In-plane and out-of-plane free vibrations of functionally graded composite arches with graphene reinforcements

This article presents in-plane and out-of-plane free vibration analyses of functionally graded graphene nanoplatelets reinforced composite (FG-GPLRC) arches. The arch is composed of multiple layers reinforced with graphene nanoplatelets (GPLs) that are evenly distributed in each layer but its weight fraction varies layer-by-layer in the thickness direction. The effective material properties are calculated by Halpin-Tsai micromechanics model for Young's modulus and the rule of mixture for both mass density and Poisson's ratio of each GPLRC layer. Analytical solutions are obtained for the fundamental frequencies of the in-plane anti-symmetric vibration and out-of-plane vibration of both fixed and pinned FG-GPLRC arches by using Hamilton's principle. A comprehensive parametric study is carried out to investigate the influences of distribution pattern, concentration and dimensions of GPLs as well as the geometrical parameters of the arch on the fundamental frequency of the FG-GPLRC arch. It is found that the fundamental frequency of the arch can be considerably improved by adding a lower quantity of GPLs as reinforcing nanofillers.

本文对功能梯度石墨烯纳米片增强复合材料（FG - GPLRC）拱进行了面内和面外自由振动分析。该拱由多层石墨烯纳米片（GPLs）增强材料组成，石墨烯纳米片在每层中均匀分布，但其重量分数在厚度方向上逐层变化。对于每个GPLRC层，采用哈尔平 - 蔡（Halpin - Tsai）细观力学模型计算杨氏模量的有效材料性能，采用混合法则计算质量密度和泊松比的有效材料性能。利用哈密顿原理，得到了固支和铰支FG - GPLRC拱的面内反对称振动和面外振动的基频解析解。进行了全面的参数研究，以探讨石墨烯纳米片的分布模式、浓度和尺寸以及拱的几何参数对FG - GPLRC拱基频的影响。研究发现，通过添加较少量的石墨烯纳米片作为增强纳米填料，拱的基频可以得到显著提高。