Free vibration of sandwich beams with graphene nanoplatelets reinforced piezoelectric face sheets

Owing to its exceptional physical properties, graphene is considered as an excellent reinforcement for composite materials. However, the existing higher-order models encounter significant hurdles when attempting to accurately predict the natural frequencies of sandwich beams with graphene nanoplatelets reinforced composite (GNPRC) piezoelectric face sheets. If transverse shear deformations are not accurately modeled, the dynamic behavior of piezoelectric sandwich beams will be noticeably influenced by the disparities of material properties at the interfaces of adjacent layers, as well as the inherent electromechanical coupling characteristic. To overcome these challenges, an advanced electro-mechanical coupling theory will be introduced for the vibration analysis of sandwich beams featuring GNPRC piezoelectric face sheets. Compared to previous higher-order models, the proposed beam model introduces an enhanced interlaminar shear stress field incorporating electromechanical properties. This improved stress field can be involved in the equations of motion based on the Hamilton principle, significantly enhancing the precision in analyzing the free vibration behavior of piezoelectric sandwich beams. Furthermore, a simplification of finite element implementation can be achieved by removing the second-order derivatives of in-plane displacements from the transverse shear stress field. Consequently, a C0-type three-node beam element is constructed for the dynamic analysis of sandwich beams with GNPRC piezoelectric face sheets. To validate the performance of the proposed theory, the 3D elasticity solutions and results obtained from alternative theoretical frameworks are used. Numerical results demonstrate that the present model offers superior accuracy over the existing higher-order theories. Additionally, a comprehensive parametric investigation is conducted to explore the influence of key parameters on the free vibration characteristics of piezoelectric sandwich beams.