Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2015, Article ID 582326, 10 pages
http://dx.doi.org/10.1155/2015/582326
Research Article

Element for Beam Dynamic Analysis Based on Analytical Deflection Trial Function

1College of Water Resources & Civil Engineering, China Agricultural University, Beijing 100083, China
2China Aerospace Construction Group Co., Ltd., Beijing 100071, China

Received 18 September 2014; Accepted 15 December 2014

Academic Editor: Chenfeng Li

Copyright © 2015 Qiongqiong Cao 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. A. K. Clough and J. Penzien, Dynamic of Structures, McGraw-Hill, New York, NY, USA, 1995.
  2. Q. Jin, “An analytical solution of dynamic response for the rigid perfectly plastic Timoshenko beam,” Chinese Journal of Theoretical and Applied Mechanics, vol. 16, no. 5, pp. 504–511, 1984. View at Google Scholar
  3. X. Guo, H. Chen, and Q. Zeng, “Dynamic characteristics analysis model of prestressed concrete T-type beam,” Chinese Journal of Computational Mechanics, vol. 17, no. 2, pp. 176–183, 2000. View at Google Scholar
  4. D.-P. Fang and Q.-F. Wang, “Dynamic behavior analysis of an externally prestressed beam with energy method,” Journal of Vibration and Shock, vol. 31, no. 1, pp. 177–181, 2012. View at Google Scholar · View at Scopus
  5. M. Lou and T. Hong, “Analytical approach for dynamic characteristics of prestressed beam with external tendons,” Journal of Tongji University: Natural Science, vol. 34, no. 10, pp. 1284–1288, 2006. View at Google Scholar · View at Scopus
  6. J. A. Carrer, S. A. Fleischfresser, L. F. Garcia, and W. J. Mansur, “Dynamic analysis of Timoshenko beams by the boundary element method,” Engineering Analysis with Boundary Elements, vol. 37, no. 12, pp. 1602–1616, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. J.-J. Wu, “Use of the elastic-and-rigid-combined beam element for dynamic analysis of a two-dimensional frame with arbitrarily distributed rigid beam segments,” Applied Mathematical Modelling: Simulation and Computation for Engineering and Environmental Systems, vol. 35, no. 3, pp. 1240–1251, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. M. A. De Rosa, C. Franciosi, and M. J. Maurizi, “On the dynamic behaviour of slender beams with elastic ends carrying a concentrated mass,” Computers and Structures, vol. 58, no. 6, pp. 1145–1159, 1996. View at Publisher · View at Google Scholar · View at Scopus
  9. R. W. Clough, “The finite element method in plane stress analysis,” in Proceedings of the 2nd ASCE Conference on Electronic Computation, Pittsburgh, Pa, USA, 1960.
  10. V. Koloušek, “Anwendung des Gesetzes der virtuellen Ver schiebungen and des in der Reziprozitatssatzes,” Stab weks Dynamik Lngenieur Archiv, vol. 12, pp. 363–370, 1941. View at Google Scholar
  11. Y.-Q. Long and S.-H. Bao, Structural Mechanics II, Higher Education Press, Beijing, China, 2nd edition, 1996.
  12. S. M. Hashemi and M. J. Richard, “Free vibrational analysis of axially loaded bending-torsion coupled beams: a dynamic finite element,” Computers & Structures, vol. 77, no. 6, pp. 711–724, 2000. View at Publisher · View at Google Scholar · View at Scopus
  13. S. Chen, M. Géradin, and E. Lamine, “An improved dynamic stiffness method and modal analysis for beam-like structures,” Computers & Structures, vol. 60, no. 5, pp. 725–731, 1996. View at Publisher · View at Google Scholar · View at Scopus
  14. J. R. Banerjee, H. Su, and C. Jayatunga, “A dynamic stiffness element for free vibration analysis of composite beams and its application to aircraft wings,” Computers & Structures, vol. 86, no. 6, pp. 573–579, 2008. View at Publisher · View at Google Scholar · View at Scopus
  15. J. R. Banerjee, S. Guo, and W. P. Howson, “Exact dynamic stiffness matrix of a bending-torsion coupled beam including warping,” Computers and Structures, vol. 59, no. 4, pp. 613–621, 1996. View at Publisher · View at Google Scholar · View at Scopus
  16. M. Shavezipur and S. M. Hashemi, “Free vibration of triply coupled centrifugally stiffened nonuniform beams, using a refined dynamic finite element method,” Aerospace Science and Technology, vol. 13, no. 1, pp. 59–70, 2009. View at Publisher · View at Google Scholar · View at Scopus
  17. A. K. Chopra, Dynamics of Structures, Prentice Hall, Englewood Cliffs, NJ, USA, 2000.
  18. X.-L. Hu and Z.-M. Dai, “On the dynamic stress concentrations in orthotropic plates with an arbitrary cutout,” Chinese Journal of Applied Mechanics, vol. 15, no. 1, pp. 12–17, 1998. View at Google Scholar
  19. X. Wang, L. Yang, and W. Gao, “Dynamic FEM analysis for the integration ballast structure based on variation principle,” Journal of Vibration and Shock, vol. 24, no. 4, pp. 99–102, 2005. View at Google Scholar · View at Scopus
  20. S. M. Hashemi and M. J. Richard, “A dynamic finite element (DFE) method for free vibrations of bending-torsion coupled beams,” Aerospace Science and Technology, vol. 4, no. 1, pp. 41–55, 2000. View at Publisher · View at Google Scholar · View at Scopus
  21. A. Pagani, E. Carrera, M. Boscolo, and J. R. Banerjee, “Refined dynamic stiffness elements applied to free vibration analysis of generally laminated composite beams with arbitrary boundary conditions,” Composite Structures, vol. 110, no. 1, pp. 305–316, 2014. View at Publisher · View at Google Scholar · View at Scopus
  22. S. M. Nabi and N. Ganesan, “A generalized element for the free vibration analysis of composite beams,” Computers and Structures, vol. 51, no. 5, pp. 607–610, 1994. View at Publisher · View at Google Scholar · View at Scopus
  23. L. Zhao and Q. Chen, “Dynamic analysis of the stochastic variational principle and stochastic finite element method for structures with random parameters,” Chinese Journal of Computational Mechanics, vol. 15, no. 3, pp. 263–274, 1998. View at Google Scholar
  24. G.-H. Wang, Y.-N. Gan, and Z.-B. Wang, “Energy-variational method for the dynamic response of thin-walled I-beams with wide flange,” Engineering Mechanics, vol. 27, no. 8, pp. 15–20, 2010. View at Google Scholar · View at Scopus