多层压电材料层合板的精确解  

Exact Solution for Laminated Piezoelectric Plates

作　　者：梅甫良[1] 曾德顺[2] 

机构地区：[1]石油大学(华东)建筑系,山东东营257061 [2]同济大学特种土木工程技术研究所,上海200092

出　　处：《力学季刊》2002年第3期386-391,共6页Chinese Quarterly of Mechanics

摘　　要：抛弃有关位移和应力的所有假设,直接从三维弹性力学理论和静电学理论,先导出了正交各向异性压电材料板的状态方程,由此得到四边简支压电材料板的状态方程,再根据矩阵分析理论,建立了单层压电材料板的上下表面状态量之间的关系,进一步建立了多层压电板上、下表面状态量之间关系式,利用上下表面已知状态量,得到上表面未知状态量的求解方程组。通过求解方程组,便得上表面未知状态量,最终可以得到任意位置处状态量。最后,同时给出了四边简支、两层不同压电材料组成、不同纵横比的层合板受正弦分布载荷作用下的精确解,其结果与现有解比较,吻合较好。In our treatise, the state transfer matrix for a layer piezoelectric plate was deduced directly from three dimensional elasticity mechanics and static electrics giving up all the assumptions with respect to displacements and stresses. On this basis, the state equation for a simple supported piezoelectric plate was obtained. A relation equation between the top and bottom state quantities for a layer piezoelectiric plate, as well as a laminated piezoelectric plate, was established according to matrix analysis theory. A set of equations to find the top surface unknown state quantities was obtained by utilizing the top and bottom surface known quantities. And then the top surface unknowns were got through solving the set of equations, and the other state quantities at anywhere were also obtained. At last, the exact solution of simple-supported laminated piezoelectric plate under sinusoid load was presented.

关 键 词：压电材料 层合板 精确解 三维弹性理论 状态转移阵 

分 类 号：TM22[一般工业技术—材料科学与工程]