摘要
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固定圆形夹杂对稳态入射反平面剪切(shearinghorizontal,SH)波的散射问题。首先构造出介质内不存在夹杂时的入射波场和反射波场,然后建立介质内存在夹杂时由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,从而利用叠加原理写出介质内的总波场。利用夹杂边界处位移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二维直角平面水平边界点的位移幅度比和相位随量纲一波数、入射波入射角及夹杂位置的不同而变化的情况,结果表明了算法的有效实用性。
Complex function method and multi-polar coordinate and Fourier series expansion technology are used to study the scattering of fixed circular inclusion in right-angled plane to steady incident planar SH-wave. The incident wave and the reflection wave in the right-angled plane which has no circular inclusion are constructed; and the scattering solution excited by the boundary of the circular inclusion existing in the space, which satisfy the free stress conditions of the two right-angled boundaries are formulated, therefore, the total displacement field can be constructed using overlapping principle. An infinite algebraic equation of unknown coefficients appearing in the scattering wave solution field can be gained using multi-polar coordinate transformation and Fourier series expansion technology and the conditions of displacement at the boundary of the circular inclusion. 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 displacement ratio and the phase of the displacement on the horizontal boundary of the right-angled plane with the variations of dimensionless wave number and the incident angle and the location of the circular inclusion. The results of the example show the effectiveness and efficiency of the method introduced here.
出处
《爆炸与冲击》
EI
CAS
CSCD
北大核心
2007年第1期57-62,共6页
Explosion and Shock Waves
基金
烟台大学博士启动基金(JX03B5)
关键词
固体力学
固定圆形夹杂
复变函数法
稳态SH波散射
二维直角平面
多极坐标变换
solid mechanics
fixed circular inclusion
complex method
scattering of steady SH-wave
right-angled plane
multi-polar coordinate transformation
