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http://dx.doi.org/10.12989/sem.2007.27.1.017

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)
Publication Information
Structural Engineering and Mechanics / v.27, no.1, 2007 , pp. 17-32 More about this Journal
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
non-linear vibration; stability; perturbation method; viscoelastic foundation;
Citations & Related Records

Times Cited By Web Of Science : 6  (Related Records In Web of Science)
Times Cited By SCOPUS : 9
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1 Wickert, J.A. and Mote, Jr, C.D. (1998), 'On the energetics of axially moving continua', J. Acoust. Soc. Am., 85, 1365-1368   DOI
2 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   DOI   ScienceOn
3 Kartik, V. and Wickert, J.A. (2006), 'Vibration and guiding of moving media with edge weave imperfections', J. Sound Vib., 291, 419-436   DOI   ScienceOn
4 Zhang, N.H. and Chen, L.Q. (2005), 'Non-linear dynamical analysis of axially moving viscoelastic string', Chaos Soliton. Fract., 24, 1065-1074   DOI   ScienceOn
5 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   DOI   ScienceOn
6 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   DOI   ScienceOn
7 Hou, Z. and Zu, J.W. (2002), 'Non-linear free oscillations of moving viscoelastic belts', Mech. Mach. Theory, 37, 925-940   DOI   ScienceOn
8 Chen, L.Q. (2005), 'Analysis and control of transverse vibrations of axially moving strings', Appl. Mech. Rev., 58,91-115   DOI   ScienceOn
9 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   DOI   ScienceOn
10 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   DOI   ScienceOn
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 Kevorkian, J. and Cole, J.D. (1981), Perturbation Methods in Applied Mathematics, New York, Springer-Verlag
13 Nayfeh, A.H. (1981), Introduction to Perturbation Techniques, New York, Wiley
14 Nayfeh, A.H. (1993), Problems in Perturbation, New York, Wiley
15 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   DOI   ScienceOn
16 Pakdemirli, M. and Ozkaya, E. (1998), 'Approximate boundary layer solution of a moving beam problem', Math. Comput. Appl., 2(3), 93-100
17 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
18 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   DOI   ScienceOn
19 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   DOI
20 Thomsen, J.J. (2003), Vibrations and Stability, Springer-Verlag, Germany
21 Wickert, J.A. (1992), 'Non-linear vibration of a traveling tensioned beam', Int. J. Nonlinear. Mech., 27, 503-517   DOI   ScienceOn
22 Wickert, J.A. and Mote, C.D. (1991), 'Traveling load response of an axially noving string', J. Sound Vib., 49(2),267-284