摘要
用多极坐标移动技术、格拉夫(Graf)加法公式和扩张原理研究含模糊波数直角平面内圆形弹性夹杂对稳态入射平面SH(shearing horizontal)波的模糊散射问题。首先利用直角平面两直角边界应力自由条件写出介质内的自由波场和散射波场;其次,利用圆形弹性夹杂边界处的应力和位移连续条件、傅里叶级数展开和Graf加法公式得到确定散射波函数中未知系数的无穷线性代数方程组。为了利用模糊波数的模糊信息,将模糊波数理解为模糊参数,将其支集等距划分,利用扩张原理通过确定性方法间接得到划分节点处的模糊波场值及其隶属度。实际计算表明,该算法收敛速度快,计算精度高,数值结果稳定,且能克服求解模糊波响应隶属度信息的困难。
Complex method and multi-coordinate transformation and Graf addition formula were used to study the fuzzy scattering problem of SH（ shearing horizontal） wave to the circular elastic inclusion in right-angle plane in which the wave number is fuzzy number. At first, the free wave functions of the complete right-angle plane in which no circular elastic inclusion exist and the scattering wave functions were given with the help of stress-free conditions on the two boundaries of right-angle plane. Then, the infinite linear algebraic equation systems of unknown coefficients appearing in the scattering functions were given with the help of the stress and displacement conditions on the boundary of the elastic circular inclusion and Fourier series expansion and Graf addition formula. In order to use the fuzzy information of the fuzzy wave number, the wave number was regarded as fuzzy parameter, its support was equal-divided, the expanding principle and the determinate method were used to obtain the fuzzy responses and their memberships. Practical computations show that the algebraic given here has a fast convergence speed and a high computation precision and a stable numerical results, it can overcome the difficulty in solving the fuzzy wave responses＇ memberships.
出处
《机械强度》
CAS
CSCD
北大核心
2012年第3期371-378,共8页
Journal of Mechanical Strength
基金
山东省科技攻关项目(2006GG3210001)
山东省自然科学基金(ZR2010AM002)资助~~
