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Advances in Mechanical Engineering
Volume 2013 (2013), Article ID 169598, 7 pages
http://dx.doi.org/10.1155/2013/169598
Research Article

Effect of Viscoelasticity on the Natural Frequencies of Axially Moving Continua

1Department of Mechanical Engineering, Celal Bayar University, Muradiye, 45140 Manisa, Turkey
2Applied Mathematics and Computation Center, Celal Bayar University, Muradiye, 45140 Manisa, Turkey

Received 29 December 2012; Revised 5 March 2013; Accepted 6 March 2013

Academic Editor: Jianqiao Ye

Copyright © 2013 B. Burak Özhan and Mehmet Pakdemirli. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. G. Ulsoy, C. D. Mote Jr., and R. Szymni, “Principal developments in band saw vibration and stability research,” Holz als Roh- und Werkstoff, vol. 36, no. 7, pp. 273–280, 1978. View at Publisher · View at Google Scholar · View at Scopus
  2. J. A. Wickert and C. D. Mote Jr., “Current research on the vibration and stability of axially moving materials,” Shock and Vibration Digest, vol. 20, no. 5, pp. 3–13, 1988.
  3. J. A. Wickert and C. D. Mote Jr., “Classical vibration analysis of axially moving continua,” Journal of Applied Mechanics, vol. 57, no. 3, pp. 738–744, 1990. View at Scopus
  4. J. A. Wickert and C. D. Mote Jr., “Response and discretization methods for axially moving materials,” Applied Mechanics Reviews, vol. 44, no. 11, pp. 279–284, 1991.
  5. A. G. Ulsoy and C. D. Mote Jr., “Analysis of bandsaw vibration,” Wood Science, vol. 13, no. 1, pp. 1–10, 1980.
  6. W. L. Miranker, “The wave equation in a medium motion,” IBM Journal of Research and Development, vol. 4, pp. 36–42, 1960.
  7. C. D. Mote Jr., “Stability of systems transporting accelerating axially moving materials,” Journal of Dynamic Systems, Measurement and Control, vol. 97, no. 1, pp. 96–98, 1975. View at Scopus
  8. M. Pakdemirli, A. G. Ulsoy, and A. Ceranoğlu, “Transverse vibration of an axially accelerating string,” Journal of Sound and Vibration, vol. 169, no. 2, pp. 179–196, 1994. View at Publisher · View at Google Scholar · View at Scopus
  9. E. M. Mockensturm, N. C. Perkins, and A. G. Ulsoy, “Stability and limit cycles of parametrically excited, axially moving strings,” Journal of Vibration and Acoustics, vol. 118, no. 3, pp. 346–351, 1996. View at Publisher · View at Google Scholar · View at Scopus
  10. M. Pakdemirli and H. Batan, “Dynamic stability of a constantly accelerating strip,” Journal of Sound and Vibration, vol. 168, no. 2, pp. 371–378, 1993. View at Publisher · View at Google Scholar · View at Scopus
  11. H. R. Öz and M. Pakdemirli, “Vibrations of an axially moving beam with time-dependent velocity,” Journal of Sound and Vibration, vol. 227, no. 2, pp. 239–257, 1999. View at Scopus
  12. M. Pakdemirli and H. R. Öz, “Infinite mode analysis and truncation to resonant modes of axially accelerated beam vibrations,” Journal of Sound and Vibration, vol. 311, no. 3–5, pp. 1052–1074, 2008. View at Publisher · View at Google Scholar · View at Scopus
  13. M. P. Païdoussis and G. X. Li, “Pipes conveying fluid: a model dynamical problem,” Journal of Fluids and Structures, vol. 7, no. 2, pp. 137–204, 1993. View at Publisher · View at Google Scholar · View at Scopus
  14. H. R. Öz and H. Boyacı, “Transverse vibrations of tensioned pipes conveying fluid with time-dependent velocity,” Journal of Sound and Vibration, vol. 236, no. 2, pp. 259–276, 2000. View at Publisher · View at Google Scholar · View at Scopus
  15. H. R. öz, “Non-linear vibrations and stability analysis of tensioned pipes conveying fluid with variable velocity,” International Journal of Non-Linear Mechanics, vol. 36, no. 7, pp. 1031–1039, 2001. View at Publisher · View at Google Scholar · View at Scopus
  16. L. Q. Chen, N. H. Zhang, and J. W. Zu, “Bifurcation and chaos of an axially moving viscoelastic string,” Mechanics Research Communications, vol. 29, no. 2-3, pp. 81–90, 2002. View at Publisher · View at Google Scholar · View at Scopus
