Large amplitude free vibration of sandwich beams with flexible core and FG Graphene Platelet Reinforced Composite (FG-GPLRC) face sheets based on extended higher-order sandwich panel theory

Abstract

The present article deals with the nonlinear free vibration analysis of sandwich beams with flexible core integrated with face sheets which are reinforced with graphene platelets (GPLs). Each layer of the composite media may have a different amount of graphene platelets which leads to a functionally graded (FG) distribution. The elastic modulus of the reinforced composite (RC) is calculated via the Halpin–Tsai model. Following the extended higher order sandwich panel theory (EHSAPT) which captures the core thickness compressibility effect and the axial stress of the core, the complete set of governing equations is obtained using the Lagrangian formulation. To analyze the effect of the inclusion of nonlinear terms in the core, hitherto not reported in the literature, results are computed considering the von Kármán type of geometrical nonlinearity assumptions for the core and face sheets. With the aid of the Ritz-based method, Chebyshev functions are implemented as admissible functions of the displacement fields. Furthermore, the nonlinear governing equations are solved using a direct displacement control technique. As the EHSAPT can be applied with any combination of the core and face sheets and not only the soft cores that the other theories demand, the results for the sandwich beam with stiff core and consist of functionally graded carbon nanotube-reinforced composite face sheets provided for validation. Since this study is the first in the open literature to develop nonlinear vibration of the sandwich beam based on EHSAPT, Timoshenko beam theory (TBT) is also applied to investigate the problem and to extract nonlinear frequencies with various stiffness of the core, meanwhile, the results are compared with those obtained by the EHSAPT. Parametric studies are conducted in detail to examine the influences of weight fraction and distribution pattern of graphene platelets, core to face sheet thickness ratio, boundary conditions, length to thickness ratio, and amplitude of vibrations. It is found that by increasing the stiffness of the core, the inclusion of nonlinear effects in the core as well as the face sheet strain nonlinearity is more significant. Finally, the nonlinear vibration analysis of sandwich beams can change the variation trend of frequency predicted in the linear analysis, and the different trends are observed depending on the vibration amplitude.