Analytical Solution of a Simply Supported Piezoelectric Beam Subjected to a Uniformly-Distributed Loading
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摘要: 采用逆解法求解了均布荷载作用下压电材料简支梁的解析解。首先给出应力函数和电位移函数的多项式表达式,进而根据相容方程以及应力和电位移、位移和电势的边界条件,求得了同时考虑材料弹性参数、密度参数和压电参数呈梯度变化时,简支梁在均布荷载作用下的解析解。作为特例还得到了常体力以及材料参数为常数时的解答。并对结果进行了讨论。Abstract: Using the inverse method,the analytical solution of a simply supported piezoelcetric beam subjected to a uniformly distributed loading has been studied.First,the polynomials of stress function and induction function are given.Then,considering the gradient properties of the elastic parameter and the potential funciton as well as the piezoelectric parameter,the analytical solution of a simply supported beam subjected to a uniformly distributed loading is obtained and discussed.
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Key words:
- simply supported beam:FGM /
- analytical solution /
- piezoelectric material /
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[1] 陶宝祺.智能材料结构[M].北京:国防工业出版社,1997. [2] Wang Z K, Zheng B L. The general solution of three-dimensional problems in pizoelectric media[J].Int J Solids Structures, 1995,32(1): 105-115. [3] Ding H J, Chen B, Liang J. General solutions for coupled equations for piezoelectric media[J]. Int J Solids Structures, 1996,33(16) :2283-2298. [4] Wang B. Three-dimensional analysis of an ellipsoidal inclusion in a piezoelectric material [J]. Int J Solids and Structures, 1992,29(3) :293-308. [5] Ha S K,Keilers C, Chang F K. Finite element analysis of composite structures containing distributed piezoelectric sensors and actuators[J].AIAA J, 1992,30(3) :772-780. [6] Hwang W S, Park H C. Finite element modeling of piezoelectric sensors and actuators[J]. AIAA J,1993,31(5) :930-937. [7] Wang Q M, Cross L E. Tip deflection and blocking force of soft PZT-based cantilever rainbow actuators[J]. JAm Ceram Soc, 1999,82(1): 103-110. [8] Kruusing A. Analysis and optimization of loaded cantilever beam microactuators[J]. Smart Mater Struct,2000,9(2): 186-196. [9] Zhu X H, Wang Q, Meng Z Y. A functionally gradient piezoelectric actuator prepared by powder metallurgical process in PNN-PZ-PT system[J]. J Materials Science Letters,1995,14(3) :516-518. [10] 石志飞,黄彬彬,杜善义.功能材料力-电耦合问题的几个基本解[J].复合材料学报,2001,18(1):105-114. [11] SHI Zhi-fei. General solution of a density functionally gradient piezoelectric cantilever and its applications[J]. Smart Materials and Structures,2002,11(1): 122-129. [12] Wu C C M, Kahn M, Moy W. Piezoelectric Ceramics with functional gradients: A new application in material design[J]. JAm Ceram Soc, 1996,79(3) :809-812. [13] 林启荣,刘正兴,金占礼.均布荷载作用下两端简支梁的解析解[J].应用数学和力学,2000,21(6):617-623.
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