Parametric study on free vibration and instability of a functionally graded cracked shaft in a rotor-disc-bearing system: Finite element approach

Abstract

Free vibration and stability analysis are studied for a rotor-disk-bearing system having a radially functionally graded (FG) shaft with a transversely fully open crack, based on finite element (FE) approach. Both viscous and hysteretic internal damping are incorporated in the FE model of FG cracked shaft using two nodded Timoshenko beam element having four degrees of freedom (DOFs) at each node. Material properties of the FG cracked shaft are assumed temperature dependent and graded along radial direction following different material gradation law. FG shaft is made of two constituents material namely zirconia (ZrO2) and stainless steel (SS) where metallic (SS) contain is decreasing towards the outer diameter of the shaft. Extended Hamilton's principle is employed to derive the system equations of motion (EOMs) of the FG cracked shaft system. A complete code is developed in MATLAB for correcting the formulation of modeling of crack and verified with existing published results. Influences of different material gradient index, temperature gradients, size and location of crack, viscous and hysteretic internal damping, slenderness ratio, and boundary condition on dynamic responses of the FG cracked shaft system are studied.