基于拉伸振动精确化理论求解含孔厚板弹性波散射问题

摘要

针对采用弹性力学平面问题求解波动／振动时常产生较大误差的问题，基于厚板拉伸振动精确化方程，采用复变函数方法对含孔平板中弹性波散射与动应力集中问题进行了研究。利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。给出了含椭圆孔厚板拉压弹性波散射与动应力集中的数值结果。研究结果表明：动应力集中系数与分布取决于入射波数、平板厚度、椭圆偏心率等无量纲化参数。%Based on longitudinal vibration equation of thick plates,using the complex functions and mapping method,elastic wave scattering and dynamic stress concentrations in thick plates with a hole were studied.Applying the orthogonal function expansion method,the problem to be solved was converted into solving a set of infinite algebraic equations.As an example,the numerical results for tension-compression elastic wave scattering and dynamic stress concentration factors in thick plates with an elliptic hole were computed.The results indicated that some parameters,such as,incident wave number,thickness of plates and elliptic eccentricity ratio have great effects on dynamic stress distributions and dynamic stress concentratuion factors of thick plates with a hole.