Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

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)
  • Received : 2016.06.28
  • Accepted : 2017.01.18
  • Published : 2017.02.25
⟨ Previous Next ⟩

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

Acknowledgement

Supported by : Inha University

References

  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. https://doi.org/10.1016/S0020-7683(03)00029-5
  3. 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. https://doi.org/10.1016/j.jsv.2006.06.068
  4. 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. https://doi.org/10.1016/j.compstruct.2013.08.022
  5. 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. https://doi.org/10.1016/j.compositesb.2014.10.022
  6. Horgan, C.O. (1999), "The pressurized hollow cylinder or disk problem for functionally graded isotropic linearly elastic materials", J. Elasticity, 55(1), 43-59. https://doi.org/10.1023/A:1007625401963
  7. Horgan, C.O. (2007), "On the torsion of functionally graded anisotropic linearly elastic bars", IMA J. Appl. Math., 72(5), 556-562. https://doi.org/10.1093/imamat/hxm027
  8. 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. https://doi.org/10.1016/j.jsv.2009.12.029
  9. Kreyszig, E. (1972), Advanced Engineering Mathematics, John Wiley & Sons, New York.
  10. Kutis, V. and Murin, J. (2006), "Stability of slender beam-column with locally varying Young's modulus", Struct. Eng. Mech. 23(1), 15-27 https://doi.org/10.12989/sem.2006.23.1.015
  11. Lee, U. (2009), Spectral Element Method in Structural Dynamics, John Wiley & Sons, Singapore.
  12. 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. https://doi.org/10.1016/j.jsv.2008.04.056
  13. Maalawi, K.Y. (2011), "Functionally graded bars with enhanced dynamic performance", J. Mech. Mater. Struct., 6(1-4), 377-393. https://doi.org/10.2140/jomms.2011.6.377
  14. 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. https://doi.org/10.1007/BF01184560
  15. 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. https://doi.org/10.1016/j.compositesb.2013.12.008
  16. MATLAB User's Guide (1993), MathWorks, Natick, MA, USA.
  17. Meirovitch, L. (1967), Analytical Methods in Vibrations, Macmillan, London.
  18. 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. https://doi.org/10.1080/15376494.2011.581409
  19. 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. https://doi.org/10.1016/j.compositesb.2012.09.084
  20. 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. https://doi.org/10.1016/j.engstruct.2016.04.042
  21. 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. https://doi.org/10.12989/sem.2008.28.6.695
  22. 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. https://doi.org/10.1016/j.compositesb.2011.05.030
  23. Newland, D.E. (1993), Random Vibrations: Spectral and Wavelet Analysis, Longman, New York.
  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. https://doi.org/10.1016/j.compositesb.2013.06.011
  25. Parker, D.F. (2009), "Waves and statics for functionally graded materials and laminates", Int. J. Eng. Sci., 47(11-12), 1315-1321. https://doi.org/10.1016/j.ijengsci.2009.04.001
  26. 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. https://doi.org/10.1016/j.compositesb.2013.02.027
  27. 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. https://doi.org/10.1155/2011/591716
  28. Timoshenko, S.P. and Goodier, J.N. (1934), Theory of Elasticity, McGraw-Hill, New York.
  29. 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. https://doi.org/10.1016/j.compositesb.2007.01.005
  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. https://doi.org/10.1016/j.jsv.2009.03.010