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首页> 外文期刊>Science in China. Series G, Physics, Mechanics & Astronomy >The refined theory of transversely isotropic piezoelectric rectangular beams
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The refined theory of transversely isotropic piezoelectric rectangular beams

机译：横观各向同性压电矩形梁的改进理论

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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.
机译：研究了横观各向同性的压电矩形梁从二维理论推导一维理论的问题。基于压电弹性理论，利用横观各向同性压电弹性和Lur'e方法的一般解，无需特殊假设，即可得出压电梁的精细理论。基于压电梁的精细理论，推导了无横向载荷的梁的精确方程，该方程由两个控制微分方程组成：四阶方程和超越方程。横向荷载作用下的梁的近似方程式是直接从精细梁理论中得出的。作为一种特殊情况，可以从压电梁的相应方程获得横向各向同性弹性梁的控制微分方程。为了说明所开发的梁理论的应用，研究了均匀加载且简单支撑的压电梁。

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