【摘要】 利用复变函数法、多极坐标变换及傅里叶级数展开技术求解二维直角平面内偏心圆形衬砌对稳态入射平面SH(shearing horizontal)波的散射问题。首先构造出介质内不存在偏心圆形衬砌时的入射波场和反射波场;其次建立介质内存在偏心圆形衬砌时由衬砌外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和衬砌外边界向衬砌介质内的折射波解以及衬砌内边界的散射波解,从而利用叠加原理可写出衬砌介质内外的总波场。利用衬砌外边界处应力位移的连续条件和内边界处应力自由条件以及傅里叶级数展开方法列出求解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,得到相应有限代数方程组的解,最后通过算例具体讨论衬砌内边界处的动应力集中系数和水平直边界位移幅度比及其相位随无量纲波数、入射波入射角、衬砌位置及其偏心度的不同而变化的情况,结果表明文中算法的有效实用性。更多还原

【Abstract】 Complex function method and multi-polar coordinate and Fourier series expansion technology are used here to study the scattering of circular eccentric lining in right-angle plane space to steady incident plane SH-wave(shearing horizontal wave). At first, the scattering solution excited by the external boundary of the circular eccentric lining existing in the space, which satisfies the free stress conditions of the two right-angle boundaries and the refraction wave solution excited by the exterior boundary of the lining and the reflection wave solution excited by the interior boundary of the lining are formulated; then the incident wave and the reflection wave in the right-angle plane space which has no circular eccentric lining are constructed; therefore, the total displacement fields inside and outside the lining can be constructed using overlapping principle. An infinite algebraic equations of unknown coefficients existing in the scattering and refraction solution fields can be gained using multi-polar coordinate transformation and Fourier series expansion technology and the conditions of displacement/stress at the boundaries of the circular eccentric lining, 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 DSCF(dynamic stress concentration factor) at the interior boundary of the circular eccentric lining and the variations of displacement ratio and the phase of the displacement on the horizontal boundary of the right-angle plane space vs the variations of dimensionless wave number and the incident angle and the location and the eccentricity of the circular eccentric lining, the results of the example show the effectiveness and efficiency of the method introduced here.更多还原