The refined theory of transversely isotropic piezoelectric rectangular beams
The refined theory of transversely isotropic piezoelectric rectangular beams
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DOI：
10.1007/s11433-006-0473-9
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发表时间：
2006-08
影响因子：
6.4
通讯作者：
Gao Yang;Wang Min-zhong
中科院分区：
文献类型：
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作者：
Gao Yang;Wang Min-zhong
研究了横观各向同性压电矩形梁的二维理论到一维理论的转化问题。本文在压电弹性理论的基础上，利用横观各向同性压电弹性理论的通解和Lur 'e方法，导出了压电梁的精化理论。基于压电梁的精细理论，推导了无横向表面载荷作用下压电梁的精确方程，该方程由两个控制微分方程组成：四阶方程和超越方程。梁在横向荷载作用下的近似方程直接从精化梁理论导出。作为一种特殊情况，横观各向同性弹性梁的控制微分方程由压电梁的相应方程得到。为了说明梁理论的应用，均布载荷和简支压电梁进行了检查。
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 withoutad hocassumptions. 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.