【摘要】 利用保角变换和多极坐标移动技术,求解四分之一空间内含有椭圆孔时椭圆孔对入射平面SH(shearing hori-zontal)波的稳态散射问题。首先利用四分之一空间两垂直边界处的应力自由条件,写出不含椭圆孔时空间介质内的反射波场;其次,通过保角映射技术考虑空间介质内含有任意主轴方向的椭圆孔时,由于椭圆孔对入射和反射波场的散射作用而产生的散射波场,并预先使得该散射波场满足四分之一空间介质两垂直边界处的应力自由条件,利用叠加原理,将入射波场、反射波场和散射波场叠加起来,即可得到问题的总位移波场。最后借助于椭圆孔边界处的应力自由条件和傅里叶级数展开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将方程组进行有限项截断,得到一个有限线性方程组并求解。通过算例具体讨论四分之一空间内椭圆孔边界处的环向动应力集中系数随入射波入射角、无量纲波数、椭圆孔方位参数的变化情况。更多还原

【Abstract】 Conformal mapping technology and multi-coordinate transformation are used to solve the steady scattering problem of an elliptical cavity in a quarter of plane space to incident plane SH(shearing horizontal)-wave.First,the stress-free conditions at the boundaries of the space can be utilized to obtain the reflecting wave field which is traveling in the space in which there is no elliptic cavity.Then,the case of which there is an arbitrary elliptical cavity in the space is considered utilizing the conformal mapping technology,the scattering wave field of the elliptic cavity to the incident and reflection SH-wave can be constructed beforehand which can satisfy the stress-free conditions at the boundaries of the space.The incident wave field,reflection wave field and the scattering wave field are overlapped to obtain the total displacement wave field.At last,the Fourier series expansion technology and the stress-free condition are used to obtain an in finite linear equations which contain the unknown coefficients included in the scattering wave field,and a limited linear equation group can be obtained using limited truncation under the satisfaction of the calculation precision and is solved.An example is given to illustrate the variations of the dynamic stress coefficient factor at the boundary of the elliptic cavity of the space vs different incident angle,different dimensionless wave numbers,different orientation parameters of the elliptical cavity.更多还原