Free and forced vibration of rotating FGM beam with piezoelectric layer

Document Type : Dynamics, Vibrations, and Control

Authors

1 Mechanical engineering department KNTU

2 Vibration research lab. mechanical engineering department KNTU

Abstract

The free and forced vibration of rotating FGM beam with piezoelectric layer using first order shear deformation theory and fixed-free boundary condition have been studied in this article. Rayleigh-Ritz method with Chebyshev series are applied to find the natural frequencies. The results showed the natural frequencies are increased as a result of increasing angular velocity or adding piezoelectric layer. More increasing the natural frequencies are caused by applying the voltage on piezoelectric layer or by increasing hub radius. Moreover, the dynamic response of the beam cause by initial conditions is studied. The frequency of the dynamic response was very near to the first natural frequency of the beam. The results had a good agreement with known reference and Abaqus software results. Also, the influence of harmonic, step and impulse force on forced vibration of the beam has been studied. Decreasing the vibration amplitude of the beam is caused by applying angular velocity and piezoelectric voltage.

Keywords

References

  1. Southwell, R. and Gough, F., “The Free Transverse Vibration of Airscrew Blade,” British A.R.C. Reports and Memoranda, Vol. 76, No. 6, 1921.##
  2. Schilhansl, M., “Bending Frequency of a Rotating Cantilever Beam,” Journal of Applied Mechanics, Vol. 25, pp. 28-30, 1958.##
  3. Yoo, H.H. and Shin, S.H., “Vibration Analysis of Rotating Cantilever Beams,” Journal of Sound and Vibration, Vol. 212, No. 5, pp. 807–828, 1998.##
  4. Lin, S.C. and Hsiao, K.M., “Vibration Analysis of a Rotating Timoshenko Beam,” Journal of Sound and Vibration, Vol. 240, No. 2, pp. 303-322, 2001.##
  5. Choi, S.C. and Park, J.S. and Kim, J.H., “Vibration Control of Pre-Twisted Rotating Composite Thin-Walled Beams With Piezoelectric Fiber Composites,” Journal of Sound and Vibration, Vol. 300, No. 1-2, pp. 176-196, 2007.##
  6. Zarrinzadeh, H. and Attarnejad, R. and Shahba, A., “Free Vibration of Rotating Axially Functionally Graded Tapered Beams,” Journal of Aerospace Engineering, Vol. 226, No. 4, pp. 363-379, 2011.##
  7. Fathabadi, M. and Jafari, A.A., “Forced Vibration of FGM Timoshenko Beam with Piezoelectric Layers Carrying Moving Load,” In Persian, Aerospace Mechanics Journal, Vol. 9, No. 2, pp. 69-77, 2013.(in persian)##
  8. Fang, J.S. and Zhou, D., “Free Vibration Analysis of Rotating Axially Functionally Graded Tapered Timoshenko Beams,” International Journal of Structural Stability and Dynamics, Vol. 16, No. 5, 19 pages, 2015.##
  9. Fang, J.S. and Zhou, D., “Free Vibration Analysis of Rotating Axially Functionally Graded-Tapered Beams Using Chebyshev – Ritz Method,” Materials Research Innovations, Vol. 19, pp. 1255-1262, 2015.##
  10.  Aksencer, T. and Aydogdu, M., “Flapwise Vibration of Rotating Composite Beams,” Composite Structures, Vol. 134, pp. 672-679, 2015.##
  11.  Xiang, H.J. and Yang, J., “Free and Forced Vibration of a Laminated FGM Timoshenko Beam of Variable Thickness Under Heat Conduction,” Composites, Vol. 39, pp. 292-303, 2008.##
  12. Simsek, M. and Kocatürk, T., “Free and Forced Vibration 0f a Functionally Graded Beam
    Subjected to a Concentrated Moving Harmonic Load,” Composite Structures, Vol. 90, pp. 465-473, 2009.##
  13.  Khalili, S.M.R. and Jafari, A.A. and Eftekhari, S.A., “A Mixed Ritz-DQ Method for Forced Vibration of Functionally Graded Beams
    Carrying Moving Loads,” Composite Structures, Vol. 92, pp. 2497-2511, 2010.##
  14.  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.##
  15.  Tavakolian, M. and Jafari, A.A. and Khalili, M.R., “Nonlinear Vibration of Functionally Graded Cylindrical Shells Embedded with a Piezoelectric Layer,” Thin-walled structure, Vol. 79, pp. 8-15, 2014.##
  16.  Chandiramani, N.K. and Librescu, L.I. and Saxena, V. and Kumar, A., “Optimal Vibration Control of a Rotating Composite Beam with Distributed Piezoelectric Sensing and Actuation,” Smart Materials and Structures, Vol. 13, No. 2, pp. 433-442, 2004.##
  17.  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.##
  18.  Rao, S.S., “Vibration of Continuous Systems,” 2th ed., John Wiley & Sons, India, 2019.##
  19.  Beer, F.B. and Johnston, E.R. and Dewolf, J.T. and Mazurek, D.F., “Mechanics of Material,” 6th ed., Mc Graw Hill, America, 2014.##
  20.  Fathabadi, M., “Vibration Analysis of a Functionally Graded Beam with Piezoelectric Layers”, Msc Thesis, KNT University, Faculty of Mechnical Engineering, 2011..##

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History

  • Receive Date: 07 February 2019
  • Revise Date: 15 April 2019
  • Accept Date: 22 April 2019
  • Publish Date: 20 March 2020

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