Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

The modal characteristics of non-uniform multi-span continuous beam bridges

  • Shi, Lu-Ning (Beijing Laboratory of Earthquake Engineering and Structure Retrofit, Beijing University of Technology) ;
  • Yan, Wei-Ming (Beijing Laboratory of Earthquake Engineering and Structure Retrofit, Beijing University of Technology) ;
  • He, Hao-Xiang (Beijing Laboratory of Earthquake Engineering and Structure Retrofit, Beijing University of Technology)
  • Received : 2014.05.26
  • Accepted : 2014.08.20
  • Published : 2014.12.10
⟨ Previous Next ⟩

Abstract

According to the structure characteristics of the non-uniform beam bridge, a practical model for calculating the vibration equation of the non-uniform beam bridge is given and the application scope of the model includes not only the beam bridge structure but also the non-uniform beam with added masses and elastic supports. Based on the Bernoulli-Euler beam theory, extending the application of the modal perturbation method and establishment of a semi-analytical method for solving the vibration equation of the non-uniform beam with added masses and elastic supports based is able to be made. In the modal subspace of the uniform beam with the elastic supports, the variable coefficient differential equation that describes the dynamic behavior of the non-uniform beam is converted to nonlinear algebraic equations. Extending the application of the modal perturbation method is suitable for solving the vibration equation of the simply supported and continuous non-uniform beam with its arbitrary added masses and elastic supports. The examples, that are analyzed, demonstrate the high precision and fast convergence speed of the method. Further study of the timesaving method for the dynamic characteristics of symmetrical beam and the symmetry of mode shape should be developed. Eventually, the effects of elastic supports and added masses on dynamic characteristics of the three-span non-uniform beam bridge are reported.

