Table of Contents Author Guidelines Submit a Manuscript
Shock and Vibration
Volume 2016, Article ID 4070627, 12 pages
http://dx.doi.org/10.1155/2016/4070627
Research Article

Application of Volterra Integral Equations in Dynamics of Multispan Uniform Continuous Beams Subjected to a Moving Load

The Faculty of Environmental Engineering and Geodesy, Wrocław University of Environmental and Life Science, Grunwaldzka 55, 50-365 Wrocław, Poland

Received 30 March 2016; Revised 6 September 2016; Accepted 8 September 2016

Academic Editor: Salvatore Russo

Copyright © 2016 Filip Zakęś and Paweł Śniady. 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. L. Frýba, Vibration of Solids and Structures under Moving Loads, Thomas Telford Publishing, London, UK, 1999. View at Publisher · View at Google Scholar
  2. C. C. Tung, “Random response of highway bridges to vehicle loads,” Journal of the Engineering Mechanics Division, vol. 93, pp. 73–94, 1967. View at Google Scholar
  3. R. Sieniawska and P. Śniady, “Life expectancy of highway bridges due to traffic load,” Journal of Sound and Vibration, vol. 140, no. 1, pp. 31–38, 1990. View at Publisher · View at Google Scholar · View at Scopus
  4. A. Rystwej and P. Śniady, “Dynamic response of an infinite beam and plate to a stochastic train of moving forces,” Journal of Sound and Vibration, vol. 299, no. 4-5, pp. 1033–1048, 2007. View at Publisher · View at Google Scholar · View at Scopus
  5. Z. Kączkowski, “Vibration of a beam under a moving load,” Proceedings of Vibration Problems, vol. 4, no. 4, pp. 357–373, 1963. View at Google Scholar
  6. P. Śniady, “Dynamic response of a Timoshenko beam to a moving force,” Journal of Applied Mechanics, vol. 75, no. 2, Article ID 024503, 2008. View at Publisher · View at Google Scholar · View at Scopus
  7. K. Misiurek and P. Śniady, “Vibrations of sandwich beam due to a moving force,” Composite Structures, vol. 104, pp. 85–93, 2013. View at Publisher · View at Google Scholar · View at Scopus
  8. M. Podwórna, “Dynamics of a bridge beam under a stream of moving elements. Part 1—modelling and numerical integration,” Structural Engineering & Mechanics, vol. 38, no. 3, pp. 283–300, 2011. View at Publisher · View at Google Scholar · View at Scopus
  9. J. Rusin, P. Śniady, and P. Śniady, “Vibrations of double-string complex system under moving forces. Closed solutions,” Journal of Sound and Vibration, vol. 330, no. 3, pp. 404–415, 2011. View at Publisher · View at Google Scholar · View at Scopus
  10. D. Bryja and P. Śniady, “Spatially coupled vibrations of a suspension bridge under random highway traffic,” Earthquake Engineering and Structural Dynamics, vol. 20, no. 11, pp. 999–1010, 1991. View at Publisher · View at Google Scholar · View at Scopus
  11. D. Bryja and P. Śniady, “Stochastic non-linear vibrations of highway suspension bridge under inertial sprung moving load,” Journal of Sound and Vibration, vol. 216, no. 3, pp. 507–519, 1998. View at Publisher · View at Google Scholar · View at Scopus
  12. C. Johansson, C. Pacoste, and R. Karoumi, “Closed-form solution for the mode superposition analysis of the vibration in multi-span beam bridges caused by concentrated moving loads,” Computers and Structures, vol. 119, pp. 85–94, 2013. View at Publisher · View at Google Scholar · View at Scopus
  13. V. D. Salvo, G. Muscolino, and A. Palmeri, “A substructure approach tailored to the dynamic analysis of multi-span continuous beams under moving loads,” Journal of Sound and Vibration, vol. 329, no. 15, pp. 3101–3120, 2010. View at Publisher · View at Google Scholar · View at Scopus
  14. H. Xu and W. L. Li, “Dynamic behavior of multi-span bridges under moving loads with focusing on the effect of the coupling conditions between spans,” Journal of Sound and Vibration, vol. 312, no. 4-5, pp. 736–753, 2008. View at Publisher · View at Google Scholar · View at Scopus
  15. A. E. Martínez-Castro, P. Museros, and A. Castillo-Linares, “Semi-analytic solution in the time domain for non-uniform multi-span Bernoulli-Euler beams traversed by moving loads,” Journal of Sound and Vibration, vol. 294, no. 1-2, pp. 278–297, 2006. View at Publisher · View at Google Scholar · View at Scopus
