Advertisement

Acta Mechanica Solida Sinica

, Volume 24, Issue 4, pp 373–382 | Cite as

On the Natural Frequencies, Complex Mode Functions, and Critical Speeds of Axially Traveling Laminated Beams: Parametric Study

  • Mergen H. Ghayesh
Article

Abstract

The dynamic response of an axially traveling laminated composite beam is investigated analytically, with special consideration to natural frequencies, complex mode functions and critical speeds of the system. The equation of motion for a symmetrically laminated system, which is in the form of a continuous gyroscopic system, is considered; the equation of motion is not discretized — no spatial mode function is assumed. This leads to analytical expressions for the complex mode functions and critical speeds. A parametric study has been conducted in order to highlight the effects of system parameters on the above-mentioned vibration characteristics of the system.

Key words

vibration gyroscopic systems critical speeds 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Wickert, J.A. and Mote, C.D., Current research on the vibration and stability of moving materials. The Shock and Vibration Digest, 1988, 20: 3–13.CrossRefGoogle Scholar
  2. [2]
    Chen, L.Q., Analysis and control of transverse vibrations of axially moving strings. Applied Mechanics Reviews, 2005, 20: 91–116.CrossRefGoogle Scholar
  3. [3]
    Baker, A., Dutton, S. and Kelly, D., Composite Materials for Aircraft Structures. AIAA Education Series, 2004.Google Scholar
  4. [4]
    Thurman, A.L. and Mote, C.D., Free, periodic, nonlinear oscillation of an axially moving strip. ASME Journal of Applied Mechanics, 1969, 36: 83–91.CrossRefGoogle Scholar
  5. [5]
    Tabarrok, B., Leech, C.M. and Kim, Y.I., On the dynamics of an axially moving beam. Journal of the Franklin Institute, 1974, 297: 201–220.CrossRefGoogle Scholar
  6. [6]
    Hwang, S.-J. and Perkins, N.C., Supercritical stability of an axially moving beam, Part 2: Vibration and stability analysis. Journal of Sound and Vibration, 1992, 154(3): 397–409.CrossRefGoogle Scholar
  7. [7]
    Parker, R.G., Supercritical speed stability of the trivial equilibrium of an axially-moving string on an elastic foundation. Journal of Sound and Vibration, 1999, 221: 205–219.CrossRefGoogle Scholar
  8. [8]
    Pellicano, F. and Vestroni, F., Nonlinear dynamics and bifurcations of an axially moving beam. Journal of Vibration and Acoustics, 2000, 122: 21–30.CrossRefGoogle Scholar
  9. [9]
    Suweken, G. and Horssen, W.T.V., On the weakly nonlinear, transversal vibrations of a conveyor belt with a low and time-varying velocity. Nonlinear Dynamics, 2003, 31: 197–223.MathSciNetCrossRefGoogle Scholar
  10. [10]
    Koivurova, H., The numerical study of the nonlinear dynamic of a light, axially moving string. Journal of Sound and Vibration, 2009, 320: 373–385.CrossRefGoogle Scholar
  11. [11]
    Hedrih, K., Transversal vibrations of axially moving sandwich belts. Archive of Applied Mechanics, 2007, 77: 523–539.CrossRefGoogle Scholar
  12. [12]
    Pakdemirli, M., Ulsoy, A.G. and Ceranoglu, A., Transverse vibration of an axially accelerating string. Journal of Sound and Vibration, 1994, 169: 179–196.CrossRefGoogle Scholar
  13. [13]
    Pakdemirli, M. and Ulsoy, A.G., Stability analysis of an axially accelerating string. Journal of Sound and Vibration, 1997, 203: 815–832.CrossRefGoogle Scholar
  14. [14]
    Pakdemirli, M. and Ozkaya, E., Approximate boundary layer solution of a moving beam problem. Mathematical and Computational Applications, 1998, 3: 93–100.CrossRefGoogle Scholar
  15. [15]
    Öz, H.R. and Pakdemirli, M., Vibrations of an axially moving beam with time dependent velocity. Journal of Sound and Vibration, 1999, 227: 239–257.CrossRefGoogle Scholar
  16. [16]
    Zhang, N.H. and Chen, L.Q., Nonlinear dynamical analysis of axially moving viscoelastic string. Chaos, Solitons and Fractals, 2005, 24: 1065–1074.CrossRefGoogle Scholar
  17. [17]
