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Abstract
The present work deals with natural and whirl frequency analysis of a porous functionally graded (FG) rotor–bearing system using the finite element method (FEM). Stiffness, mass and gyroscopic matrices are derived for porous and non-porous FG shafts by developing a novel two-noded porous FG shaft element using Timoshenko beam theory (TBT), considering the effects of translational inertia, rotatory inertia, gyroscopic moments and shear deformation. A functionally graded shaft whose inner core is comprised of stainless steel (SS) and an outer layer made of ceramic (ZrO2) is considered. The effects of porosity on the volume fractions and the material properties are modelled using a porosity index. The non-linear temperature distribution (NLTD) method based on the Fourier law of heat conduction is used for the temperature distribution in the radial direction. The natural and whirl frequencies of the porous and non-porous FG rotor systems have been computed for different power law indices, volume fractions of porosity and thermal gradients to investigate the influence of porosity on fundamental frequencies. It has been found that the power law index, volume fraction of porosity and thermal gradient have a significant influence on the natural and whirl frequencies of the FG rotor–bearing system.
Highlights
An important aspect to take into consideration for a superior structural performance is the material strength of the system
A dynamic analysis of a porous functionally graded rotor–bearing system has been carried out using the finite element method
The effects of porosity, power law index and thermal gradients on the natural and whirl frequencies of an functionally graded (FG) rotor system have been analysed and the following conclusions can be drawn from the analysis:
Summary
An important aspect to take into consideration for a superior structural performance is the material strength of the system. Traditional composite materials are impotent when they are subjected to thermo-mechanical loading, due to inter-laminar stresses which cause the de-lamination of layers. Metals are preferred because of their high strength and toughness [1]. At high temperatures, the strength of the metal drastically deteriorates. The development of a new class of composites, functionally graded materials (FGMs), mitigated the problems of de-bonding, de-lamination and residual stresses in fibre-reinforced composites at elevated temperature, while making use of the advantages of both metal and ceramic material properties. FGM is an inhomogeneous micromechanical composite typically made from different phases of metal and ceramic material constituents. The volume fraction of constituent materials is arranged in the desired direction based on material laws for smooth and continuous change from one layer to another
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