Vibration analysis of a functionally Graded cracked shaft system and AI-based design optimization

This paper presents a novel AI-based framework for the design optimization of shafts made of Functionally Graded Materials (FGMs), along with a detailed vibration analysis for multiple conditions. Functionally Graded Material (FGM) shafts combine the high-temperature resistance of ceramics with the toughness of metals, making them valuable in high-performance rotating machinery. However, their dynamic behavior becomes significantly more complex in the presence of cracks, thermal gradients, and material gradation. In this work, a comprehensive numerical study of the vibration response of unbalanced FGM shafts with a transverse breathing crack is conducted across different material gradations, thermal gradients, and rotational speeds. To reduce the computational cost of the design optimization process, an integrated Artificial Intelligence framework combining Artificial Neural Networks (ANNs) and Genetic Algorithms (GAs) is introduced. The ANN serves as an accurate surrogate model for predicting key performance indicators, including critical speed, static deflection, weight, and effective fracture toughness, while the GA efficiently explores the design space for optimal shaft configurations. The results highlight the influence of FGM gradation and thermal loading on the vibrational characteristics of cracked rotors and demonstrate that the proposed ANN-GA framework delivers excellent multi-objective optimization performance with high predictive accuracy. This work provides both deeper insight into the dynamics of cracked FGM shafts and a computationally efficient tool for their design optimization, supporting more reliable rotor-bearing systems.