二维直角平面内多个圆孔对稳态平面SH波的散射

Scattering of several circular cavities in right-angle planar space to steady incident planar SH-wave

利用复变函数法、多极坐标及傅立叶级数展开技术求解了二维直角平面内多个圆孔对稳态入射平面SH波的散射问题。首先构造出介质内不存在圆孔时的入射波场和反射波场;其次建立介质内存在圆孔时由圆孔边界产生的能够自动满足直角边应力自由条件的散射波解,从而利用叠加原理可写出介质内的总波场。利用圆孔边界处应力自由条件和傅立叶级数展开方法列出求解散射波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,得到相应有限代数方程组的解,最后通过算例具体讨论了介质中含有两个圆孔时其中一个圆孔边界处的动应力集中系数以及直角平面水平边界点的位移幅度比随无量纲波数、入射波入射角及两圆孔相互位置的不同而变化的情况,结果表明了本文算法的有效实用性。

Complex function method and multi-polar coodinate and Fourier series expansion technology are used here to study the scattering of several circular cavities in right-angle planar space to steady incident planar SH-wave. At first, the incident wave and the reflection wave in the right-angle planar space which has no circular cavity are constructed;then the scattering solution excited by the external boundary of the several circular cavities existing in the space,which satisfy the free stress conditions of two right-angle boundaries are 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 transformation and Fourier series expansion technology and the free stress conditions of the boundaries of the several circular cavities,it can be solved by using limit items in the infinite series which can give a high computation precision. An example is given to illustrate the variations of the tangential dynamic stress concentration factor at boundary of one circular cavity and the variations of displacement ratio and the phase of the displacement on the horizontal boundary of the right-angle planar space vs different dimensionless wave numbers and the incident angles and the locations of the circular cavities,the results of the example show the effectiveness and efficiency of the method introduced in this paper.