含双圆孔 Mindlin 板弹性波散射与动应力集中

摘要

Based on Mindlin's theory of plates,elastic wave scattering and dynamic stress concentrations in plates with two circular cutouts were studied by using the wave function expansion method and local coordinate system. Numerical results of dynamic moment concentration factors around the cutouts were obtained by setting different parameters and the influence of the parameters on dynamic moment distributions were discussed.It is shown that unlike single-cutout situation,the complex changes take place on dynamic moment concentration factors at two-cutout situation due to the interaction between two openings.Sometimes the dynamic moment was increased,or sometimes the one was reduced.When the plate is thicker at the high-frequency,the opening spacing of the non-significant influence is larger.Therefore,in the dynamic design the comprehensive dynamic stress analysis would be done instead of directly applying the static standard and code for the structure design.%基于 Mindlin 平板理论，采用波函数展开法和局部坐标系方法，对含双圆孔平板结构中弹性波散射与动应力集中问题进行了研究。文中对 Mindlin 板含双圆孔时的开孔动弯矩集中系数做了数值计算，并分析了开孔间距对动弯矩分布的影响。结果表明：与单圆孔情况相比，由于开孔之间的相互影响，双圆孔间的动弯矩分布会发生比较复杂的变化。孔间距相互作用有时会使动应力集中得到缓解，而有时会使动应力集中加剧。在低频和平板较薄的情况下，平板开孔动弯矩互不影响间距较小；在较高频率和平板较厚的情况下，平板开孔动弯矩互不影响间距较大。所有这些现象都与入射波波长与孔径等特征尺度有关。因此，在工程结构动力学分析与强度设计中，应对不同波长和特征尺度下的动应力作具体的分析计算，而不是简单地套用静载强度设计标准或规范。