Boundary conditions for the bending of a piezoelectric beam  

作　　者：GAO Yang1, XU SiPeng2 & ZHAO BaoSheng3 1 College of Science, China Agricultural University, Beijing 100083, China 2 College of Engineering, Ocean University of China, Qingdao 266071, China 3 School of Mechanical Engineering, University of Science and Technology Liaoning, Anshan 114044, China 

出　　处：《Science China(Physics,Mechanics & Astronomy)》2008年第7期847-856,共10页中国科学：物理学、力学、天文学（英文版）

基　　金：the National Natural Science Foundation of China (Grant Nos. 10702077, 10372003 and 10602001)

摘　　要：For beam bending in transversely isotropic piezoelectric media, the reciprocal theorem and the general solution of piezoelasticity are applied in a novel way to obtain the appropriate stress and mixed boundary conditions accurate to all orders for the beam of general edge geometry and loadings. By generalizing the method developed by Gregory and Wan, a set of necessary conditions on the edge-data for the existence of a rapidly decaying solution is established. The prescribed edge-data of the beam must satisfy these conditions in order that they could generate a decaying state within the beam. When stress and mixed conditions are imposed on the beam edge, these decaying state conditions for the case of bending deformation of piezoelectric beam are derived explicitly. They are then used for the correct formulation of boundary conditions for the beam theory solution (or the interior solution). Besides, an analytical solution of elastic beam is formulated to verify validity of our boundary conditions. For the stress data, our boundary conditions coincide with those obtained in conventional forms of beam theories. More importantly, the appropriate boundary conditions with two sets of mixed edge-data are obtained for the first time.For beam bending in transversely isotropic piezoelectric media, the reciprocal theorem and the general solution of piezoelasticity are applied in a novel way to obtain the appropriate stress and mixed boundary conditions accurate to all orders for the beam of general edge geometry and loadings. By generalizing the method developed by Gregory and Wan, a set of necessary conditions on the edge-data for the existence of a rapidly decaying solution is established. The prescribed edge-data of the beam must satisfy these conditions in order that they could generate a decaying state within the beam. When stress and mixed conditions are imposed on the beam edge, these decaying state conditions for the case of bending deformation of piezoelectric beam are derived explicitly. They are then used for the correct formulation of boundary conditions for the beam theory solution (or the interior solution). Besides, an analytical solution of elastic beam is formulated to verify validity of our boundary conditions. For the stress data, our boundary conditions coincide with those obtained in conventional forms of beam theories. More importantly, the appropriate boundary conditions with two sets of mixed edge-data are obtained for the first time.

关 键 词：BOUNDARY conditions beam BENDING PIEZOELECTRIC media decaying STATES REGULAR STATES 

分 类 号：O482[理学—固体物理]