Free Vibration Analysis Of Thick Functionally Graded Rotating Beam By Differential Transform Method

Abstract

In this paper, the free vibration of a functionally graded (FG) rotating beam based on Timoshenko beam theory has been
analyzed. The FG rotating beam assumed to be graded across the thickness and the material properties of the FG beam
assumed to vary continuously through the thickness of the beam according to a power law distribution of the volume
fraction of the constituent materials. Governing equations are solved using differential transform method. To verify the
present analysis, the results of this study are compared with the available results from the existing literature. The effect
of beam parameters such as constituent volume fractions, slenderness ratios, hub rotation speed and hub radius on the
natural frequencies and mode shapes of the rotating beam is comprehensively investigated. The functionally graded
composite material plays a significant role in vibration characteristics of the rotating FGM thick beams.

Keywords

p>Smiley face

References

  1. Zhou, J.K. "Differential Transformation and Its
    Application for Electrical Circuits", Huazhong
    University Press, Wuhan China, 1986.
    2. Ho, S.H., and Chen, C.K. "Free Transverse
    Vibration of an Axially Loaded Non-uniform
    Spinning Twisted Timoshenko Beam Using
    Differential Transform." International Journal of
    Mechanical Sciences Vol. 48, No. 11, pp. 1323-
    1331, 2006.
    3. Mei, C. "Application of Differential Transformation
    Technique to Free Vibration Analysis of a
    Centrifugally Stiffened Beam", Comput. Struct,
    Vol. 86, No,s. 11-12, 2008.
    4. Hodges, D.H. and Rutkowski, M.J. "Free Vibration
    Analysis of Rotating Beams by a Variable Order
    Finite Element Method", American Institute of
    Aeronautics and Astronautics Journal, Vol. 19, No.
    11, pp. 1459-1466, 1981.
    5. Wright, A., Smith, C., Thresher, R. and Wang, J.
    "Vibration Modes of Centrifugally Stiffened
    Beams", Journal of Applied Mechanics, Vol. 49,
    No. 1, pp. 197-202, 1982.
    6. Banerjee, J.R. "Free Vibration of Centrifugally
    Stiffened Uniform and Tapered Beams Using the
    Dynamic Stiffness Method", Journal of Sound and
    Vibration, Vol. 233, No. 5, pp. 857-875, 1999.
    7. Stafford, R.O. and Giurgiutiu, V. "Semi-analytic
    Methods for Rotating Timoshenko Beams",
    International Journal of Mechanical Sciences Vol.
    17, No,s. 11-12, pp. 719-727, 1975.
    8. Giurgiutiu, V. and Stafford R.O. "Semi-analytic
    Methods for Frequencies and Mode Shapes of
    Rotor Blades", Erotica, Vol. 1, pp. 291-306, 1977
    9. Yokoyama, T., "Free Vibration Characteristics of
    Rotating Timoshenko Beams", International Journal
    of Mechanical Sciences, Vol. 30, No. 10, pp. 743-
    755, 1988.
    10. Du, H., Lim, M.K. and Liew K.M. "A Power Series
    Solution for Vibration of a Rotating Timoshenko
    Beam", Journal of Sound and vibration Vol. 175,
    No. 4, pp. 505-523, 1994.
    11. Reddy, J.N., "On the Dynamic Behavior of the
    Timoshenko Beam Finite Elements". Sadhana, Vol.
    24, No. 3, pp. 175–98, 1997.
    12. Kaya, M.O., "Free Vibration Analysis of a Rotating
    Timoshenko Beam by Differential Transform
    Method". Aircraft Engineering and Aerospace
    Technology. Vol. 78, No. 3, pp. 194–203, 2006.
    13. Civalek, O. Kiracioglu, O. “Free Vibration Analysis
    of Timoshenko Beams by DSC Method”.
    Communications in Numerical Methods in
    Engineering, 2009
    14. Li, X.F. “A Unified Approach for Analyzing Static
    and Dynamic Behaviors of Functionally Graded
    Timoshenko and Euler-Bernoulli Beam”, Journal of
    Sound and Vibration, Composite Structures, Vol.
    82,No.3 pp. 390-402 , 2008.
    15. Kapuria, S., Bhattacharyya, M., and Kumar, A.N.
    “Bending and Free Vibration Response of Layered
    Functionally Graded Beams, a Theoretical Model
    and its Experimental Validation”. Composite
    Structure, Vol. 82, No. 3, pp. 390-402, 2008.
    16. Ke, L.L., Yang, J., and Kitippornachi, S. “An
    analytical Study on Nonlinear Vibration of
    Functionally Graded Beams”. Meccanica, Vol. 45,
    No. 6, pp. 743-752, 2010.
    17. Jafari A, and Fathabadi M. “Forced Vibration of
    FGM Timoshenko Beam with Piezoelectric Layers
    Carrying Moving Load”. Aerospace Mechanics
    Journal, Vol. 9, No. 2, pp. 69-77, 2013(In Persian).
    18. Mousavi Z. “Free Vibration Analysis of Thick
    Functionally Graded Rectangular Plates Based on
    The Higher-Order Shear and Normal Deformable”.
    Aerospace Mechanics Journal. Vol. 12, No. 1, pp.
    1-12, 2016 (In Persian).
    19. Pradhan, K.K., Chakraverty , S. "Free vibration of
    Euler and Timoshenko Functionally Graded Beams
    by Rayleigh – Ritz Method" , Composites Part B:
    Engineering Vol. 51 , pp. 175-184, 2013.
    20. Sina, S.A., Navazi, H.M. and Haddadpour, H. "An
    Analytical Method for Free Vibration Analysis of
    Functionally Graded Beams". Materials and Design,
    Vol. 30, No. 3, pp. 741–747, 2009.
    21. Şimşek M. "Fundamental Frequency Analysis of
    Functionally Graded Beams by Using Different
    Higher-order Beam Theories". Nucl Eng Des, Vol.
    240, No. 4, pp.697-705, 2010.
    22. Shahba, A., Attarnejad, R., Zarrinzadeh, H. "Free
    Vibration Analysis of Centrifugally Stiffened
    Tapered Functionally Graded Beams". Mechanics
    of Advanced Materials and Structures, Vol. 20, pp.
    331–338, 2013
    23. Abdel-Halim Hassan, I.H. "On Solving Some
    Eigenvalue Problems by Using a Differential
    Transformation" Applied Mathematics and
    Computation, Vol. 127, No. 1, pp. 1-22, 2012.

Files

History

  • Receive Date: 15 May 2016
  • Revise Date: 02 December 2016
  • Accept Date: 17 January 2017
  • Publish Date: 07 February 2017

Share

How to cite

Statistics