Free Vibration Analysis of Functionally Graded Shaft System with a Surface Crack

Abstract

Free vibration analysis of functionally graded (FG) non-spinning simply supported shaft having a transverse surface crack has been carried out. Material properties of the FG shaft are assumed to be graded radially following the power law of material gradation. Local flexibility coefficients as a function of depth of crack are computed with the help of Paris’ equation along with Castigliano’s theorem. Finite element (FE) formulation has been done using Timoshenko beam elements with two nodes and having four degrees of freedom per node. Based on the formulation, FE analysis has been performed to understand the effects of shaft’s slenderness, crack’s depth and location, gradient parameter and thermal gradient on the free vibration response of the cracked FG shaft. FE analysis show that for a cracked FG shaft, both gradation parameter and crack parameters have significant influence on the free vibration response. Gradation parameter could be suitably chosen in the design of FG shafts so as to minimize the increase in flexibility due to appearance of cracks.