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Free vibration of FG-CNT reinforced composite skew plates

机译：FG-CNT增强复合斜板的自由振动

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摘要

Present study deals with the free vibration analysis of skew plates made from functionally graded carbon nanotube reinforced composites. Carbon nanotubes as reinforcements are distributed across the thickness of the plate. Distribution pattern may be uniform or functionally graded. The developed formulation from a Cartesian coordinate system is transformed to an oblique coordinate system to satisfy the boundary conditions. The virtual strain and kinetic energies of the plate are obtained using the first order shear deformation plate theory. Ritz method whose shape functions are developed according to the Gram Schmidt process is implemented to construct an eigenvalue problem associated to the natural frequencies of the plate. The developed solution method is general and may be used for arbitrary boundary conditions of the plate. Results are compared for isotropic homogeneous and composite laminated plates in skew shape with the available data in the open literature. Afterwards numerical results are provided for skew plates reinforced with carbon nanotubes. It is shown that volume fraction of carbon nanotubes and their distribution pattern are both influential of natural frequencies of the carbon nanotube reinforced plates. Generally, the higher the volume fraction of carbon nanotubes, the higher the natural frequencies of the skew plate. (C) 2016 Elsevier Masson SAS. All rights reserved.
机译：本研究涉及功能梯度碳纳米管增强复合材料制成的斜板的自由振动分析。碳纳米管作为增强材料分布在整个板的厚度上。分布模式可以是均匀的，也可以是功能上分级的。从笛卡尔坐标系开发的公式转换为倾斜坐标系，以满足边界条件。使用一阶剪切变形板理论获得板的虚拟应变和动能。实施了根据Gram Schmidt过程开发形状函数的Ritz方法，以构造与板的固有频率相关的特征值问题。改进的求解方法是通用的，可用于板的任意边界条件。将偏心形状的各向同性均质和复合层压板的结果与公开文献中的可用数据进行比较。之后，提供了用碳纳米管增强的斜板的数值结果。结果表明，碳纳米管的体积分数及其分布规律均对碳纳米管增强板的固有频率有影响。通常，碳纳米管的体积分数越高，斜板的固有频率越高。 （C）2016 Elsevier Masson SAS。版权所有。

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