Nonlinear Dynamic Analysis of Oscillatory Behavior of Graphene Nano/Microelectromechanical System Using a Hybrid Morlet Wavelet Neural Network Framework

The Nano/microelectromechanical systems (N/MEMS), particularly graphene-based devices, exhibit highly nonlinear and oscillatory dynamic behavior that is complicated to solve accurately utilizing the conventional numerical and theoretical approaches. This study aims to design an advanced and efficient computational framework to analyze the dynamic response of graphene N/MEMS systems. In this paper, a hybrid morlet wavelet neural network (MWNN) algorithm is proposed to approximate the solution of the governing nonlinear model. The Morlet wavelet-based activation function is employed due to its strong capability to capture localized oscillatory patterns inherent in N/MEMS dynamics. To further enhance accuracy and convergence, a hybrid optimization strategy is integrated, where advanced optimization algorithms are used to initialize and update neural network parameters efficiently. This hybridization significantly improves convergence speed, stability, and prediction accuracy compared to a single neural network approach. The proposed framework is applied to estimate the dynamic displacement response of the graphene N/MEMS system under varying nonlinear stiffness and electrostatic actuation parameters. The obtained results are validated against reference numerical solutions, demonstrating high accuracy and robustness. Performance evaluation is carried out using Theil’s inequality coefficient (TIC), mean square error (MSE), and mean absolute deviation (MAD), confirming the effectiveness of the proposed approach.