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首页> 外文期刊>International journal of mechanics and materials in design >Hierarchic models for the free vibration analysis of functionally gradient plates
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Hierarchic models for the free vibration analysis of functionally gradient plates

机译：功能梯度板的自由振动分析的层次模型

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摘要

Hierarchic models for the modal analyses of ceramic-metal functional gradient (FG) plates are introduced. This study was motivated by the fact that the free vibration analyses of those structures are usually conducted by the first- or higher-order shear deformation theories (SDT). Meanwhile, a hierarchic model does not only include these classical theories, but their model level varies from the first order to the 3D full elasticity. In fact, in the hierarchic models, the part of displacement field through the thickness is assumed a priori using polynomials with the desired highest order. Hence, they can be numerically implemented using 2D finite element or mesh-free method, by discretizing only the mid-surface of 3D structures. The global mass and global stiffness matrices of FG plates are computed by adopting the Gaussian quadrature rules for the mid-surface integral and the trapezoidal rule for the thickness-wise integral. The proposed hierarchic models are numerically illustrated and their characteristics are investigated. In addition, the modal characteristics of FG plates are parametrically examined to the key factors of gradient layer. The hierarchic models approach the same limit and show a sequence of model accuracy. Meanwhile, the modal responses of metal-ceramic FG plate structures are dependent of the volume fraction pattern and the relative thickness ratio of gradient layer.
机译：介绍了陶瓷金属功能梯度（FG）板模态分析的层次模型。该研究的激励是，这些结构的自由振动分析通常由第一或高阶剪切变形理论（SDT）进行。同时，层次模型不仅包括这些经典理论，而且它们的模型水平从第一个顺序变化到3D完全弹性。事实上，在层次模型中，通过厚度的位移场的一部分假设使用具有所需最高阶的多项式的优先级。因此，通过仅离散3D结构的中表面，可以使用2D有限元或无网形成方法来数控地实现。通过采用用于中表面整体的高斯正数规则和厚度明智积分的梯形规则来计算FG板的全局质量和全局刚度矩阵。提出的层级模型进行了数值图示，并研究了它们的特性。此外，FG板的模态特性是参数检查梯度层的关键因素。分层模型接近相同的限制并显示一系列模型精度。同时，金属陶瓷FG板结构的模态反应取决于体积分数图案和梯度层的相对厚度比。

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