【摘要】 将半空间表面假定为大半径的圆弧,运用波函数展开法,将入射波、半空间表面的反射波、衬砌外侧和半空间的散射波以及衬砌内的折射波的势函数展开成Fourier-Bessel函数的无穷级数形式,由Graf加法定理得到同一坐标系下的势函数的表达式.将半空间内圆形衬砌的散射问题转化为大圆弧和圆形衬砌的多重散射问题,根据衬砌外侧与周围的弹性介质之间应力和位移连续、衬砌内侧与半空间表面完全自由的边界条件,得到了散射问题中各势函数的待定复系数的理论解.通过数值计算,着重分析了平面P波垂直向上入射时,无量纲入射频率、衬砌埋藏深度、衬砌厚度等对衬砌内侧的动应力集中因子和半空间表面的归一化水平和竖向位移的影响.更多还原

【Abstract】 The semi-infinite surface is taken as a large curved arc,the potential functions of incident waves,reflected waves by the semi-infinite surface,scattered waves by the circular lining’s outer side and the curved arc,and refracted waves in the lining are all expanded to the infinite serials of Fourier-Bessel functions based on the expansion theory of wave functions,and then the single scattering problem of a lining in semi-infinite space is turned to a multiple scattering problem by the lining and the curved arc based on Graf’s addition theorem. According to the boundary conditions,which are that the stresses and displacements at the interface of the lining and adjacent elastic media are continuous and the surfaces of semi-infinite space and the inner side of the lining are free,the theoretical solutions of the complex coefficients of the potential functions are obtained,and the influences of the normalized incident frequency,lining depth and lining thickness on the normalized displacements of the semi-infinite space surface and the dynamic stress concentration factor of the lining’s inner side are studied by theoretical simulation when the P waves are incident vertically.更多还原