Transverse Vibration and Stability of a Cracked Functionally Graded Rotating Shaft System

Transverse vibration and stability of functionally graded (FG) shafts containing a transverse surface crack are studied considering material nonlinearity. Based on Timoshenko beam theory (TBT), a finite element (FE) model is developed for an FG shaft. Under thermal environment, material properties of radially graded FG shafts are considered using power law of material gradation. Stainless steel (SS), alumina (Al2O3) and zirconia (ZrO2) are used as constituent materials of FGM I (SS/Al2O3) and FGM II (SS/ZrO2). Local flexibility coefficients (LFCs) are computed as functions of temperature, size of crack and material gradient index based on linear elastic fracture mechanics. Influences of FGM type, material gradient, temperature gradient and crack size on dynamics of cracked FG rotors system are studied. Results show that beside the crack and geometric parameters, the choice of gradient index has importance on dynamics of the FG shaft for high-temperature applications.