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首页> 外文期刊>IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control >An asymptotic theory for vibrations of inhomogeneous/laminated piezoelectric plates
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An asymptotic theory for vibrations of inhomogeneous/laminated piezoelectric plates

机译：非均质/叠层压电板振动的渐近理论

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摘要

An asymptotic theory for the vibration analysis of inhomogeneous monoclinic piezoelectric plates is developed by using small parameter expansion. The theory includes the important special case of a laminated plate in which each layer is homogeneous and orthotropic, but distinct from the other layers by having a different material or a different orientation. A hierarchy of two-dimensional equations of the same homogeneous operator for each order is reduced from the three-dimensional framework of linear piezoelectricity. The elasticity version of the leading-order equation is the same as that of the classical Kirchhoff inhomogeneous plate theory and, therefore, is easily solvable. By contrast, it is not straightforward to find solutions of the higher-order equations. The solvability condition is thus established for this purpose, by which higher-order frequency parameters are derived. The present theoretical formulation is examined by comparing the present asymptotic results with an exact three-dimensional solution for a piezoelectric bimorph strip, and excellent agreement is reached. Some new results are presented.
机译：通过小参数展开，建立了非均质单斜压电板振动分析的渐近理论。该理论包括层压板的重要特殊情况，其中每一层都是均匀且正交各向异性的，但由于具有不同的材料或不同的方向而与其他层不同。从线性压电的三维框架中，减少了每个阶均相同的齐次算子的二维方程的层次。前导方程的弹性形式与经典基尔霍夫非均质板理论的弹性形式相同，因此很容易求解。相比之下，要找到高阶方程的解并不容易。因此为此目的建立了可溶性条件，通过该条件可导出高阶频率参数。通过将当前的渐近结果与压电双压电晶片带材的精确三维解进行比较，检验了本理论公式。提出了一些新结果。

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