Browse > Article
http://dx.doi.org/10.12989/sem.2017.61.4.551

An approximate spectral element model for the dynamic analysis of an FGM bar in axial vibration  

Lee, Minsik (Department of Mechanical Engineering, Inha University)
Park, Ilwook (Department of Mechanical Engineering, Inha University)
Lee, Usik (Department of Mechanical Engineering, Inha University)
Publication Information
Structural Engineering and Mechanics / v.61, no.4, 2017 , pp. 551-561 More about this Journal
Abstract
As FGM (functionally graded material) bars which vibrate in axial or longitudinal direction have great potential for applications in diverse engineering fields, developing a reliable mathematical model that provides very reliable vibration and wave characteristics of a FGM axial bar, especially at high frequencies, has been an important research issue during last decades. Thus, as an extension of the previous works (Hong et al. 2014, Hong and Lee 2015) on three-layered FGM axial bars (hereafter called FGM bars), an enhanced spectral element model is proposed for a FGM bar model in which axial and radial displacements in the radial direction are treated more realistic by representing the inner FGM layer by multiple sub-layers. The accuracy and performance of the proposed enhanced spectral element model is evaluated by comparison with the solutions obtained by using the commercial finite element package ANSYS. The proposed enhanced spectral element model is also evaluated by comparison with the author's previous spectral element model. In addition, the effects of Poisson's ratio on the dynamics and wave characteristics in example FGM bars are numerically investigated.
Keywords
functionally graded material (FGM); three-layered FGM axial bar; spectral element method; dynamic responses; waves;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 ANSYS Release 11.0 (2006), Documentation for ANSYS, ANSYS, Inc, Canonsburg, PA, USA.
2 Chakraborty, A. and Gopalakrishinan, S. (2003), "A spectrally formulated finite element for wave propagation in functionally graded beams", Int. J. Solid. Struct., 40(10), 2421-2448.   DOI
3 Mashat, D.S., Carrera, E., Zenkour, A.M., Khateeb, S.A.A. and Filippi, M. (2014), "Free vibration of FGM layered beams by various theories and finite elements", Compos. Part B-Eng., 59, 269-278.   DOI
4 Meirovitch, L. (1967), Analytical Methods in Vibrations, Macmillan, London.
5 Menaa, R., Tounsi, A., Mouaici, F., Mechab, I., Zidi, M. and Bedia, E.A.A. (2012), "Analytical solutions for static shear correction factor of functionally graded rectangular beams", Mech. Adv. Mater. Struct., 19(8), 641-652.   DOI
6 Murin, J., Aminbaghai, M., Hrabovsky, J., Kutis, V. and Kugler, S. (2013), "Modal analysis of the FGM beams with effect of the shear correction function", Compos. Part B-Eng., 45(1), 1575-1582.   DOI
7 Murin, J., Aminbaghai, M., Hrabovsky, J., Gogola, R. and Kugler, S. (2016), "Beam finite element for modal analysis of FGM structures", Eng. Struct., 121, 1-18.   DOI
8 Murin, J., Kutis, V. and Masny, M. (2008), "An effective solution of electro-thermo-structural problem of uni-axially graded material", Struct. Eng. Mech., 28(6), 695 -713.   DOI
9 Hong, M. and Lee, U. (2015), "Dynamics of a functionally graded material axial bar: spectral element modeling and analysis", Compos. Part B-Eng., 69, 427-434.   DOI
10 Hong, M., Park, I. and Lee, U. (2014), "Dynamics and waves characteristics of the FGM axial bars by using spectral element method", Compos. Struct., 107, 585-593.   DOI
11 Horgan, C.O. (1999), "The pressurized hollow cylinder or disk problem for functionally graded isotropic linearly elastic materials", J. Elasticity, 55(1), 43-59.   DOI
12 Horgan, C.O. (2007), "On the torsion of functionally graded anisotropic linearly elastic bars", IMA J. Appl. Math., 72(5), 556-562.   DOI
13 Huang, Y. and Li, X.F. (2010), "A new approach for free vibration of axially functionally graded beams with non-uniform crosssection", J. Sound Vib., 329(11), 2291-2303.   DOI
14 Kreyszig, E. (1972), Advanced Engineering Mathematics, John Wiley & Sons, New York.
15 Kutis, V. and Murin, J. (2006), "Stability of slender beam-column with locally varying Young's modulus", Struct. Eng. Mech. 23(1), 15-27   DOI
16 Lee, U. (2009), Spectral Element Method in Structural Dynamics, John Wiley & Sons, Singapore.
17 Li, X.F. (2008), "A unified approach for analyzing static and dynamic behavior of functionally graded Timoshenko and Euler-Bernoulli beams", J. Sound Vib. 318(4-5), 1210-1229.   DOI
18 Efraim, E. and Eisenberger, M. (2007), "Exact solution analysis of variable thickness thick annular isotropic and FGM plates", J. Sound Vib., 299(4-5), 720-738.   DOI
19 Maalawi, K.Y. (2011), "Functionally graded bars with enhanced dynamic performance", J. Mech. Mater. Struct., 6(1-4), 377-393.   DOI
20 Murin, J., Kutis, V., Paulech, J. and Hrabovsky, J. (2011), "Electric-thermal link finite element made of FGM with spatially variation of material properties", Compos. Part B-Eng., 42, 1966-1979.   DOI
21 Newland, D.E. (1993), Random Vibrations: Spectral and Wavelet Analysis, Longman, New York.
22 Parker, D.F. (2009), "Waves and statics for functionally graded materials and laminates", Int. J. Eng. Sci., 47(11-12), 1315-1321.   DOI
23 MATLAB User's Guide (1993), MathWorks, Natick, MA, USA.
24 Nguyen, T.K., Vo, T.P. and Thai, H.T. (2013), "Static and free vibration of axially loaded functionally graded beams based on the first-order shear deformation theory", Compos. Part B-Eng., 55, 147-157.   DOI
25 Markworth, A.J., Ramesh, K.S. and Parks Jr., W.P. (1995), "Modeling studies applied to functionally graded materials", J. Mater. Sci., 30(9), 2183-2193.   DOI
26 Xiang, H.J. and Yang, J. (2008), "Free and forced vibration of a laminated FGM Timoshenko beam of variable thickness under heat conduction", Compos. Part B-Eng., 39(2), 292-303.   DOI
27 Pradhan, K.K. and Chakraverty, S. (2013), "Free vibration of Euler and Timoshenko functionally graded beams by Rayleigh-Ritz method", Compos. Part B-Eng., 51, 175-184.   DOI
28 Shahba, A., Attarnejad, R. and Hajilar, S. (2011), "Free vibration and stability of axially functionally graded tapered Euler-Bernoulli beams", Shock Vib., 18(5), 683-696.   DOI
29 Timoshenko, S.P. and Goodier, J.N. (1934), Theory of Elasticity, McGraw-Hill, New York.
30 Yu, Z. and Chu, F. (2009), "Identification of crack in functionally graded material beams using the p-version of finite element method", J. Sound. Vib., 325(1-2), 69-84.   DOI