A Polynomial Approach for Thermoelastic Wave Propagation in Functionally Gradient Material Plates

Functionally gradient material (FGM) in service often experience temperature variations that can affect the propagation characteristics of guided waves. This investigation aims to study the propagation of thermoelastic guided waves in the FGM plate. A computational method for the state vector and Legendre polynomials hybrid approach, which is proposed based on the Green–Nagdhi theory of thermoelasticity. The heat conduction equation is introduced into the governing equations, and optimized using univariate nonlinear regression for arbitrary gradient distributions of the material components. To study their dispersion characteristics, a non-hierarchical calculation for the dispersion curves of FGM plates versus temperature is realized. In addition, a frequency domain simulation model is developed and compared with theoretical data to evaluate the accuracy and feasibility of the proposed theory. Then, the influence of Legendre orthogonal polynomial cut-off order on dispersion curve convergence is investigated. Subsequently, the shift of the gradient index and temperature variation on the fundamental mode in dispersion curve is analyzed. The results indicate that changes in both gradient index and temperature lead to a systematic shift in the phase velocity of fundamental modes in the low frequency range. Meanwhile, anti-symmetric modes exhibit higher sensitivity. On this basis, the study can provide theoretical support for the acoustic non-destructive characterization of FGM plates versus temperature.