Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Vibration analysis of a uniform beam traversed by a moving vehicle with random mass and random velocity

  • Chang, T.P. (Department of Construction Engineering, National Kaohsiung First University of Science and Technology) ;
  • Liu, M.F. (Department of Applied Mathematics, I-Shou University) ;
  • O, H.W. (Department of Construction Engineering, National Kaohsiung First University of Science and Technology)
  • Received : 2008.02.27
  • Accepted : 2009.03.20
  • Published : 2009.04.20
⟨ Previous Next ⟩

Abstract

The problem of estimating the dynamic response of a distributed parameter system excited by a moving vehicle with random initial velocity and random vehicle body mass is investigated. By adopting the Galerkin's method and modal analysis, a set of approximate governing equations of motion possessing time-dependent uncertain coefficients and forcing function is obtained, and then the dynamic response of the coupled system can be calculated in deterministic sense. The statistical characteristics of the responses of the system are computed by using improved perturbation approach with respect to mean value. This method is simple and useful to gather the stochastic structural response due to the vehicle-passenger-bridge interaction. Furthermore, some of the statistical numerical results calculated from the perturbation technique are checked by Monte Carlo simulation.

Keywords

Acknowledgement

Supported by : National Science Council

References

  1. Bolotin, V.V. (1965), Statistical Methods in Engineering Mechanics, Stroiizdat, Moscow
  2. Chang, T.P. and Chang, H.C. (1994), "Stochastic dynamic finite element analysis of a nonuniform beam", Int. J. Solids Struct., 31, 587-597 https://doi.org/10.1016/0020-7683(94)90139-2
  3. Chang, T.P. and Liu, Y.N. (1996), "Dynamic finite element analysis of a nonlinear beam subjected to a moving load", Int. J. Solids Struct., 33, 1673-1688 https://doi.org/10.1016/0020-7683(95)00128-X
  4. Chang, T.P., Lin, G.L. and Chang, E. (2006), "Vibration analysis of a beam with an internal hinge subjected to a random moving oscillator", Int. J. Solids Struct., 43, 6398-6412 https://doi.org/10.1016/j.ijsolstr.2005.10.013
  5. ElBeheiry, E.M. (2000), "Effects of small travel speed variations on active vibration control in modern vehicles", J. Sound Vib., 232, 857-875 https://doi.org/10.1006/jsvi.1999.2777
  6. Elishakoff, I., Ren, Y.J. and Shinozuka, M. (1995), "Improved finite element method for stochastic problems", Chaos Soliton. Fract., 5, 833-846 https://doi.org/10.1016/0960-0779(94)00157-L
  7. Esmailzadeh, E. and Ghorashi, M. (1995), "Vibration analysis of beams traversed by uniform partially distributed moving masses", J. Sound Vib., 184, 9-17 https://doi.org/10.1006/jsvi.1995.0301
  8. Esmailzadeh, E. and Jalilib, N. (2003), "Vehicle-passenger-structure interaction of uniform bridges traversed by moving vehicles", J. Sound Vib., 260, 611-635 https://doi.org/10.1016/S0022-460X(02)00960-4
  9. Feng, Q. and He, H. (2003), "Modeling of the mean Poincare' map on a class of random impact oscillators", Eur. J. Mech. A-Solid, 22, 267-281 https://doi.org/10.1016/S0997-7538(03)00015-9
  10. Fryba, L. (1999), Vibration of Solids and Structures Under Moving Loads, Telford, London
  11. Katz, R., Lee, C.W., Ulsoy, A.G. and Scott, R.A. (1988), "The dynamic response of rotating shaft subject to a moving load", J. Sound Vib., 122, 131-148 https://doi.org/10.1016/S0022-460X(88)80011-7
  12. Kleiber, M. and Hein, T.D. (1992), The Stochastic Finite Element Method, Wiley, Chichester
