Abstract Graphene platelets (GPLs) can be used to enhance mechanical and electric properties of the polymer polyvinylidene fluoride (PVDF), which efficiently controls and improves dispersion characteristics of wave motion in piezoelectric composite structures. Based on the first order shear deformation shell theory and the higher-order spectral elements, this paper proposes a semi-analytical formulation to investigate wave characteristics in the piezoelectric polymer nanocomposite cylindrical shell. The cylindrical shell is composed of PVDF reinforced with graphene platelets that are dispersed along the thickness direction, following various functionally graded patterns UD, FG-X and FG-O. Governing equation of waves in the piezoelectric composite shell is derived from Hamilton’s principle. By employing the Fourier transform, a second-order polynomial eigenvalue problem is obtained for wave analysis in frequency domain. Comparisons with other methods indicate that the present approach has the higher efficiency and accuracy on computation. Then, the study of significant parameters are conducted for analyzing the effects on wave propagation and the results show that dispersion behaviors of the piezoelectric nanocomposite shell are improved apparently by the addition of a small amount of GPLs. The increasing content of GPLs promotes the propagation of elastic waves and the richer concentration on the boundaries of the shells is beneficial to only the out-of-plane modes. Meanwhile, size parameters of GPLs provide an efficient means for the modulation of wave characteristics in nanocomposite shells. It is envisaged that the present work can provide guidelines to develop novel smart nanocomposites and structures.

中文翻译：

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石墨烯增强压电聚合物纳米复合圆柱壳半解析波特性分析

摘要 石墨烯薄片 (GPL) 可用于增强聚合物聚偏二氟乙烯 (PVDF) 的机械和电学性能，可有效控制和改善压电复合材料结构中波动的色散特性。基于一阶剪切变形壳理论和高阶光谱元素，本文提出了一种半解析公式来研究压电聚合物纳米复合圆柱壳中的波特性。圆柱壳由 PVDF 组成，石墨烯薄片沿厚度方向分散，遵循各种功能梯度图案 UD、FG-X 和 FG-O。压电复合壳中波的控制方程是从哈密顿原理推导出来的。通过使用傅里叶变换，获得了用于频域波浪分析的二阶多项式特征值问题。与其他方法的比较表明，本方法具有更高的计算效率和准确性。然后，进行了重要参数的研究，以分析对波传播的影响，结果表明，加入少量 GPLs 后，压电纳米复合材料壳的色散行为得到明显改善。GPLs 含量的增加促进了弹性波的传播，壳边界上更丰富的浓度仅对面外模式有利。同时，GPL 的尺寸参数为调制纳米复合材料壳中的波特性提供了一种有效的手段。