含双圆孔平板弹性波散射与动应力分析

DYNAMIC STRESS CONCENTRATIONS IN THIN PLATES WITH TWO CIRCULAR CUTOUTS 1)

利用复变量及局部坐标系方法，对平板中含双圆孔弹性波的衍射与动应力集中问题进行了研究，给出了不同方向入射弯曲波条件下该问题一般解的函数逼近序列和边界条件的表达式用正交函数展开的方法将待解的问题归结为对一组无穷代数方程组的求解给出了双圆孔附近的动应力集中系数的数值结果。

The problem of elastic wave motion and dynamic stress concentration in infinite plates, because of its technical importance, has been the subject of many investigators A number of analytic methods were established for the investigation of stress concentrations, among which, the method developed by N I Muskhelishvili is prominent The problem of static stress concentrations on the edge of an arbitrary cutout can be solved by Muskhelishvili’s method Scattering of flexural waves and dynamic stress concentrations in plates are different from static stress problem In 60s, Y H Pao investigated scattering of elastic waves and dynamic stress concentrations in thin plates from a circular cavity by using special function method and had given numerical results In this paper, based on the governing equation for flexural waves of thin plates, diffraction of elastic waves by two cutouts and dynamic stress concentrations in the plate have been studied in terms of the complex variable method and transformation of local coordinates With reduced order of the governing equations, Helmholtz type equations are obtained Thus the complex variable method and comformal mapping technique proposed by D K Liu can be used for solving diffraction of flexural waves by two cutouts The general solution of the plate bending problem to satisfy the boundary conditions on the contour of cutouts is obtained An analytic method to solve dynamic stress concentrations in the plate with two cutouts is established Using the orthogonal function expansion technique, the dynamic stress problem can be reduced to the solution of a set of infinite algebraic equations Computational formulas of dynamic stress concentration factors are developed As examples, numerical results for dynamic moment factors of plates with two circular cutouts are presented under different conditions and some discussions about influence of different parameters, for instance incident waves and structure parameters, on the dynamic stress concentration factors have been made