Scattering of Circular Cavity in Right-Angular Planar Space to Steady SH-Wave
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摘要: 利用复变函数方法和多极坐标移动技术，研究了直角平面内圆孔在直边分布有反平面稳态载荷时的SH波散射问题．首先构造出直角平面内不含有圆孔时满足边界应力条件的Green函数解；其次提出直角平面内存在圆孔时满足边界应力自由条件的散射波解，并利用叠加原理写出问题的位移总波场．借助于多极坐标移动技术和圆孔边界处应力自由条件,列出求解散射波解中未知系数的无穷代数方程组，在满足计算精度的前提下，通过有限项截断进行求解．作为算例，具体讨论了圆孔边界处的环向动应力随不同波数、圆孔位置及载荷分布位置和分布范围大小的变化情况，算例结果说明了算法的有效实用性．Abstract: Complex function method and multi-polar coordinate transformation technology are used here to study scattering of circular cavity in right-angular planar space to SH-wave with out-of-plane loading on the horizontal straight boundary. At first, Green function of right-angular planar space which has no circular cavity was constructed; then the scattering solution which satisfies the free stress conditions of the two right-angular boundaries with the circular cavity existing in the space was formulated, therefore, the total displacement field can be constructed using overlapping principle. An infinite algebraic equations of unknown coefficients existing in the scattering solution field can be gained using multi-polar coordinate and the free stress condition at the boundary of the circular cavity, it can be solved by using limit items in the infinite series which can give a high computation precision. An example was given to illustrate the variations of the tangential stress at the boundary of the circular cavity to different dimensionless wave numbers and the location of the circular cavity and the loading center and the distributing range of out-of-plane loading. The results of the example show the efficiency and the effectiveness of the method introduced here.
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