Dynamic analysis of graphene-reinforced sandwich plates with piezoelectric macro fiber composite face sheets

Abstract

Graphene is considered as an ideal candidate for composite materials owing to the outstanding physical characteristics. However, existing higher-order shear deformation theories in the literature may meet severe challenges for the accurate prediction of natural frequencies of graphene-reinforced sandwich plates with piezoelectric macro fiber composite (MFC) face sheets. If transverse shear deformations cannot be described accurately, the dynamic behaviors of piezoelectric sandwich plates with graphene reinforcements will be significantly impacted by the large differences of material properties at interfaces of adjacent layers and electro-mechanical coupling characteristic. Thereby, a novel electro-mechanical coupling theory is to be proposed for the free vibration of graphene-reinforced sandwich plates with MFC face sheets. Based on the Reissner mixed variational theorem (RMVT), the precision of the interlaminar shear stresses including the electro-mechanical coupling effect can be improved. The modified interlaminar shear stress field is absorbed in the strain energy, which can enhance the accuracy of the free vibration response of piezoelectric sandwich plates. Additionally, the second-order derivatives of in-plane displacements have been eliminated from the interlaminar shear stress components, which can substantially simplify the finite element implementation. Thus, a simple C0-type finite element formulation is developed for the free vibration of piezoelectric sandwich plates with graphene reinforcements. The 3D elasticity solutions and the results obtained from other theories are used to evaluate the performance of the proposed theory. In comparison with the existing higher-order theories, the proposed theory can produce more accurate results. In addition, a comprehensive parametric study is conducted to explore the impacts of significant parameters on the free vibration behaviors of piezoelectric graphene-reinforced sandwich plates.