FE approach for dynamic response of a functionally graded spinning shaft system containing a transverse fully open crack

Abstract

Free vibration and stability analysis are studied for a rotor-disc-bearing system having a radially functionally graded (FG) shaft with a transversely fully open crack, based on finite element (FE) approach. Both internal viscous and hysteretic damping are incorporated in the FE model of FG cracked shaft using two nodded Timoshenko beam element having four degrees of freedom at each node. Material properties of the FG shaft are assumed temperature dependent and graded with different material law of gradation. Aluminium Oxide (Al2O3) and stainless steel (SS) are composed as FG material. Local flexibility coefficients (LFCs) are derived analytically as a function of crack size, power-law gradient index and temperature using Paris’s equation and Castigliano’s theorem to compute the stiffness matrix at each instant in the FE analysis. Using the developed MATLAB code, the FE formulation and the cracked model are verified with the published results. Parametric studies are conducted to study the influences of different material gradient index, temperature gradient, crack size, internal damping, slenderness ratio and boundary conditions on the vibration responses of the FG cracked shaft system.