含圆孔直角域压电介质的动力反平面特性

Dynamic anti-plane behavior for a quarter-infinite piezoelectric medium with a subsurface circular cavity

为了研究直角域附近缺陷对压电材料的动力学行为的影响,利用复变函数法及镜像法研究含界面附近圆孔的直角域压电介质的动应力集中问题,得到了直角域压电介质中圆形孔洞对时间谐和的反平面剪切波散射引起的动应力集中系数和电场强度集中系数的解析表达式,并给出了它们随入射波频率、材料的物理常数和结构几何参数变化的计算结果图.结果表明,在某些参数组合情况下,压电直角域界面附近圆孔边界动应力集中系数的最大值为半无限压电域界面附近圆孔的2～3倍,且电场强度集中系数在低频情况下非常大.对含缺陷直角域压电介质进行动力学分析非常必要.

In order to research the influence of the defect in the vicinity of right-angle space on the dynamic behavior of piezoelectric medium,the dynamic anti-plane behavior for a quarter-infinite piezoelectric medium with a subsurface circular cavity was theoretically investigated.Based on complex variables and mirror imaging methods,the expressions were obtained at the cavity＇s edge by a dynamic stress concentration factor（DSCF） and an electric field intensity concentration factor（EFICF） which were caused by the scattering of anti-plane shear waves.This scattering satisfied the boundary conditions on both the right-angle surface and the cavity＇s surface under time-harmonic anti-plane shearing.Some calculating cases were plotted as examples to show the frequencies of incident waves,the medium＇s parameters,and the structure＇s geometry influence on the DSCF and EFICF.The calculation results indicate that the maximum number of DSCFs possible in presently used methods is nearly two or three times those on a semi-infinite piezoelectric medium,and the EFICF was more significant at a lower frequency.Dynamic analysis is of importance to a quarter-infinite piezoelectric medium with subsurface defects.