Resonance analysis of composite curved microbeams reinforced with graphene nanoplatelets

Abstract

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.