Structural Engineering and Mechanics

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Non-linear vibration and stability analysis of a partially supported conveyor belt by a distributed viscoelastic foundation

  • Ghayesh, M.H. (Mechanical & Aerospace Engineering Department, Tarbiat Modarres University) ;
  • Khadem, S.E. (Mechanical & Aerospace Engineering Department, Tarbiat Modarres University)
  • Received : 2006.07.13
  • Accepted : 2007.04.10
  • Published : 2007.09.10
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Abstract

The main source of transverse vibration of a conveyor belt is frictional contact between pulley and belt. Also, environmental characteristics such as natural dampers and springs affect natural frequencies, stability and bifurcation points of system. These phenomena can be modeled by a small velocity fluctuation about mean velocity. Also, viscoelastic foundation can be modeled as the dampers and springs with continuous characteristics. In this study, non-linear vibration of a conveyor belt supported partially by a distributed viscoelastic foundation is investigated. Perturbation method is applied to obtain a closed form analytic solutions. Finally, numerical simulations are presented to show stiffness, damping coefficient, foundation length, non-linearity and mean velocity effects on location of bifurcation points, natural frequencies and stability of solutions.

Keywords

References

  1. Chen, L.Q. (2005), 'Analysis and control of transverse vibrations of axially moving strings', Appl. Mech. Rev., 58,91-115 https://doi.org/10.1115/1.1849169
  2. Chen, L.Q. and Yang, X.D. (2005), 'Steady state response of axially moving viscoelastic beams with pulsating speed: Comparison of two nonlinear models', Int. J. Solids Struct., 42, 37-50 https://doi.org/10.1016/j.ijsolstr.2004.07.003
  3. Chen, L.Q. and Zhao, W.J. (2005), 'A conserved quantity and the stability of axially moving non-linear beams', J. Sound Vib., 286, 663-668 https://doi.org/10.1016/j.jsv.2005.01.011
  4. Chen, L.Q., Zhabo, W.J. and Zu, J.W. (2005), 'Simulation of transverse vibrations of an axially moving string: A modified difference approach', Appl. Math. Comput., 166, 596-607 https://doi.org/10.1016/j.amc.2004.07.006
  5. Chen, L.Q., Zhang, N.H. and Zu, J.W. (2002), 'Bifurcation and chaos of an axially moving viscoelastic string', Mech. Res. Commun., 29,81-90 https://doi.org/10.1016/S0093-6413(02)00241-0
  6. Hou, Z. and Zu, J.W. (2002), 'Non-linear free oscillations of moving viscoelastic belts', Mech. Mach. Theory, 37, 925-940 https://doi.org/10.1016/S0094-114X(02)00031-9
  7. Kartik, V. and Wickert, J.A. (2006), 'Vibration and guiding of moving media with edge weave imperfections', J. Sound Vib., 291, 419-436 https://doi.org/10.1016/j.jsv.2005.06.021
  8. Kevorkian, J. and Cole, J.D. (1981), Perturbation Methods in Applied Mathematics, New York, Springer-Verlag
  9. Nayfeh, A.H. (1981), Introduction to Perturbation Techniques, New York, Wiley
  10. Nayfeh, A.H. (1993), Problems in Perturbation, New York, Wiley
  11. Oz, H.R. and Pakdemirli, M. (1999), 'Vibrations of an axially moving beam with time-dependent velocity', J. Sound Vib., 27, 239-257
  12. Oz, H.R., Pakdemirli, M. and Boyaci, H. (2001), 'Non-linear vibrations and stability of an axially moving beam with time-dependent velocity', Int. J. Nonlinear Mech., 36, 107-115 https://doi.org/10.1016/S0020-7462(99)00090-6
  13. Pakdemirli, M. and Ozkaya, E. (1998), 'Approximate boundary layer solution of a moving beam problem', Math. Comput. Appl., 2(3), 93-100
  14. Parker, R.G. (1999), 'Supercritical speed stability of the trivial equilibrium of an axially-moving string on an elastic foundation', J. Sound Vib., 221(2), 205-219 https://doi.org/10.1006/jsvi.1998.1936
  15. Suweken, G. and Van Horssen, W.T. (2003a), 'On the transversal vibrations of a conveyor belt with a low and time varying velocity. Part I: The string like case', J. Sound Vib., 267,117-133
  16. Suweken, G. and Van Horssen, W.T. (2003b), 'On the transversal vibrations of a conveyor belt with a low and time varying velocity. Part II: The beam like case', J. Sound Vib., 267, 1007-1027 https://doi.org/10.1016/S0022-460X(03)00219-0
  17. Suweken, G. and Van Horssen, W.T. (2003c), 'On the weakly nonlinear, transversal vibrations of a conveyor belt with a low and time-varying velocity', Nonlinear Dynam., 31, 197-223 https://doi.org/10.1023/A:1022053131286
  18. Thomsen, J.J. (2003), Vibrations and Stability, Springer-Verlag, Germany
  19. Wickert, J.A. (1992), 'Non-linear vibration of a traveling tensioned beam', Int. J. Nonlinear. Mech., 27, 503-517 https://doi.org/10.1016/0020-7462(92)90016-Z
  20. Wickert, J.A. and Mote, C.D. (1991), 'Traveling load response of an axially noving string', J. Sound Vib., 49(2),267-284
  21. Wickert, J.A. and Mote, Jr, C.D. (1998), 'On the energetics of axially moving continua', J. Acoust. Soc. Am., 85, 1365-1368 https://doi.org/10.1121/1.397418
  22. Zhang, N.H. and Chen, L.Q. (2005), 'Non-linear dynamical analysis of axially moving viscoelastic string', Chaos Soliton. Fract., 24, 1065-1074 https://doi.org/10.1016/j.chaos.2004.09.113

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