Stability behavior of two-crack functionally graded shaft in a rotor-disc system: finite element approach

Abstract

Stability behavior of a rotor-disc system having a functionally graded (FG) shaft with fully open transverse cracks are studied through a finite element (FE) approach, considering the rigid end bearing conditions, various crack parameters, shaft internal damping and geometrical parameters. FG shaft is modeled with considering the effect of internal damping using Timoshenko beam theory (TBT)using two nodded with four degrees of freedom (DOFs) per node are taken into the formulation. Zirconia (ZrO2) and stainless steel (SS) are considered as FG material where material properties are considered temperature dependent and radially graded in the cracked FG shaft. Local flexibility coefficients (LFCs) are derived analytically with depth of crack, gradient index and temperature using Castigliano's theorem and Paris’s equation to compute the modified stiffness matrix at each instant of shaft rotation. Carrying out several numerical examples, the present formulation is validated with availableresults. Influences of shaft internal damping coefficients, gradient index, temperature gradient, shaft’s slenderness and relative locations of crack on the dynamic responses of the FG cracked shaft system are computed and discussed in detail.