Keywords

Acknowledgement

Supported by : Natural Science Foundation of China

References

  1. Bahrami, M.N., Arani, M.K. and Saleh, N.R. (2011), "Modified wave approach for calculation of natural frequencies and mode shapes in arbitrary non-uniform beams", Scientia Iranica, 18(5), 1088-1094. https://doi.org/10.1016/j.scient.2011.08.004
  2. Bambill, D.V., Rossit, C.A., Rossi, R.E., Felix, D.H. and Ratazzi, A.R. (2013), "Transverse free vibration of non uniform rotating Timoshenko beams with elastically clamped boundary conditions", Meccanica, 48(6), 1289-1311. https://doi.org/10.1007/s11012-012-9668-5
  3. Bedon, C. and Morassi, A. (2014), "Dynamic testing and parameter identification of a base-isolated bridge", Eng. Struct., 60(1-2), 85-99. https://doi.org/10.1016/j.engstruct.2013.12.017
  4. Burden, R.L. and Faires, J.D. (1997), Numerical Analysis, sixth edition, Brooks Cole Publishing Company, Pacific Grove, California, USA.
  5. Chen, D.W. and Wu, J.S. (2002), "The exact solution for the natural frequencies and mode shapes of nonuniform beams with multiple spring-mass systems", J. Sound Vib., 255(2), 299-322. https://doi.org/10.1006/jsvi.2001.4156
  6. Clough, R.W. and Penzien, J. (2003), Dynamics of Structures, second edition, Computers and Structures, New York, USA.
  7. DeRosa, M.A., Franciosi, C. and Maurizi, M.J. (1996), "On the dynamic behavior of slender beams with elastic ends carrying a concentrated mass", Comput. Struct., 58(6), 1145-1159. https://doi.org/10.1016/0045-7949(95)00199-9
  8. Elishakoff, I. and Johnson, V. (2005), "Apparently the first closed-form solution of vibrating inhomogeneous beam with a tip mass", J. Sound Vib., 286(4-5), 1057-1066. https://doi.org/10.1016/j.jsv.2005.01.050
  9. Kamke, E. (1980), Ordinary Differential Equation Manual, Science Press, Beijing, China.
  10. Firouz-Abadi, R.D., Haddadpour, H. and Novinzadeh, A.B. (2007), "An asymptotic solution to transverse free vibrations of variable-section beams", J. Sound Vib., 304(3-5), 530-540. https://doi.org/10.1016/j.jsv.2007.02.030
  11. Ho, S.H. and Chen, C.K. (1998), "Analysis of general elastically end restrained non-uniform beams using differential transform", Appl. Math. Model., 22(4-5), 219-234. https://doi.org/10.1016/S0307-904X(98)10002-1
  12. Hsu, J.C., Lai, H.Y. and Chen, C.K. (2008), "Free vibration of non-uniform Euler-Bernoulli beams with general elastically end constraints using Adomian modified decomposition method", J. Sound Vib., 318(4-5), 965-981. https://doi.org/10.1016/j.jsv.2008.05.010
  13. Huang, Y. and Li, X.F. (2010), "A new approach for free vibration of axially functionally graded beams with non-uniform cross-section", J. Sound Vib., 329(11), 2291-2303. https://doi.org/10.1016/j.jsv.2009.12.029
  14. Pratiher, B. (2012), "Vibration control of a transversely excited cantilever beam with tip mass", Arch. Appl. Mech., 82(1), 31-42. https://doi.org/10.1007/s00419-011-0537-9
  15. Jovanovic, V. (2011), "A Fourier series solution for the transverse vibration response of a beam with a viscous boundary", J. Sound Vib., 330(7), 1504-1515. https://doi.org/10.1016/j.jsv.2010.10.007
  16. Lee, S.Y. and Yhim, S.S. (2005), "Dynamic behavior of long-span box girder bridges subjected to moving loads: numerical analysis and experimental verification", Int. J. Solid. Struct., 42(18-19), 5021-5035. https://doi.org/10.1016/j.ijsolstr.2005.02.020
  17. Lou, M.L., Duan, Q.H. and Chen, G. (2005), "Modal perturbation method for the dynamic characteristics of Timoshenko beams", Shock Vib., 12(6), 425-434. https://doi.org/10.1155/2005/824616
  18. Lou, M.L. and Wu, J.N. (1997), "An approach solve dynamic problems of complicated beams", Shanghai J. Mech., 18(3), 234-240.
  19. Mao, Q.B. (2011), "Free vibration analysis of multiple-stepped beams by using Adomian decomposition method", Math. Comput. Model., 54(1), 756-764. https://doi.org/10.1016/j.mcm.2011.03.019
  20. Sarkar, K. and Ganguli, R. (2013), "Closed-form solutions for non-uniform Euler-Bernoulli free-free beams", J. Sound Vib., 332(23), 6078-6092. https://doi.org/10.1016/j.jsv.2013.06.008
  21. Pan, D.G., Chen, G.D. and Lou, M.L. (2012), "A modified modal perturbation method for vibration characteristics of non-prismatic Timoshenko beams", Struct. Eng. Mech., 40(5), 689-703. https://doi.org/10.12989/sem.2011.40.5.689
  22. Qian, B. and Yue, H.Y. (2011), "Numerical calculation of natural frequency of transverse vibration of nonuniform beam", Mech. Eng., 33(6), 45-49.
  23. Timoshenko, S. (1974), Vibration Problems in Engineering, fourth edition, John Wiley& Sons, New York, USA.
  24. Xia, J., Zhu, M.C. and Ma, D.Y. (2000), "Analysis of lateral natural vibration of beams with lumped masses and elastic supports", Mech. Eng., 22(5), 27-30.
  25. Yang, M.J., Qiao, P.Z., McLean, D.I. and Khaleghi, B. (2010), "Effects of overheight truck impacts on intermediate diaphragms in prestressed concrete bridge girders", PCI J., 55(1), 58-78. https://doi.org/10.15554/pcij.01012010.58.78

Cited by

  1. Effects of deformation of elastic constraints on free vibration characteristics of cantilever Bernoulli-Euler beams vol.59, pp.6, 2016, https://doi.org/10.12989/sem.2016.59.6.1139
  2. Free vibration analysis of continuous bridge under the vehicles vol.61, pp.3, 2014, https://doi.org/10.12989/sem.2017.61.3.335