Browse > Article
http://dx.doi.org/10.12989/sem.2010.36.2.149

Nonlinear vibrations of axially moving beams with multiple concentrated masses Part I: primary resonance  

Sarigul, M. (Department of Mechanical Engineering, Celal Bayar University)
Boyaci, H. (Department of Mechanical Engineering, Celal Bayar University)
Publication Information
Structural Engineering and Mechanics / v.36, no.2, 2010 , pp. 149-163 More about this Journal
Abstract
Transverse vibrations of axially moving beams with multiple concentrated masses have been investigated. It is assumed that the beam is of Euler-Bernoulli type, and both ends of it have simply supports. Concentrated masses are equally distributed on the beam. This system is formulated mathematically and then sought to find out approximately solutions of the problem. Method of multiple scales has been used. It is assumed that axial velocity of the beam is harmonically varying around a mean-constant velocity. In case of primary resonance, an analytical solution is derived. Then, the effects of both magnitude and number of the concentrated masses on nonlinear vibrations are investigated numerically in detail.
Keywords
axially moving beam; concentrated mass; method of multiple scales; nonlinear vibrations;
Citations & Related Records

Times Cited By Web Of Science : 0  (Related Records In Web of Science)
Times Cited By SCOPUS : 0
연도 인용수 순위
  • Reference
1 Lee, U. and Jang, I. (2007), "On the boundary conditions for axially moving beams", J. Sound Vib., 306, 675-690.   DOI
2 Nayfeh, A.H. (1981), Introduction to Perturbation Techniques, Willey, New York.
3 Ozkaya, E., Sarigul, M. and Boyaci, H. (2009), "Nonlinear transverse vibrations of a slightly curved beam carrying a concentrated mass", Acta Mech. Sinica, 25(6), 871-882.   DOI   ScienceOn
4 Parker, R.G. and Lin, Y. (2001), "Parametric instability of axially moving media subjected to multifrequency tension and speed fluctuations", J. Appl. Mech., 68(1), 49-57.   DOI   ScienceOn
5 Pasin, F. (1972), "Ueber die stabilitat der beigeschwingungen von in laengsrichtung periodisch hin und herbewegten staben", Ingenieur-Archiv, 41, 387-393.   DOI   ScienceOn
6 Pellicano, F. and Vestroni, F. (2002), "Complex dynamics of high-speed axially moving systems", J. Sound Vib., 258(1), 31-44.   DOI   ScienceOn
7 Pellicano, F. and Zirilli, F. (1998), "Boundary layers and non-linear vibrations in an axially moving beam", Int. J. Nonlin. Mech., 33, 691-711.   DOI   ScienceOn
8 Pellicano, F., Fregolent, A., Bertuzzi, A. and Vestroni, F. (2001), "Primary and parametric non-linear resonances of a power transmission belt: Experimental and theoretical analysis", J. Sound Vib., 244(4), 669-684.   DOI   ScienceOn
9 Simpson, A. (1973), "Transverse modes and frequencies of beams translating between fixed end supports", J. Mech. Eng. Sci., 15, 159-164.   DOI   ScienceOn
10 Abrate, A.S. (1992), "Vibration of belts and belt drives", Mech. Mach. Theory, 27, 645-659.   DOI   ScienceOn
11 Chakraborty, G., Mallik, A.K. and Hatwal, H. (1999), "Non-linear vibration of a traveling beam", Int. J. Nonlin. Mech., 34, 655-670.   DOI   ScienceOn
12 Chen, L.Q. and Yang, X.D. (2007), "Nonlinear free transverse vibration of an axially moving beam; Comparison of two models", J. Sound Vib., 299, 348-354.   DOI
13 Koivurova, H. (1998), "Dynamic behaviour of an axially moving membrane interacting with the surrounding air and making contact with supporting structures", Academic Dissertation of the Faculty of Technology, University of Oulu, Finland.
14 Ozkaya, E. and Oz, H.R. (2002), "Determination of natural frequencies and stability region of axially moving beams using artifical neural networks method", J. Sound Vib., 252, 782-789.   DOI   ScienceOn
15 Stylianou, M. and Tabarrok, B. (1994), "Finite element analysis of an axially moving beam, part 2: stability analysis", J. Sound Vib., 178, 455-481.   DOI   ScienceOn
16 Stylianou, M. and Tabarrok, B. (1994), "Finite element analysis of an axially moving beam, part 1: time integration", J. Sound Vib., 178, 433-453.   DOI   ScienceOn
17 Tang, Y.Q., Chen, L.Q. and Yang, X.D. (2008), "Natural frequencies, modes and critical speeds of axially moving Timoshenko beams with different boundary conditions", Int. J. Mech. Sci., 50(10-11), 1148-1458.
18 Ulsoy, A.G., Mote, Jr. and Syzmani, R. (1978), "Principal developments in band saw vibration and stability research", Holz Roh-Werkst, 36, 273-280.   DOI
19 Wickert, J.A. and Mote, C.D. (1988), "Current research on the vibration and stability of axially moving materials", Shock Vib. Dig., 20(5), 3-13.   DOI
20 Wickert, J.A. and Mote, C.D. (1990), "Classical vibration analysis of axially moving contina", J. Appl. Mech., 57, 738-744.   DOI
21 Oz, H.R., Pakdemirli, M. and Ozkaya, E. (1998), "Transition behavior from string to beam for an axially accelarating material", J. Sound Vib., 215, 571-576.   DOI   ScienceOn
22 Wickert, J.A. and Mote, C.D. (1991), "Response and discretization methods for axially moving materials", J. Appl. Mech., 44, 279-284.   DOI
23 Oz, H.R. (2001), "On the vibrations of an axially travelling beam on fixed supports with variable velocity", J. Sound Vib., 239, 556-564.   DOI   ScienceOn
24 Oz, H.R. (2003), "Natural frequencies of axially travelling tensioned beams in contact with a stationary mass", J. Sound Vib., 259, 445-456.   DOI   ScienceOn
25 Oz, H.R., Pakdemirli, M. and Boyac , H. (2001), "Non-linear vibrations and stability of an axially moving beam with time-dependent velocity", Int. J. Nonlin. Mech., 36, 107-115.   DOI   ScienceOn
26 Ozkaya, E. and Pakdemirli, M. (2000), "Vibrations of an axially accelerating beam with small flexural stiffness", J. Sound Vib., 234, 521-535.   DOI   ScienceOn
27 Ravindra, B. and Zhu, W.D. (1998), "Low dimensional chaotic response of axially accelerating continuum in the supercritical regime", Achieve Appl. Mech., 68, 195-205.   DOI   ScienceOn