【摘要】 浅埋的管道或衬砌等结构物的地震响应问题,都可视为半空间内圆柱形壳体对地震波的散射问题.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SV波、半空间表面的反射波、圆柱形壳体外侧和半空间的散射波以及壳体内的折射波的势函数展开成Fourier-Bessel函数的无穷级数形式,假定壳体与周围弹性介质之间应力和位移连续,半空间表面和壳体内侧完全自由,得到了散射问题中各势函数的待定复系数的理论解.花岗岩中浅埋混凝土衬砌为算例,分析了入射频率、衬砌厚度对衬砌内侧动应力集中因子的影响,并对有无衬砌时围岩的动应力集中因子进行了对比.更多还原

【Abstract】 The half space surface was taken as a large curved arc,the potential functions of incident waves,reflected waves by the half surface,scattered waves by the outer side of the circular cylindrical shell and the curved arc,and refracted waves in the shell were 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 circular cylindrical shell in half space was turned to a multiple scattering problem by the shell and the curved arc based on Graf’s addition theorem.According to the boundary conditions,which were that the stresses and displacements at the interface of the shell and adjacent elastic media were continuous and the surfaces of half space and the inner side of the shell were free,and then the theoretical solutions of the complex coefficients of the potential functions were obtained.A circular concrete lining buried shallow in granite half space scattered by incident plane SV waves were taken as an example,the influence of incident frequency of SV waves and the thickness of the lining on the dynamic stress concentration factors of the inner side of the lining were studied,and the dynamic stress concentration factors of the granites were compared when their were lining or not.更多还原