Nonlinear dynamics and chaos in cracked FGM rectangular plates under thermal variations

Functionally graded material (FGM) plates serve as critical engineering components owing to their exceptional strength and toughness under extreme operating conditions, particularly when subjected to rapid and cyclic temperature changes. Prolonged exposure to such conditions inevitably leads to structural damage, such as fatigue cracks, which significantly affects the dynamic behavior of the plates. While existing studies on cracked FGM plates primarily address damage-induced frequency reduction and deflection increase, the coupled effect of thermal variations and damage stages on nonlinear dynamic behaviors remains underexplored. To this end, this study develops a novel nonlinear vibration model for cracked FGM plates. The model incorporates temperature-dependent structural properties and employs a modified line spring crack model to accurately represent crack-related terms in the governing equations. The validity and accuracy of the model are rigorously verified through comparisons with finite element simulations and published data. Furthermore, the coupled effect of thermal variations and damage stages on nonlinear frequency responses and chaotic motions is thoroughly examined. Analytical and numerical results indicate that chaotic dynamics may emerge even at relatively small excitation amplitudes under elevated synchronously rising temperatures, leading to significantly intricate transitions between periodic and chaotic motions. These insights suggest a prospective concept for damage identification approaches in FGM plate structures by leveraging chaotic features.