Utilizing optimal physics-informed neural networks for dynamical analysis of nanocomposite one-variable edge plates

Abstract

This study presents an innovative Physics-Informed Neural Network (PINN) approach designed to predict the dynamic responses of the One-Variable Edge Plate (OVEP), a unique plate structure characterized by an edge defined by arbitrary mathematical functions. The OVEP is constructed from a nanocomposite material reinforced with graphene nanoplatelets. Utilizing an optimized PINN pipeline, this research successfully predicts the vibration characteristics of the OVEP, encompassing linear, nonlinear vibrations, and beating phenomena. The study also demonstrates that the optimal PINN outperforms conventional neural network in terms of stability, accuracy (achieving above 99% accuracy), and efficiency in predicting long-duration vibrations. Additionally, the computational time required for generating testing results is notably diminished compared to traditional partial differential equation (PDE) solvers (reduced by about 3 to 12 times). To demonstrate model robustness, synthetic noise is intentionally introduced into the training data. The results not only enhance our understanding of the complex dynamics of the OVEP but also highlight the effectiveness of the proposed PINN framework in capturing and forecasting the dynamic behaviors of advanced plate structures. This research presents a promising potential for addressing dynamic problems in the fields of aerospace, civil, and mechanical engineering.