    Zhang, N.H., Dynamic analysis of an axially moving viscoelastic string by the Galerkin method using translating string eigenfunctions. Chaos, Solitons and Fractals, 2008, 35: 291–302.MathSciNetCrossRefGoogle Scholar
  18. [18]
    Chen, L.Q. and Yang, X.D., Steady state response of axially moving viscoelastic beams with pulsating speed: comparison of two nonlinear models. International Journal of Solids and Structures, 2005, 42: 37–50.CrossRefGoogle Scholar
  19. [19]
    Chen, L.Q. and Yang, X.D., Vibration and stability of an axially moving viscoelastic beam with hybrid supports. European Journal of Mechanics, 2006, 25: 996–1008.MathSciNetCrossRefGoogle Scholar
  20. [20]
    Chen, L.Q., Tang, Y.Q. and Lim, C.W., Dynamic stability in parametric resonance of axially accelerating viscoelastic Timoshenko beams. Journal of Sound and Vibration, 2010, 329: 547–565.CrossRefGoogle Scholar
  21. [21]
    Chen, L.Q. and Zhao, W.J., A conserved quantity and the stability of axially moving nonlinear beams. Journal of Sound and Vibration, 2005, 286: 663–668.CrossRefGoogle Scholar
  22. [22]
    Chen, L.Q., Zhao, W.J. and Zu, J.W., Simulation of transverse vibrations of an axially moving string: a modified difference approach. Applied Mathematics and Computation, 2005, 166: 596–607.MathSciNetCrossRefGoogle Scholar
  23. [23]
    Chen, L.Q., The energetics and the stability of axially moving string undergoing planar motion. International Journal of Engineering Science, 2006, 44: 1346–1352.MathSciNetCrossRefGoogle Scholar
  24. [24]
    Tang, Y.Q., Chen, L.Q. and Yang, X.D., Parametric resonance of axially moving Timoshenko beams with time-dependent speed. Nonlinear Dynamics, 2009, 58: 715–724.CrossRefGoogle Scholar
  25. [25]
    Tang, Y.Q., Chen, L.Q. and Yang, X.D., Non-linear vibrations of axially moving Timoshenko beams under weak and strong external excitations. Journal of Sound and Vibration, 2009, 320: 1078–1099.CrossRefGoogle Scholar
  26. [26]
    Yang, X.D., Tang, Y.Q., Chen, L.Q. and Lim, C.W., Dynamic stability of axially accelerating Timoshenko beams: averaging method. European Journal of Mechanics A/Solid, 2010, 29: 81–90.MathSciNetCrossRefGoogle Scholar
  27. [27]
    Ghayesh, M.H., Nonlinear transversal vibration and stability of an axially moving viscoelastic string supported by a partial viscoelastic guide. Journal of Sound and Vibration, 2008, 314: 757–774.CrossRefGoogle Scholar
  28. [28]
    Ghayesh, M.H. and Balar, S., Non-linear parametric vibration and stability of axially moving visco-elastic Rayleigh beams. International Journal of Solids and Structures, 2008, 45: 6451–6467.CrossRefGoogle Scholar
  29. [29]
    Ghayesh, M.H., Stability characteristics of an axially accelerating string supported by an elastic foundation. Mechanism and Machine Theory, 2009, 44: 1964–1979.CrossRefGoogle Scholar
  30. [30]
    Ghayesh, M.H. and Balar, S., Non-linear parametric vibration and stability analysis for two dynamic models of axially moving Timoshenko beams. Applied Mathematical Modelling, 2010, 34: 2850–2859.MathSciNetCrossRefGoogle Scholar
  31. [31]
    Ghayesh, M.H., Parametric vibrations and stability of an axially accelerating string guided by a non-linear elastic foundation. International Journal of Non-Linear Mechanics, 2010, 45: 382–394.CrossRefGoogle Scholar
  32. [32]
    Ghayesh, M.H. and Moradian, N., Nonlinear dynamic response of axially moving, stretched viscoelastic strings. Archive of Applied Mechanics, 2011, 81: 781–799.CrossRefGoogle Scholar
  33. [33]
    Ghayesh, M.H., Yourdkhani, M., Balar, S. and Reid, T., Vibrations and stability of axially traveling laminated beams. Applied Mathematics and Computation, 2010, 217: 545–556.MathSciNetCrossRefGoogle Scholar
  34. [34]
    Agarwal, B.D., Broutman, L.J. and Chandrashekhara, K., Analysis and Performance of Fiber Composites. New York: Wiley, 2006.Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2011

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringMcGill UniversityMontrealCanada

Personalised recommendations