Polynomial Solutions to Piezoelectric Beams(Ⅱ)——Analytical Solutions to Typical Problems
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摘要: 从正交各向异性压电介质平面问题，对于材料3个特征根互不相等情况下，以3个拟调和位移函数表达位移、电势、应力和电位移的通解出发，利用调和多项式的显式表达式，结合试凑法，给出了平面压电梁的若干典型问题的解析解，包括悬臂压电梁自由端作用横向集中力和点电荷，悬臂压电梁表面作用线性电势和均布载荷，以及两端简支压电梁作用均布载荷等的解析解．Abstract: For the orthotropic piezoelectric plane problem,a series of piezoelectric beams is solved and the corresponding analytical solutions are obtained with the trial-and-error method on the basis of the general solution in the case of three distinct eigenvalues,in which all displacements,electrical potential,stresses and electrical displacements are expressed by three displacement functions in terms of harmonic polynomials.These problems are cantilever beam with cross force and point charge at free end,cantilever beam and simply-supported beam subjected to uniform loads on the upper and lower surfaces,and cantilever beam subjected to linear electrical potential.
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Key words:
- piezoelectric beam /
- plane problem /
- harmonic polynomial /
- analytical solution
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[1] 丁皓江，江爱民.压电梁的多项式解（Ⅰ）—若干精确解[J].应用数学和力学，2005，26(9)：1009—1015. [2] Timoshenko S P,Goodier J N.Theory of Elasticity[M].3rd Ed.New York:McGraw-Hill,1970. [3] Wang Q,Quek S T,Sun C T,et al.Analysis of piezoelectric coupled circular plate[J].Smart Materials and Structures,2001,10(2):229—239. doi: 10.1088/0964-1726/10/2/308 -
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