【摘要】 利用复变函数法、多极坐标及傅里叶级数展开技术求解了二维直角平面介质边界固定半圆形夹杂对稳态入射平面SH波的散射问题。首先构造出介质边界处不存在固定半圆形夹杂时的入射波场和反射波场;其次建立介质边界处存在固定半圆形夹杂时夹杂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。利用夹杂边界处位移条件和傅里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二维直角平面水平边界点的位移幅度比和相位随无量纲波数、入射波入射角、及夹杂位置的不同而变化的情况,结果表明了该算法的有效实用性。更多还原

【Abstract】 Complex function method,multi-polar coordinate and Fourier series expansion technology are used here to study scattering of fixed half circular inclusion located at horizontal boundary of a right-angular planar space to steady incident planar SH-wave.At first,incident wave and reflection wave in the right-angular planar space which has no circular inclusion are constructed;then the scattering solution excited by the boundary of the fixed circular half inclusion,which satisfies the free stress conditions of the two right-angle boundaries,is formulated.Therefore,the total displacement field can be constructed using superposition principle.An infinite set of algebraic equations of unknown coefficients appearing in the scattering wave solution field can be gained using multi-polar coordinate transformation,Fourier series expansion technology and the conditions of displacement at the boundary of the fixed half circular inclusion.It can be solved by using limit terms in the infinite series which can give a high computation precision.An example is given to illustrate the variations of the displacement ratio and the phase of the displacement on the horizontal boundary of the right-angle planar space vs the variations of dimensionless wave numbers and the incident angles and the different locations of the fixed half circular inclusion.The example results show the effectiveness and feasibility of the method proposed.更多还原