This paper studies nonlinear vibration analysis of a graphene nanoplatelets’ composite sandwich. The core and two face-sheets of composite sandwich plate are fabricated from a honeycomb material and graphene nanoplatelet (GNP) reinforcements, respectively. Displacement field of sandwich plate is developed based on first-order shear deformation theory. Geometric nonlinearity is accounted in the constitutive relations based on von-Karman assumptions. After derivation of the governing partial differential motion equations through Hamilton’s principle, Galerkin’s approach is used to reduce them into a nonlinear equation of motion in terms of transverse deflection. The nonlinear frequency is found based on linear frequency and initial conditions, analytically. The nonlinear-to-linear frequency ratio is computed based on significant input parameters of honeycomb structure and graphene nanoplatelets such as thickness-to-length and thickness-to-height ratios, angle of honeycomb, various distribution, weigh fraction and geometric characteristics of graphene nanoplatelets. Before presentation of full numerical results, the comprehensive comparative study is presented for verification of the derivation and solution method.

本文研究了石墨烯纳米片复合夹层结构的非线性振动分析。复合夹层板的核心和两个面板分别由蜂窝材料和石墨烯纳米片 (GNP) 增强材料制成。基于一阶剪切变形理论开发了夹层板的位移场。基于冯卡门假设的本构关系考虑了几何非线性。通过哈密顿原理推导了控制偏微分运动方程后，利用伽辽金方法将其简化为横向偏转的非线性运动方程。非线性频率是基于线性频率和初始条件，解析地找到的。非线性与线性频率比的计算基于蜂窝结构和石墨烯纳米片的重要输入参数，例如厚长比和厚高比、蜂窝角度、各种分布、重量分数和石墨烯的几何特征纳米血小板。在给出完整的数值结果之前，先进行综合比较研究，以验证推导和求解方法。