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Shock and Vibration
Volume 2015, Article ID 507581, 11 pages
http://dx.doi.org/10.1155/2015/507581
Research Article

Transverse Free Vibration of Axially Moving Stepped Beam with Different Length and Tip Mass

1State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, China
2Department of Mechanics, Shanghai University, Shanghai 200444, China

Received 10 April 2015; Accepted 26 May 2015

Academic Editor: Rafał Burdzik

Copyright © 2015 Guoliang Ma et al. 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. E. J. Leigh and D. L. Kunz, “Simulation of a moving elastic beam using Hamilton's weak principle,” AIAA Journal, vol. 45, no. 2, pp. 471–476, 2007. View at Publisher · View at Google Scholar · View at Scopus
  2. C. D. Mote Jr., “A study of band saw vibrations,” Journal of the Franklin Institute, vol. 279, no. 6, pp. 430–444, 1965. View at Publisher · View at Google Scholar · View at Scopus
  3. A. Simpson, “Transverse modes and frequencies of beams translating between fixed and supports,” Journal of Mechanical Engineering Science, vol. 15, no. 3, pp. 159–164, 1973. View at Publisher · View at Google Scholar · View at Scopus
  4. 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 Publisher · View at Google Scholar · View at Scopus
  5. M. Stylianou and B. Tabarrok, “Finite element analysis of an axially moving beam, part I: time integration,” Journal of Sound and Vibration, vol. 178, no. 4, pp. 433–453, 1994. View at Publisher · View at Google Scholar · View at Scopus
  6. 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 Publisher · View at Google Scholar · View at Scopus
  7. S. V. Ponomareva and W. T. van Horssen, “On the transversal vibrations of an axially moving continuum with a time-varying velocity: transient from string to beam behavior,” Journal of Sound and Vibration, vol. 325, no. 4-5, pp. 959–973, 2009. View at Publisher · View at Google Scholar · View at Scopus
  8. S. H. Sandilo and W. T. van Horssen, “On boundary damping for an axially moving beam and on the variable length induced vibrations of an elevator cable,” in Proceedings of the 7th European Nonlinear Oscillations Conference, pp. 24–29, Rome, Italy, July 2011.
  9. M. H. Ghayesh and M. Amabili, “Steady-state transverse response of an axially moving beam with time-dependent axial speed,” International Journal of Non-Linear Mechanics, vol. 49, pp. 40–49, 2013. View at Publisher · View at Google Scholar · View at Scopus
  10. S. Park, H. H. Yoo, and J. Chung, “Vibrations of an axially moving beam with deployment or retraction,” AIAA Journal, vol. 51, no. 3, pp. 686–696, 2013. View at Publisher · View at Google Scholar · View at Scopus
  11. R. A. Malookani and W. T. van Horssen, “On resonances and the applicability of Galerkin's truncation method for an axially moving string with time-varying velocity,” Journal of Sound and Vibration, vol. 344, pp. 1–17, 2015. View at Publisher · View at Google Scholar
  12. S. Kazemirad, M. H. Ghayesh, and M. Amabili, “Thermal effects on nonlinear vibrations of an axially moving beam with an intermediate spring-mass support,” Shock and Vibration, vol. 20, no. 3, pp. 385–399, 2013. View at Publisher · View at Google Scholar
  13. H. Oh, J. Kim, and U. Lee, “Spectral element model for the vibration of an axially moving timoshenko beam,” in Proceedings of the 44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, AIAA-2003- 1692, Norfolk, Va, USA, April 2003. View at Scopus
  14. M. H. Ghayesh and M. Amabili, “Three-dimensional nonlinear planar dynamics of an axially moving Timoshenko beam,” Archive of Applied Mechanics, vol. 83, no. 4, pp. 591–604, 2013. View at Publisher · View at Google Scholar · View at Scopus
  15. H. Ding and L.-Q. Chen, “Nonlinear models for transverse forced vibration of axially moving viscoelastic beams,” Shock and Vibration, vol. 18, no. 1-2, pp. 281–287, 2011. View at Publisher · View at Google Scholar · View at Scopus
  16. L.-Q. Chen, H. Ding, and C. W. Lim, “Principal parametric resonance of axially accelerating viscoelastic beams: multi-scale analysis and differential quadrature verification,” Shock and Vibration, vol. 19, no. 4, pp. 527–543, 2012. View at Publisher · View at Google Scholar · View at Scopus
  17. H. Lv, Y. Li, L. Li, and Q. Liu, “Transverse vibration of viscoelastic sandwich beam with time-dependent axial tension and axially varying moving velocity,” Applied Mathematical Modelling, vol. 38, no. 9-10, pp. 2558–2585, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. K. Marynowski and T. Kapitaniak, “Dynamics of axially moving continua,” International Journal of Mechanical Sciences, vol. 81, pp. 26–41, 2014. View at Publisher · View at Google Scholar · View at Scopus
  19. A. K. Gupta, “Vibration of tapered beams,” Journal of Structural Engineering, vol. 111, no. 1, pp. 19–36, 1985. View at Publisher · View at Google Scholar · View at Scopus
  20. S. Y. Lee and H. Y. Ke, “Free vibrations of a non-uniform beam with general elastically restrained boundary conditions,” Journal of Sound and Vibration, vol. 136, no. 3, pp. 425–437, 1990. View at Publisher · View at Google Scholar · View at Scopus
  21. M. C. Ece, M. Aydogdu, and V. Taskin, “Vibration of a variable cross-section beam,” Mechanics Research Communications, vol. 34, no. 1, pp. 78–84, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  22. Q. Mao and S. Pietrzko, “Free vibration analysis of stepped beams by using Adomian decomposition method,” Applied Mathematics and Computation, vol. 217, no. 7, pp. 3429–3441, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus