Thermo-Mechanical Analysis of a Rotor-Bearing System Having a Functionally Graded Shaft with Transverse Breathing Cracks

Purpose: The dynamic behavior of two-cracked functionally graded (FG) shaft system under thermal environment has been carried out. The finite element (FE)-based formulation is used to model metal-ceramic FG (SS/ZrO₂) shaft using Timoshenko beam theory (TBT). Power law of material gradation is used to derive effective thermo-elastic properties of radially graded FG shaft. Methods: The governing system equations of motion are formulated using Hamilton’s principle. The local flexibility coefficients (LFCs) are derived as functions of material gradient, temperature, size and orientation of crack, for the cracked FG circular cross-sectional FG shaft, using linear elastic fracture mechanics, Castigliano’s theorem and energy method. Results: Numerical simulations are performed to analyze the effects of geometric, material and temperature gradient parameters on the natural frequencies of the cracked FG shaft system. Conclusion: LFCs are functions of material gradient and temperature besides crack size. Even though the reduction in eigenfrequencies is decided by crack parameters, material gradient and temperature, however, the reduction in eigenfrequencies is greatly influenced by gradient index and the index may be selected properly to design FG shafts for high-temperature applications.