广义压电动态■积分的守恒性及其应用  

The independent of the generalized piezoelectric dynamic ■ integral and its application

作　　者：黄尚安[1] 刘志久[1] 刘文胜[2] 杨慧[3] 黎振兹[1] 

机构地区：[1]中南大学土木建筑学院,湖南长沙410083 [2]中南大学粉末冶金国家重点实验室,湖南长沙410083 [3]中南大学资源与安全工程学院,湖南长沙410083

出　　处：《中南大学学报（自然科学版）》2005年第6期1084-1088,共5页Journal of Central South University:Science and Technology

基　　金：国家自然科学基金资助项目(10272043)

摘　　要：在裂纹绝缘与应力自由的条件下,证明了考虑压电效应与惯性效应的广义压电动态■积分与围道Γ的选择无关,这一特性称为广义压电动态■积分的守恒性。若所有电场量为零,广义压电动态■积分变为断裂动力学中的■积分。在线弹性情况下,导出了压电动态■积分与KⅢ(t)的关系。以压电陶瓷(BaTiO3)板中央有限裂纹对入射反平面剪切谐波的散射为例,给出了规范化动应力强度因子K-Ⅲ(t)随规范化圆频率-ω的变化曲线。研究结果表明在该曲线上存在峰值与谷值;当ω-→1时,(K-Ⅲ)max=1.372,该峰值比其相应的静态值高27%,因此,惯性效应不能忽略;当-ω→3时,(K-Ⅲ)min=0.247;当ω-→0时,K-Ⅲ→1,即动应力强度因子趋近于相应的静态值。The generalized piezoelectric dynamic J^ is unaffected by the selection of contour, if the surface of the crack. Therefore, the generalized integral including piezoelectric and inertia effects conditions σinnj=0, Djnj=0 are satisfied on the piezoelectric dynamic J^ integral equation can be called the path-independent of the generalized piezoelectric dynamic J^ integral of the contour Γ. If all the electrical field quantities are made to vanish, then equation （1） reduces to the dynamic J- integral of fracture mechanics. For example, the scattering of an incident anti-plane shear wave by a finite crack in an infinite piezoelectric ceramics （BaTiO3） plate is studied. The curve of variation of normalized DSIF K^-Ⅲ against normalized circular frequency ω^- is plotted. The results show that the curve of variation of K^-Ⅲ against ω^- has peak value and minimum value. As ω^-→1, （K^Ⅲ）max =1. 372. This peak value （K^-Ⅲ）max is about 27% larger than corresponding static value. Therefore, inertia effect cannot be omitted. As ω^-→3, （K^-Ⅲ）min=0. 247. As ω^-→0, K^-Ⅲ→1. This is to say, the mode-Ⅲ dynamic stress intensity factor approaches to corresponding static value.

关 键 词：动态J^积分 守恒性 反平面剪切波散射 动应力强度因子 

分 类 号：O346.1[理学—固体力学]