  17. L. Q. Chen, N. H. Zhang, and J. W. Zu, “The regular and chaotic vibrations of an axially moving viscoelastic string based on fourth order Galerkin truncation,” Journal of Sound and Vibration, vol. 261, no. 4, pp. 764–773, 2003. View at Publisher · View at Google Scholar · View at Scopus
  18. L. Q. Chen, H. Chen, and C. W. Lim, “Asymptotic analysis of axially accelerating viscoelastic strings,” International Journal of Engineering Science, vol. 46, no. 10, pp. 976–985, 2008. View at Publisher · View at Google Scholar · View at Scopus
  19. U. Lee and H. Oh, “Dynamics of an axially moving viscoelastic beam subject to axial tension,” International Journal of Solids and Structures, vol. 42, no. 8, pp. 2381–2398, 2005. View at Publisher · View at Google Scholar · View at Scopus
  20. L. Q. Chen and X. D. Yang, “Stability in parametric resonance of axially moving viscoelastic beams with time-dependent speed,” Journal of Sound and Vibration, vol. 284, no. 3–5, pp. 879–891, 2005. View at Publisher · View at Google Scholar · View at Scopus
  21. L. Q. Chen, X. D. Yang, and C. J. Cheng, “Dynamic stability of an axially accelerating viscoelastic beam,” European Journal of Mechanics A, vol. 23, no. 4, pp. 659–666, 2004. View at Publisher · View at Google Scholar · View at Scopus
  22. M. H. Ghayesh, “Nonlinear transversal vibration and stability of an axially moving viscoelastic string supported by a partial viscoelastic guide,” Journal of Sound and Vibration, vol. 314, no. 3–5, pp. 757–774, 2008. View at Publisher · View at Google Scholar · View at Scopus
  23. L. N. Panda and R. C. Kar, “Nonlinear dynamics of a pipe conveying pulsating fluid with combination, principal parametric and internal resonances,” Journal of Sound and Vibration, vol. 309, no. 3–5, pp. 375–406, 2008. View at Publisher · View at Google Scholar · View at Scopus
  24. B. B. Özhan and M. Pakdemirli, “A general solution procedure for the forced vibrations of a continuous system with cubic nonlinearities: primary resonance case,” Journal of Sound and Vibration, vol. 325, no. 4-5, pp. 894–906, 2009. View at Publisher · View at Google Scholar · View at Scopus
  25. B. B. Özhan and M. Pakdemirli, “A general solution procedure for the forced vibrations of a system with cubic nonlinearities: three-to-one internal resonances with external excitation,” Journal of Sound and Vibration, vol. 329, no. 13, pp. 2603–2615, 2010. View at Publisher · View at Google Scholar · View at Scopus
  26. B. B. Özhan and M. Pakdemirli, “Principal parametric resonances of a general continuous system with cubic nonlinearities,” Applied Mathematics and Computation, vol. 219, pp. 2412–2423, 2012.
  27. L. Q. Chen and X. D. Yang, “Transverse nonlinear dynamics of axially accelerating viscoelastic beams based on 4-term Galerkin truncation,” Chaos, Solitons & Fractals, vol. 27, no. 3, pp. 748–757, 2006. View at Publisher · View at Google Scholar · View at Scopus
  28. L. Q. Chen and X. D. Yang, “Vibration and stability of an axially moving viscoelastic beam with hybrid supports,” European Journal of Mechanics A, vol. 25, no. 6, pp. 996–1008, 2006. View at Publisher · View at Google Scholar · View at Scopus
  29. L. Q. Chen and B. Wang, “Stability of axially accelerating viscoelastic beams: asymptotic perturbation analysis and differential quadrature validation,” European Journal of Mechanics A, vol. 28, no. 4, pp. 786–791, 2009. View at Publisher · View at Google Scholar · View at Scopus
  30. M. P. Païdoussis, Fluid-Structure Interactions, Slender Structures and Axial Flow, vol. 1, Academic Press, New York, NY, USA, 1998.
  31. O. Doaré, “Dissipation effect on local and global stability of fluid-conveying pipes,” Journal of Sound and Vibration, vol. 329, no. 1, pp. 72–83, 2010. View at Publisher · View at Google Scholar · View at Scopus