机电冲击荷载下狭长压电板双共线反平面裂纹的瞬态响应  

Transient response of a rallow long piezoelectric strip with bi-collinear antiplane cracks under the mechanical and electrical impact loadings

作　　者：刘志久[1] 李慧剑[2] 黎振兹[1] 黄尚安[1] 刘文胜[3] 杨慧[4] 

机构地区：[1]中南大学土木建筑学院 [2]燕山大学建筑工程与力学学院,河北秦皇岛066004 [3]中南大学粉末冶金研究所,湖南长沙410083 [4]中南大学资源与安全工程学院,湖南长沙410083

出　　处：《燕山大学学报》2007年第1期27-32,共6页Journal of Yanshan University

基　　金：国家自然科学基金(No.10272043)

摘　　要：对机电组合冲击荷载下狭长压电板双共线反平面裂纹的动态响应问题进行了分析。采用积分变换方法将一个电弹性混合边值问题化为奇异积分方程组,进一步利用Gauss-Chebyshev求积公式将其化为一组代数方程,求解这些代数方程并完成拉普拉斯逆变换,获得了裂纹顶端动应力和动电位移强度因子。结合压电陶瓷材料BaTO3,对动应力强度因子进行了数值计算。结果表明:无量纲动应力强度因子随时间T由零迅速增大,很快达到一个峰值,然后缓慢衰减:当T较大时,在其对应的静态值附近作微小振荡。裂纹两端动应力强度因子的峰值随比值b／h增大而增大,且稍右移。本文方法较常用的Fredholm积分方程方法,推导简便、易于数值计算。The dynamic response problem of the impermeable bi-collinear anti-plane cracks in a rallow long piezoelectric strip is analyzed under the action of combined mechanical and electrical impact loadings in this paper. The integral transform method is employed to reduce the electro-elastic mixed boundary value problem into singular integral equations. Furthermore, which is transformed into a system of linear algebraic equations by using Gauss-Chebyshev integral formula. This linear algebraic system is solved and the Laplace inverse transform are finished. The dynamic stress and dynamic electric displacement intensity factor of the bi-collinear crack tips are obtained. Numerical calculations of dynamic stress intensity factors (DSIF) for the piezoelectric material BaTiO3 is carried out. The numerical results show that the value of the normalized DSIF increases quickly from zero with time, reaches a peak value and then decreases slowly, finally oscillating around the corresponding static value when the time approach the large value. The peak value of the DSIF on the cracks tip will increase as the ratio b/h increases. In this paper the method of singular integral equations are used to solve bi-collinear cracks in a rallow long piezoelectric strip and compared with Fredholm integral equation method, the former method is to derive conveniently and easy to numerical calculated.

关 键 词：双共线裂纹 奇异积分方程 动应力强度因子 压电材料 

分 类 号：O346.1[理学—固体力学]