针对功能梯度多孔磁电弹（Functional graded porous magneto electro elastic, FGP-MEE）板结构，本文基于等几何分析法（Isogeometric analysis, IGA），采用一阶剪切变形理论（First-order shear deformation theory, FSDT）建立了等几何数值分析模型。首先，根据修正幂律（Modified power law, MPL）方法得到了具有四种不同孔隙分布形式（Vu，Vo，Vx，Vv）功能梯度多孔磁电弹结构的等效材料参数；然后，利用磁-电-弹耦合本构方程、哈密顿变分原理以及等几何分析方法推导了FGP-MEE板的控制方程，并通过与已有文献对比，验证了所建模型的有效性和准确性；最后，研究了孔隙系数、功能梯度指数、孔隙分布形式、结构的几何参数（宽厚比、长宽比）以及边界条件对FGP-MEE板自由振动的影响。研究结果表明：材料中孔隙分布形式、孔隙系数以及功能梯度指数的变化对FGP-MEE板的固有频率有较大影响，且在孔隙呈Vo型分布时板的固有频率最大。
Abstract
Based on Isogeometric analysis (IGA), an isogeometric numerical analysis model is established for functionally graded porous magneto electro elastic (FGP-MEE) plates by using the first-order shear deformation theory (FSDT). Firstly, according to the modified power law (MPL) method, the equivalent material properties of the FGP-MEE plate with four different porosity distribution types (Vu，Vo，Vx，Vv) are determined. Then, the governing equations of the FGP-MEE plate are derived by using the magneto-electro-elastic coupling constitutive equations, Hamilton variational principle and IGA methods, and the effectiveness and accuracy of the model are verified by comparing with the existing literatures. Finally, the effects of porosity coefficient, functional gradient index, porosity distribution types, geometrical parameters (width-to-thickness ratio, length-to-width ratio) and boundary conditions on the free vibration of the FGP-MEE plate are studied. The results show that the natural frequency of the plate is greatly affected by the porosity distribution types, porosity coefficient and functional gradient index, and the plate with porosity distribution Vo possesses the highest stiffness.
关键词
功能梯度多孔磁电弹板 /
等几何分析法 /
一阶剪切变形理论 /
自由振动
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Key words
functionally graded porous magneto electro elastic plate /
Isogeometric analysis /
first-order shear deformation theory /
free vibration
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