Vibration Analysis of FGM Plate: A Hybrid Analytical and Machine Learning Approach

This study explores the free vibration characteristics of functionally graded material (FGM) plates using both analytical solutions and machine learning (ML) techniques. Initially, we derive equilibrium equations for FGM plates through Hamilton's principle to determine their natural frequencies under various conditions. We then develop an Artificial Neural Network (ANN) model, trained on a comprehensive dataset from prior research, to predict these vibrational frequencies [1]. The ANN's predictions are rigorously compared with our analytical results and validated against existing studies, demonstrating its high precision and computational efficiency. Our research highlights that the ANN model can significantly streamline the analysis process, effectively handling complex patterns that challenge traditional methods. This integration of analytical rigor with ML innovation presents a novel approach to enhancing the structural analysis and design of FGM plates, potentially transforming material science and engineering practices. The accuracy with which the ANN model predicts natural frequencies across diverse FGM plates underscores the power of data-driven approaches in engineering analysis. Integrating ML not only enhances the precision of traditional methods but also introduces adaptability and scalability previously unattainable. Our findings suggest that combining computational mechanics with artificial intelligence holds great promise for future material design and optimization, offering a more comprehensive understanding of the dynamic properties of FGM plates. This study also sets a precedent for applying ML to complex engineering problems, encouraging further exploration into hybrid methodologies that bridge theoretical analysis and practical engineering solutions [2]. Through this approach, we aim to advance FGM technology, paving the way for more resilient and efficient structural components.