Vibration analysis of composite beams integrated with graphene nanoplatelets reinforced piezoelectric layer

Abstract

Graphene nanoplatelets (GNP) possess distinctive physical properties, making them a remarkable material for a wide range of engineering applications. Nonetheless, the existing higher-order theories documented in the literature may not effectively predict the natural frequencies of composite beams that incorporate GNP-reinforced piezoelectric layers. This limitation arises from the electromechanical coupling effects and the pronounced variability in material properties at the interfaces between layers. To overcome these limitations, this study proposes a refined beam theory specifically designed to examine the vibrational behavior of composite beams embedded with GNP-reinforced piezoelectric layers. By enforcing the continuity of interlaminar stresses and incorporating the free-surface conditions for interlaminar shear stresses, the formulation eliminates the dependence on layer-specific unknown variables, leading to a simplified yet accurate displacement field. In contrast to earlier higher-order theories, the current model introduces a refined interlaminar shear stress field incorporating the effects of electromechanical coupling. By utilizing Hamilton's principle, the enhanced shear stress field is incorporated into the governing equations of motion, which leads to a notable improvement in the prediction of natural frequencies for piezoelectric sandwich and laminated beams. Key results show that the proposed model achieves deviations below 3% compared to exact solutions, while existing models exhibit errors exceeding 280%. Additionally, geometric parameters such as the length-to-thickness ratio and layer thickness significantly influence natural frequencies, whereas the GNP volume fraction and electrical boundary conditions have minimal impact. The proposed theory's effectiveness is demonstrated through exact solutions and comparative studies with other models. The results reveal that the proposed theory offers superior accuracy in predicting natural frequencies compared to conventional higher-order models for composite beams. Moreover, a parametric analysis is performed to explore the influences of various key parameters on the vibration properties of smart composite beams with GNP reinforcements.