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Natural Frequency Analysis of a Porous Functionally Graded Shaft System

Authors: Natural Frequency Analysis of a Porous Functionally Graded Shaft System


The vibration characteristics of a functionally graded (FG) rotor model having porosities and micro-voids is investigated using three-dimensional finite element analysis. The FG shaft is mounted with a steel disc located at the midspan. The shaft ends are supported on isotropic bearings. The FG material is composed of a metallic (stainless-steel) and ceramic phase (zirconium oxide) as its constituent phases. The layer wise material property variation is governed by power law. Material property equations are developed for the porosity modelling. Python code is developed to assign the material properties to each layer including the effect of porosities. ANSYS commercial software is used to extract the natural frequencies and whirl frequencies for the FG shaft system. The obtained results show the influence of porosity volume fraction and power-law index, on the vibration characteristics of the ceramic-based FG shaft system.

Keywords: Finite element method, functionally graded material, porosity volume fraction, power law.

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[1] Wattanasakulpong, N. and Ungbhakorn, V. (2014) “Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities,” Aerospace Science and Technology 32(1), 111–120
[2] Dimentberg FM, Flexural vibrations of rotating shafts. London: Butterworths, 1961
[3] Ruhl R, Booker JF, A finite element model for distributed parameter turbo rotor systems. J Eng Ind 1972; 94: 128–132
[4] Nelson HD, Mcvaugh JM, The dynamics of rotor bearing systems using finite elements. J Eng Ind 1976; 98: 593–600
[5] Nelson HD, A finite rotating shaft element using Timoshenko beam theory. J Mech Des 1980; 102: 793–803
[6] Chakraborty A, Gopalakrishnan S, Reddy JN. A new beam finite element for the analysis of functionally graded materials. Int J Mech Sci 2003; 45: 519–539.
[7] Xiang HJ, Yang J. Free and forced vibration of a laminated FGM Timoshenko beam of variable thickness under heat conduction. Compos Part B: Eng 2008; 39: 292–303
[8] Reddy J.N., Chin C.D., 1998. Thermoelastical analysis of functionally graded cylinders and plates. J. Therm. Stresses. 21(6), 593-626
[9] Aydogdu, M. and Taskin, V. (2007) “Free vibration analysis of functionally graded beams with simply supported edges. ”Materials & Design 28(5), 1651–1656.
[10] Simsek, M. and Aydın, M. (2017) “Size-dependent forced vibration of an imperfect functionally graded (FG) microplate with porosities subjected to a moving load using the modified couple stress Theory,” Composite Structures 160, 408–421.
[11] Gayen D, Roy T (2014) Finite element based vibration analysis of functionally graded spinning shaft system. J Mech Eng Sci Part C 228(18):3306–3321
[12] Gayen, Chakraborty, Tiwari, Free Vibration Analysis of Functionally Graded Shaft System with a Surface Crack. Journal of Vibration Engineering & Technologies (2018) 6:483–494
[13] Arnab B, Prabhakar S, Natural frequency analysis of a functionally graded rotor system using the three-dimensional finite element method, Vibroengineering PROCEDIA,
[14] Jahwari, F. and Naguib, H. E. (2016) “Analysis and homogenization of functionally graded viscoelastic porous structures with a higher order plate theory and statistical based model of cellular distribution,” Applied Mathematical Modelling 40(3), 2190–2205.
[15] Mechab, I., Mechab, B., Benaissa, S., Serier, B. and Bouiadjra, B. B. (2016b) “Free vibration analysis of FGM nanoplate with porosities resting on Winkler Pasternak elastic foundations based on two-variable refined plate theories,” Journal of the Brazilian Society of Mechanical Sciences and Engineering 38, 2193–2211.
[16] Atmane, H. A., Tounsi, A., Bernard, F. and Mahmoud, S. R. (2015) “A computational shear displacement model for vibrational analysis of functionally graded beams with porosities,” Steel and Composite Structures 19(2), 369–384.
[17] Ebrahimi, F. and Jafari, A. (2016) “A higher-order thermomechanical vibration analysis of temperature-dependent FGM beams with porosities,” Journal of Engineering 2016
[18] Seref Doguscan Akbas, Thermal Effects on the Vibration of Functionally Graded Deep Beams with Porosity, International Journal of Applied Mechanics Vol. 9, No. 5 (2017) 1750076
[19] Touloukian YS. Thermophysical properties of high-temperature solid materials. New York: McMillan; 1967.
[20] Sekhar A.S., Prasad P.B. Dynamic analysis of a rotor system considering a slant crack in the shaft. Journal of Sound and Vibration (1997) 208(3), 457–474
[21] ANSYS Theory Manual
[22] Gayen D, Chakraborty D, Tiwari R, Whirl frequencies and critical speeds of a rotor-bearing system with a cracked functionally graded shaft – Finite element analysis, European Journal of Mechanics / A Solids (2016)