  16. Y. A. Dugush and M. Eisenberger, “Vibrations of non-uniform continuous beams under moving loads,” Journal of Sound and Vibration, vol. 254, no. 5, pp. 911–926, 2002. View at Publisher · View at Google Scholar · View at Scopus
  17. D. Y. Zheng, Y. K. Cheung, F. T. K. Au, and Y. S. Cheng, “Vibration of multi-span non-uniform beams under moving loads by using modified beam vibration functions,” Journal of Sound and Vibration, vol. 212, no. 3, pp. 455–467, 1998. View at Publisher · View at Google Scholar · View at Scopus
  18. K. Henchi, M. Fafard, G. Dhatt, and M. Talbot, “Dynamic behaviour of multi-span beams under moving loads,” Journal of Sound and Vibration, vol. 199, no. 1, pp. 33–50, 1997. View at Publisher · View at Google Scholar · View at Scopus
  19. Y.-B. Yang, S.-S. Liao, and B.-H. Lin, “Impact formulas for vehicles moving over simple and continuous beams,” Journal of Structural Engineering, vol. 121, no. 11, pp. 1644–1650, 1995. View at Publisher · View at Google Scholar · View at Scopus
  20. H. P. Lee, “Dynamic response of a beam with intermediate point constraints subject to a moving load,” Journal of Sound and Vibration, vol. 171, no. 3, pp. 361–368, 1994. View at Publisher · View at Google Scholar · View at Scopus
  21. P. K. Chatterjee, T. K. Datta, and C. S. Surana, “Vibration of continuous bridges under moving vehicle,” Journal of Sound and Vibration, vol. 169, no. 5, pp. 619–632, 1994. View at Publisher · View at Google Scholar
  22. T. Hayashikawa and N. Watanabe, “Dynamic behavior of continuous beams with moving load,” Journal of Engineering Mechanics Division, vol. 107, pp. 229–246, 1981. View at Google Scholar
  23. M. Ichikawa, Y. Miyakawa, and A. Matsuda, “Vibration analysis of the continuous beam subjected to a moving mass,” Journal of Sound and Vibration, vol. 230, no. 3, pp. 493–506, 2000. View at Publisher · View at Google Scholar · View at Scopus
  24. H. P. Lee, “Dynamic response of a beam on multiple supports with a moving mass,” Structural Engineering & Mechanics, vol. 4, no. 3, pp. 303–312, 1996. View at Publisher · View at Google Scholar · View at Scopus
  25. Y. K. Cheung, F. T. K. Au, D. Y. Zheng, and Y. S. Cheng, “Vibration of multi-span non-uniform bridges under moving vehicles and trains by using modified beam vibration functions,” Journal of Sound and Vibration, vol. 228, no. 3, pp. 611–628, 1999. View at Publisher · View at Google Scholar · View at Scopus
  26. A. Ariaei, S. Ziaei-Rad, and M. Malekzadeh, “Dynamic response of a multi-span Timoshenko beam with internal and external flexible constraints subject to a moving mass,” Archive of Applied Mechanics, vol. 83, no. 9, pp. 1257–1272, 2013. View at Publisher · View at Google Scholar · View at Scopus
  27. R.-T. Wang and T.-Y. Lin, “Random vibration of multi-span Timoshenko beam due to a moving load,” Journal of Sound and Vibration, vol. 213, no. 1, pp. 127–138, 1998. View at Publisher · View at Google Scholar · View at Scopus
  28. R.-T. Wang, “Vibration of multi-span Timoshenko beams to a moving force,” Journal of Sound and Vibration, vol. 207, no. 5, pp. 731–742, 1997. View at Publisher · View at Google Scholar · View at Scopus
  29. H. Abramovich, M. Eisenberger, and O. Shulepov, “Vibrations of multi-span non-symmetric composite beams,” Composites Engineering, vol. 5, no. 4, pp. 397–404, 1995. View at Publisher · View at Google Scholar · View at Scopus
  30. S. He and M. D. Rao, “Vibration and damping analysis of multi-span sandwich beams with arbitrary boundary conditions,” Journal of Sound and Vibration, vol. 164, no. 1, pp. 125–142, 1993. View at Publisher · View at Google Scholar · View at Scopus
  31. Z. Reipert, “Vibration of frames under moving load,” Archiwum Inzynierii Ladowej, vol. 16, no. 3, pp. 419–447, 1970. View at Google Scholar
  32. P. Linz, “Numerical methods for Volterra integral equations of the first kind,” The Computer Journal, vol. 12, no. 4, pp. 393–397, 1969. View at Publisher · View at Google Scholar