| 自由端受集中力作用下压电悬臂梁弯曲问题解析解 |
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| 引用本文： | 杨德庆,刘正兴.自由端受集中力作用下压电悬臂梁弯曲问题解析解[J].上海力学,2003,24(3):327-333. |
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| 作者姓名： | 杨德庆 刘正兴 |
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| 作者单位： | [1]上海交通大学船舶与海洋工程学院，上海200030 [2]上海交通大学建筑工程与力学学院，上海200030 |
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| 基金项目： | 上海市博士后科研资助计划项目，国家自然科学基金(1013201) |
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| 摘 要： | 本文对由横观各向同性压电介质构成的悬臂梁，在自由端受集中力作用下的弯曲问题进行了研究。首先根据问题的特点，得到简化的线弹性压电悬臂梁的基本方程。然后根据正交各向异性材料悬臂梁应力分布特点，采用逆解法，建立了该问题的应力函数与电势分布函数，进而得到精确多项式解析解。该解析解形式简单，便于应用。文中对自由端受集中力的常规材料和压电材料悬臂梁的挠度也进行了比较。
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| 关 键 词： | 悬臂梁 压电 横观各向同性材料 逆解法 多项式解 |
| 修稿时间： | 2002年12月16 |
Analytical Solution for Bending of a Piezoelectric Cantilever Beam under an End Load |
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| YANG De-qing,LIU Zheng-xing.Analytical Solution for Bending of a Piezoelectric Cantilever Beam under an End Load[J].Chinese Quarterly Mechanics,2003,24(3):327-333. |
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| Authors: | YANG De-qing LIU Zheng-xing |
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| Abstract: | In this paper, the bending of transversely isotropic cantilever beam under an end load was investigated. The simplified linear elastic equations of piezoelectric cantiever beam were derived according to the characters of the problem. Using the inverse method, the stress function and the electric potential function were established, and then the analytical expressions of stress, electric displacement and electric potential were obtained in the form of polynomial. The present polynomial solutions are very simple and easy to be used than that of the solutions in Fourier series or in integration transformation. Finally the deflections at the free end are compared between the isotropic beam and the piezoelectric beam. |
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| Keywords: | cantilever beam piezoelectricity transversely isotropic material inverse method polynomial solution |
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