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A unified Fourier series solution for vibration analysis of FG-CNTRC cylindrical, conical shells and annular plates with arbitrary boundary conditions

机译：具有任意边界条件的FG-CNTRC圆柱，圆锥壳和环形板振动分析的统一傅里叶级数解

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摘要

This research paper presents a unified Fourier series solution to solve the vibration problem of functionally graded carbon nanotube-reinforcement composite (FG-CNTRC) cylindrical shells, conical shells and annular plates subjected to general boundary conditions, so as to enrich the existing research results on FG-CNTRC structures. Utilizing a micro-mechanical model based on the developed rule of mixtures, the effective material properties of the FG-CNTRC structures which is strengthened by single-walled carbon nanotubes (SWCNTs) are scrutinized. The first-order shear deformation theory (FSDT) and the virtual boundary method are applied to achieve the energy expressions of FG-CNTRC structures. On the basis of that, the unified Fourier series solution in conjugation with the modified Fourier series and Ritz method, is utilized to receive characteristic equation of the structural vibration. The correctness, convergence and several advantages of the present methodology are verified by numerous numerical examples. Furthermore, some novel numerical results, including the vibration results of FG-CNTRC cylindrical shells, conical shells and annular plates accompanied with classical boundary, elastic boundary, classical-elastic mixed boundary and parameterized results of structure and material parameters, will be presented for future researchers.
机译：本研究提出了一个统一的傅里叶级数解，以解决功能梯度碳纳米管增强复合材料圆柱壳，圆锥壳和环形板在一般边界条件下的振动问题，从而丰富了已有的研究成果。 FG-CNTRC结构。利用基于混合物的发展规律的微力学模型，对由单壁碳纳米管（SWCNT）增强的FG-CNTRC结构的有效材料性能进行了研究。应用一阶剪切变形理论（FSDT）和虚拟边界方法来获得FG-CNTRC结构的能量表达式。在此基础上，结合改进的傅里叶级数和Ritz方法，采用统一的傅里叶级数解，得到结构振动的特征方程。通过大量的数值例子验证了本方法的正确性，收敛性和几个优点。此外，还将提出一些新颖的数值结果，包括FG-CNTRC圆柱壳，圆锥壳和环形板的振动结果，以及经典边界，弹性边界，经典弹性混合边界以及结构和材料参数的参数化结果，以供将来使用。研究人员。

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