Application of the Transfer Function Method to Vibration Analysis of Functionally Graded Beams in Thermal Environments

Characterized by a continuous gradient in both microstructure and material properties, functionally graded materials (FGMs) are well-suited for integrated heat protection and load-bearing structures. Thermal vibration of FGMs is the basis to ensure service safety under a thermo-dynamic load environment. Current research predominantly relies on numerical algorithms, with a notable absence of analytical expressions for frequency characteristics. This study extends the application of the transfer function method (TFM) to the vibration of FGM beams. Firstly, the thermal vibration governing equations were derived based on Timoshenko beam theory and Hamilton’s principle. Then, the frequencies of the two types of FGM beams were calculated using the TFM. Finally, the adaptability of the TFM was validated, and the time cost was analyzed. The results indicated that the analytical transfer-function formulation and solution obtained by the TFM agree well with the Navier method and the generalized differential quadrature method, demonstrating the high applicability of the present approach.