Dynamic characteristics analysis of graphene-reinforced annular sandwich composite plates: A combined generalized differential quadrature and artificial neural networks approaches

Abstract

By employing the Generalized Differential Quadrature (GDQ) technique alongside adaptive modeling through Artificial Neural Networks (ANN), the intrinsic vibrational properties of annular sandwich plates resting on an elastic foundation have been comprehensively examined within a thermal context. The sandwich structure features a core composed of graphene platelets, enveloped by two functionally graded (FG) layers. The Halpin-Tsai micromechanical model was utilized to ascertain the material properties of the composite structure. Furthermore, the material characteristics of the two FGM face sheets exhibit a continuous variation across the thickness, conforming to a power-law distribution. The governing partial differential equations and boundary conditions of the plate are formulated using the third-order shear deformation theory (TSDT) in accordance with Hamilton's principle. These equations are discretized in the spatial domain via the GDQ method, enabling the calculation of the natural frequencies of the plates. The precision of the numerical approach is validated by juxtaposing the results with existing literature. Additionally, an adaptive ANN is employed to forecast the frequencies of the sandwich annular plates. This methodology involves training a Neural Network (NN) with a dataset of frequency solutions derived from the GDQ method. The Levenberg-Marquardt backpropagation algorithm is utilized for the training process. Subsequently, the ANN model is refined for accurate predictions in novel scenarios. The findings indicate that both the GDQ method and the adaptive ANN can reliably predict the frequencies of the sandwich structure featuring a graphene platelet-reinforced core. The study explores the impact of various factors, including the FG power index, volume fraction of graphene platelets, the presence of an elastic foundation, and temperature variations on the natural vibrational behavior of annular sandwich plates supported on an elastic foundation. The ANN model proves to be highly effective for predicting the natural frequency of the sandwich disk, significantly reducing computational time and costs. It has been demonstrated that the proposed ANN model can accurately forecast natural frequencies without necessitating the resolution of any differential equations or engaging in time-consuming other numerical methods or procedures.