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Geometrically nonlinear static and free vibration analysis of functionally graded piezoelectric plates

机译：功能梯度压电板的几何非线性静，自由振动分析

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摘要

In this paper, nonlinear static and free vibration analysis of functionally graded piezoelectric plates has been carried out using finite element method under different sets of mechanical and electrical loadings. The plate with functionally graded piezoelectric material (FGPM) is assumed to be graded through the thickness by a simple power law distribution in terms of the volume fractions of the constituents. Only the geometrical nonlinearity has been taken into account and electric potential is assumed to be quadratic across the FGPM plate thickness. The governing equations are obtained using potential energy and Hamilton's principle that includes elastic and piezoelectric effects. The finite element model is derived based on constitutive equation of piezoelectric material accounting for coupling between elasticity and electric effect using higher order plate elements. The present finite element is modeled with displacement components and electric potential as nodal degrees of freedom. Results are presented for two constituent FGPM plate under different mechanical boundary conditions. Numerical results for PZT-4/ PZT-5H plate are given in dimensionless graphical forms. Effects of material composition and boundary conditions on nonlinear response are also studied. The numerical results obtained by the present model are in good agreement with the available solutions reported in the literature.
机译：本文采用有限元方法，在不同的机械和电气载荷作用下，对功能梯度压电板进行了静态和自由振动的非线性分析。假定具有功能梯度压电材料（FGPM）的板通过简单的幂定律分布按照厚度按组分的体积分数进行分级。仅考虑了几何非线性，并且假定电势在FGPM板厚度上为二次方。使用势能和汉密尔顿原理（包括弹性和压电效应）获得控制方程。基于压电材料的本构方程导出有限元模型，该方程考虑了使用高阶板单元的弹性和电效应之间的耦合。用位移分量和电势作为节点自由度对当前有限元建模。给出了两种在不同机械边界条件下组成的FGPM板的结果。 PZT-4 / PZT-5H平板的数值结果以无量纲图形形式给出。还研究了材料成分和边界条件对非线性响应的影响。通过本模型获得的数值结果与文献中报道的可用解决方案非常吻合。

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