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首页> 外文期刊>IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control >Governing equations for a piezoelectric plate with graded properties across the thickness
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Governing equations for a piezoelectric plate with graded properties across the thickness

机译：在整个厚度范围内具有渐变特性的压电板的控制方程

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摘要

Two-dimensional first-order governing equations for electroded piezoelectric crystal plates with general symmetry and thickness-graded material properties are deduced from the three-dimensional equations of linear piezoelectricity by Mindlin's general procedure of series expansion. Mechanical displacements and thickness-graded material properties, i.e., the elastic stiffnesses, piezoelectric coefficients, dielectric permittivities, and mass density, are expanded in powers of the thickness coordinate, while electric potential is expanded in a special series in order to accommodate the specified electric potentials at electroded faces of the plate. The effects of graded material properties on the piezoelectrically induced stresses or deformations by the applied surface potentials are clearly exhibited in these newly derived equations which reduce to Mindlin's first-order equations of elastic anisotropic plates when the material properties are homogeneous. Closed form solutions are obtained from the three-dimensional equations of piezoelectricity and from the present two-dimensional equations for both homogeneous plates and bimorphs of piezoelectric ceramics. Dispersion curves for homogeneous plates and bimorphs and resonance frequencies for bimorph strips with finite width are computed from the solutions of three-dimensional and two-dimensional equations. Comparison of the results shows that predictions from the two-dimensional equations are very close to those from the three-dimensional equations.
机译：根据Mindlin的级数展开一般程序，从线性压电的三维方程中推导了具有对称性和厚度梯度材料特性的带电压电晶体板的二维一阶控制方程。机械位移和厚度分级的材料特性（即弹性刚度，压电系数，介电常数和质量密度）以厚度坐标的幂扩展，而电势按特殊序列扩展以适应指定的电板的电极面上的电位。这些新推导的方程清楚地显示了梯度材料特性对施加的表面电势引起的压电感应应力或变形的影响，当材料特性均质时，这些方程简化为Mindlin的弹性各向异性板的一阶方程。从压电的三维方程和压电陶瓷的均质板和双压电晶片的当前二维方程，可以获得封闭形式的解。根据三维方程和二维方程的解，计算出均质板和双压电晶片的色散曲线以及双宽度有限的双压电晶片的共振频率。结果比较表明，二维方程的预测与三维方程的预测非常接近。

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