Investigation of thermo-acoustoelastic guided waves by semi-analytical finite element method

Guided waves are sensitive to variations in propagation environments. Many recent studies have focused on the uniform thermal effect on Lamb waves. However, there is little research on the thermal effect in a more complex situation, such as a nonuniform thermal effect and wave propagation in an arbitrary cross-section. In this study, a thermo-acoustoelastic theory combined with the semi-analytical finite element (TAE-SAFE) method is proposed to investigate both uniform and nonuniform thermal effects on acoustoelastic guided wave propagation. In the TAE-SAFE method, effective thermo-acoustoelastic constants including third-order elastic constants are employed. Then, an acoustoelastic wave equation of the thermal effect is formulated by Hamilton's principle and computed by the semi-analytical finite element (SAFE) method. The phase velocity, group velocity, velocity thermal sensitivity, and displacement mode shape shift can be extracted by the proposed method. To validate this method, numerical results of Lamb waves in an aluminum plate subjected to a uniform thermal effect are compared with the results of a previous theoretical analysis. The results show computational veracity and validity. Two typical cases are investigated: (1) an isotropic aluminum plate under a linear temperature gradient condition; (2) a uniform temperature case in a rail track with a constant irregular cross-section. This study provides an effective numerical method to analyze thermo-acoustoelastic guided wave propagation.