In this paper, the forced resonance vibration analysis of curved micro-size beams made of graphene nanoplatelets (GNPs) reinforced polymer composites is presented. The approximating of the effective material properties is on the basis of Halpin–Tsai model and a modified rule of mixture. The Timoshenko beam theory is applied to describe the displacement field for the microbeam. To incorporate small-size effects, the modified strain gradient theory, possessing three independent length scale coefficients, is employed. Hamilton principle is applied to formulate the size-dependent governing motion equations, which then is solved by Navier solution method. Ultimately, the influences of length scale coefficients, opening angle, weight fraction and the total number of layers in GNPs on composite curved microbeams corresponding to different GNPs distribution are discussed in detail through parametric studies. It is shown that, the resonance position is significantly affected by changing these parameters.

本文介绍了由石墨烯纳米片（GNPs）增强的聚合物复合材料制成的弯曲微尺寸梁的强迫共振分析。有效材料性能的近似值基于Halpin-Tsai模型和混合的修改规则。季莫申科束理论被用来描述微束的位移场。为了合并小尺寸效应，采用了具有三个独立的长度比例系数的改进的应变梯度理论。利用汉密尔顿原理来建立与尺寸有关的控制运动方程，然后用Navier解法求解。最终，长度比例系数，开度角，通过参数研究详细讨论了复合弯曲微束上GNP的重量分数和总GNP层数（对应于不同GNP分布）。结果表明，改变这些参数会明显影响共振位置。