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Vibrations of graphene nanoplatelet reinforced functionally gradient piezoelectric composite microplate based on nonlocal theory

机译：基于非局部理论的石墨烯纳米克薄板增强功能梯度压电复合微孔板的振动

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摘要

This paper investigates the small-scale effect on the linear and nonlinear vibrations of the graphene nanoplatelet (GNPL) reinforced functionally gradient piezoelectric composite microplate based on the nonlocal constitutive relation and von Karman geometric nonlinearity. The GNPL reinforced functionally gradient piezoelectric composite microplate is resting on the Winkler elastic foundation and is subjected to an external electric potential. The parallel model of Halpin Tsai is used to compute the effective Young's modulus of the GNPL reinforced functionally gradient piezoelectric composite microplate. The Poisson's ratio, mass density and piezoelectric properties of the GNPL reinforced functionally gradient piezoelectric composite microplate are calculated by using the rule of mixture. Hamilton's principle is adopted to obtain the higher-order nonlinear partial differential governing equations of motion for the GNPL reinforced functionally gradient piezoelectric composite microplate. The partial differential governing equations of motion are reduced to a system of the nonlinear algebraic eigenvalue equations by using the differential quadrature (DQ) method and are solved by an iteration progress. The efficiency and accuracy of the present approach are verified by comparing with the existed results. Both uniformly and functionally distributing graphene nanoplatelets (GNPLs) are considered to investigate the effects of the GNPL concentration, external voltage, nonlocal parameter, geometrical and piezoelectric characteristics of the GNPLs as well as the elasticity coefficient of the Winkler elastic foundation on the linear and nonlinear dynamic behaviors of the GNPL reinforced functionally gradient piezoelectric composite microplate with various boundary conditions. The numerical results clearly manifest that the GNPLs can significantly enhance the structural stiffness of the micro-electro-mechanical system (MEMS).
机译：本文研究了石墨烯纳米片（GNPL）的线性和非线性振动的小规模效应基于非本周本构系和von Karman几何非线性的基于非本周构成关系和von Karman几何非线性的线性和非线性振动。 GNPL增强功能梯度压电复合微型板在闪光灯弹性基础上搁置并经受外部电位。 Halpin Tsai的并联模型用于计算GNPL增强功能梯度压电复合微孔板的有效杨氏模量。通过使用混合物规则计算Gnpl增强功能梯度压电复合微板的Gnpl增强功能梯度压电复合微板的泊松比，质量密度和压电性能。采用汉密尔顿原则来获得GNPL增强功能梯度压电复合微孔板的高阶非线性部分差动控制运动的运动。通过使用差分正交（DQ）方法，通过迭代正交（DQ）方法来减少运动的部分差分管理方程，通过差分正交（DQ）方法来减少非线性代数特征值方程。通过与存在的结果进行比较来验证本方法的效率和准确性。均匀且功能地分布的石墨烯纳米片（GNPL）被认为是研究GNPL浓度，外部电压，非本地参数，几何和压电特性的影响，以及线性和非线性的Winkler弹性基础的弹性系数具有各种边界条件的GNPL增强功能梯度压电复合微孔板的动态行为。数值结果清楚地表明，GNPLS可以显着提高微电机械系统（MEMS）的结构刚度。

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