Size-dependent nonlinear vibrations of functionally graded origami-enabled auxetic metamaterial plate: Application of artificial intelligence networks for solving the engineering problem

Auxetic metamaterials are a kind of advanced materials that have distinct mechanical and physical characteristics that are not seen in traditional materials. This study presents a new concept for a microplate composed of graphene origami (GOri)-enabled auxetic metamaterials (GOEAMs) with functionally graded (FG) properties. The research also examines the nonlinear free vibration behavior of the microplate, which is reinforced by the GOEAMs. The microplate is composed of many layers of GOEAMs, with the GOri content varying in a layer-wise manner across the thickness. This variation in content allows for the graded modification of the auxetic property and other material characteristics. These modifications may be accurately determined using micromechanical models helped by genetic programming (GP). The modified couple stress theory (MCST) is used to accurately represent the microstructure of the current plate, given its size. This theory incorporates a single-length scale parameter. This study uses the first -order shear deformation theory and includes von K ' arm ' an type nonlinearity to establish the nonlinear kinematic equations. These equations are then solved numerically using the generalized differential quadrature (GDQ) method and pseudo-arc-length continuation approach. This article utilizes mathematical modeling to collect data on the nonlinear frequency and deflection of the FG microplate made of GOEAMs. The data is then preprocessed by normalizing the input features and splitting the dataset into training and validation sets. Subsequently, an artificial intelligence network (AIN) architecture is constructed, consisting of an input layer, hidden layers, and an output layer. Once the AIN has been utilized to test, train, and validate the findings, this approach may be used in future studies on the nonlinear frequency and deflection of FG microplates built of GOEAMs, with reduced computational cost. Ultimately, the findings suggest that the nonlinear free vibration characteristics of the microplate may be successfully adjusted by manipulating the GOri parameter and distribution.