  13. Lee, H.P. (1994), "Dynamic response of a beam with intermediate point constraints subject to a moving load", J. Sound Vib., 171, 361-368 https://doi.org/10.1006/jsvi.1994.1126
  14. Lewis, E.E. (1987), Introduction to Reliability Engineering, John Wiley & Sons, New York
  15. Muscolino, G. (1996), "Dynamically modified linear structures: deterministic and stochastic response", J. Struct. Eng., ASCE, 122, 1044-1051
  16. Muscolino, G. and Sidoti A. (1999), "Dynamics of railway bridges subjected to moving mass with stochastic velocity", Structural Dynamics Eurodyn'99, 711-716
  17. Muscolino, G., Ricciardi, G. and Impollonia, N. (2000), "Improved dynamic analysis of structures with mechanical uncertainties under deterministic input", Prob. Eng. Mech., 15, 199-212 https://doi.org/10.1016/S0266-8920(99)00021-1
  18. Muscolino, G., Benfratello, S. and Sidoti, A. (2002), "Dynamics analysis of distributed parameter system subjected to a moving oscillator with random mass, velocity and acceleration", Prob. Eng. Mech., 17, 63-72 https://doi.org/10.1016/S0266-8920(01)00009-1
  19. Ricciardi, G. (1994), "Random vibration of beam under moving loads", J. Struct. Eng., ASCE, 120, 2361-2381
  20. Sadiku, S. and Leipholz, H.H.E. (1987), "On the dynamics of elastic systems with moving concentrated masses", Ing. Arch., 57, 223-242 https://doi.org/10.1007/BF02570609
  21. Sniady, P., Biemat, S., Sieniawska, R. and Zukowski, S. (1999), "Vibrations of the beam due to a load moving with stochastic velocity", Spanos, P.D. et al., editors. Proceedings of Computational Stochastic Mechanics (CSM'98), Amsterdam, Balkema
  22. Sobczyk, K., Wedrychowicz, S. and Spencer B.F. (1996), "Dynamics of structural systems with spatial randomness", Int. J. Solids Struct., 33, 1651-1669 https://doi.org/10.1016/0020-7683(95)00113-1
  23. Timoshenko, S. (1922), "On the forced vibration of bridge", Philos. Mag. Series, 43, 1018 https://doi.org/10.1080/14786442208633953
  24. Wang, R., Duan, Y.B. and Zang, Z. (2002), "Resonance analysis of finite-damping nonlinear vibration system under random disturbances", Eur. J. Mech. A-Solid, 21, 1083-1088 https://doi.org/10.1016/S0997-7538(02)01237-8
  25. Zibdeh, H.S. (1995), "Stochastic vibration of an elastic beam due to random moving loads and deterministic axial forces", Eng. Struct., 17, 530-535 https://doi.org/10.1016/0141-0296(95)00051-8
  26. Zibdeh, H.S. and Abu-Hilal, M. (2003), "Stochastic vibration of laminated composite coated beam traversed by a random moving load", Eng. Struct., 25, 397-404 https://doi.org/10.1016/S0141-0296(02)00181-5

Cited by

  1. Uncertainty Analysis on Vehicle-Bridge System with Correlative Interval Variables Based on Multidimensional Parallelepiped Model 2017, https://doi.org/10.1142/S0219876218500305
  2. Beam structural system moving forces active vibration control using a combined innovative control approach vol.12, pp.2, 2013, https://doi.org/10.12989/sss.2013.12.2.121
  3. Stochastic dynamic finite element analysis of bridge–vehicle system subjected to random material properties and loadings vol.242, 2014, https://doi.org/10.1016/j.amc.2014.05.038
  4. Dynamic analysis of bridge–vehicle system with uncertainties based on the finite element model vol.25, pp.4, 2010, https://doi.org/10.1016/j.probengmech.2010.05.004
  5. Dynamic analysis of bridge with non-Gaussian uncertainties under a moving vehicle vol.26, pp.2, 2011, https://doi.org/10.1016/j.probengmech.2010.08.004
  6. Evaluating the response statistics of an uncertain bridge–vehicle system vol.27, 2012, https://doi.org/10.1016/j.ymssp.2011.07.019
  7. Simulation of vibrations of Ting Kau Bridge due to vehicular loading from measurements vol.40, pp.4, 2011, https://doi.org/10.12989/sem.2011.40.4.471