Abstract This paper presents a unified solution for free vibration analysis of thick functionally graded porous graphene platelet reinforced composite (FGP-GPLRC) cylindrical shells embedded in elastic foundations. The three-dimensional (3-D) theory of shell theory is introduced for theoretical formulation. The Rayleigh-Ritz method in conjugation with artificial spring technique are employed, where the arbitrary boundary conditions can be conveniently obtained. A unified solution which comprises of six different displacement functions is developed. The calculation performances including convergence rate and calculating efficiency with respect to different displacement functions are compared extensively. Besides, three elastic foundations (Winkler/ Pasternak/ Kerr foundations), four types of porosity distributions and three categories of GPL patterns are considered. Some benchmark results are provided for free vibration of FGP-GPLRC cylindrical shells resting on elastic foundations. At last, the effects of different boundary conditions, elastic foundations with various parameters, porosity coefficient, GPL weight fraction and geometrical parameters on the vibration are elucidated.

中文翻译：

---

弹性基础上 FGP-GPLRC 圆柱壳自由振动的三维解：比较和参数研究

摘要 本文提出了一种统一的解决方案，用于对嵌入弹性基础中的厚功能梯度多孔石墨烯薄片增强复合材料 (FGP-GPLRC) 圆柱壳进行自由振动分析。引入壳理论的三维（3-D）理论进行理论表述。采用Rayleigh-Ritz方法结合人工弹簧技术，可以方便地获得任意边界条件。开发了一个包含六个不同位移函数的统一解决方案。对不同位移函数的计算性能包括收敛速度和计算效率进行了广泛的比较。此外，三个弹性基础（Winkler/Pasternak/Kerr基础），考虑了四种类型的孔隙度分布和三类 GPL 模式。提供了一些基准结果，用于固定在弹性基础上的 FGP-GPLRC 圆柱壳的自由振动。最后阐明了不同边界条件、不同参数的弹性地基、孔隙度系数、GPL重量分数和几何参数对振动的影响。