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.
Highlights
Shafts are basic components in high-performance rotating machinery equipment, used in the requirement of higher power, high operational speed
Designing in functionally graded (FG) shafts gradient index can play great role to expose larger temperature gradients and higher spinning speeds and FG shaft has an advantage over shaft made of stainless steel (SS)
Material gradient index and temperature gradient yields a significant role on natural frequencies and stability threshold speeds of the FG cracked shaft system
Summary
Shafts are basic components in high-performance rotating machinery equipment, used in the requirement of higher power, high operational speed. Gayen et al [15] reported dynamic responses of a rotor-bearing system with a fully open transverse cracked FG shaft using FEM. Even though a large number of works reported in the direction of analysis of FGM structure, free vibration and stability analysis of homogeneous cracked shaft for a long time. Hardly any works available in the area of temperature dependent free vibration and stability analysis of cracked FG shaft system. Aim of the presentstudy is to develop a FE model for analysis of cracked FG shaft system with temperature dependent material properties and to study the effect of important parameters such as gradient index, temperature gradient, size and location of crack, internal viscous and hysteretic damping, slenderness ratio and boundary condition on the dynamic responses
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