Effects of graphene platelet presence and porosity distribution on the vibration of piezoelectric sinusoidal sandwich beam

In recent years, the focus on vibration analysis of multilayer smart structures has attracted considerable attention in many engineering applications. In this work, vibration analysis of a three- layer microporous beam with a core amplified by a composite material reinforced with graphene platelets and two piezoelectric thin films is discussed. It is assumed that piezoelectric layers with a thickness of 0.01 core are very thin and the properties of the matrix and reinforcement vary in the thickness directions. The governing equations of motion are obtained using an energy approach and the method of numerical differential quadrature to solve them. The results of this work are compared to other research and there is good agreement between them. The influences of the volumetric weight fraction of graphene wafers, different graphene platelets distributions, porosity distribution, mass scale parameters and thin ratio of graphene platelets take into account the natural dimensionless frequencies of the micro- beam. The results of this study show that the symmetric distribution of graphene platelets based on the symmetric porosity distribution has a great influence on the natural frequencies without basic dimension of the micro- beam, while the shape ratios of graphene platelets do not have a significant influence on natural frequency changes.