructed by these coefficients which satisfy the stress boundary condition at bulge boundary in circular field. Then the circular field corresponds with semi-circular space in the common boundary using the wave function. Numerical computations are performed for upright incidence of harmonic SH-waves, and variations of the coefficients of dynamic stress concentration with the frequency parameter and thickness of lining are depicted graphically at different values of two types of lining parame- ters. Coefficients of dynamic stress concentration change with lining aperture, thickness of lining, wave number and type of lining.