The refined theory of transversely isotropic piezoelectric rectangular beams  

作　　者：GAO Yang1 & WANG Minzhong2 1. College of Science, China Agricultural University, Beijing 100083, China 2. State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Engi- neering Science, Peking University, Beijing 100871, China 

出　　处：《Science China(Physics,Mechanics & Astronomy)》2006年第4期473-486,共14页中国科学：物理学、力学、天文学（英文版）

基　　金：Support from the National Natural Science Foundation of China (Grant No.10372003) is acknowledged.

摘　　要：The problem of deducing one-dimensional theory from two-dimensional theory for a transversely isotropic piezoelectric rectangular beam is investigated. Based on the piezoelasticity theory, the refined theory of piezoelectric beams is derived by using the general solution of transversely isotropic piezoelasticity and Lur'e method without ad hoc assumptions. Based on the refined theory of piezoelectric beams, the exact equations for the beams without transverse surface loadings are derived, which consist of two governing differential equations: the fourth-order equation and the transcendental equation. The approximate equations for the beams under transverse loadings are derived directly from the refined beam theory. As a special case, the governing differential equations for transversely isotropic elastic beams are obtained from the corresponding equations of piezoelectric beams. To illustrate the application of the beam theory developed, a uniformly loaded and simply supported piezoelectric beam is examined.The problem of deducing one-dimensional theory from two-dimensional theory for a transversely isotropic piezoelectric rectangular beam is investigated. Based on the piezoelasticity theory, the refined theory of piezoelectric beams is derived by using the general solution of transversely isotropic piezoelasticity and Lur’e method without ad hoc assumptions. Based on the refined theory of piezoelectric beams, the exact equations for the beams without transverse surface loadings are derived, which consist of two governing differential equations: the fourth-order equation and the transcendental equation. The approximate equations for the beams under transverse loadings are derived directly from the refined beam theory. As a special case, the governing differential equations for transversely isotropic elastic beams are obtained from the corresponding equations of piezoelectric beams. To illustrate the application of the beam theory developed, a uniformly loaded and simply supported piezoelectric beam is examined.

关 键 词：RECTANGULAR beams  the refined theory  piezoelectric  transversely isotropic. 

分 类 号：O231[理学—运筹学与控制论]