Structural Engineering and Mechanics

  • 제65권3호
  • /
  • Pages.263-274
  • /
  • 2018
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Vibration analysis of a multi-span beam subjected to a moving point force using spectral element method

  • Jeong, Boseop (Department of Mechanical Engineering, Inha University) ;
  • Kim, Taehyun (Department of Mechanical Engineering, Inha University) ;
  • Lee, Usik (Department of Mechanical Engineering, Inha University)
  • 투고 : 2017.05.20
  • 심사 : 2017.12.26
  • 발행 : 2018.02.10
⟨ 이전 논문 다음 논문 ⟩

초록

In this study, we propose a frequency domain spectral element method (SEM) for the vibration analysis of a multi-span beam subjected to a moving point force. This study is an extension of the authors' previous study for a single-span beam subjected to a moving point force, where the two-element model-based SEM was applied. In this study, each span of a multi-span beam is represented by the Timoshenko beam model and the moving point force is transformed into the frequency domain as a series of each stationary point force distributed on the multi-span beam. The span at which a stationary point force is located is represented by two-element model, but all other spans are represented by one-element models. The vibration responses to a moving point force are obtained by superposing all individual vibration responses generated by each stationary point force. The high accuracy and computational efficiency of the proposed SEM are verified by comparing the solutions by SEM with exact analytical solutions by the integral transform method (ITM) as well as the solutions by the finite element method (FEM).

키워드

과제정보

연구 과제 주관 기관 : Inha University

참고문헌

  1. Ariaei, A., Ziaei-Rad, S. and Ghayour, M. (2011), "Transverse vibration of a multiple-Timoshenko beam system with intermediate elastic connections due to a moving load", Arch. Appl. Mech., 81(3), 263-281. https://doi.org/10.1007/s00419-010-0410-2
  2. Ariaei, A., Ziaei-Rad, S. and Malekzdeh, M. (2013), "Dynamic response of a multi-span Timoshenko beam with internal and external flexible constraints subject to a moving mass", Arch. Appl. Mech., 83(9), 1257-1272. https://doi.org/10.1007/s00419-013-0745-6
  3. Asnachinda, P., Pinkaew, T. and Laman, J.A. (2008), "Multiple vehicle axle load identification from continuous bridge bending moment response", Eng. Struct., 30(10), 2800-2817. https://doi.org/10.1016/j.engstruct.2008.02.018
  4. Azizi, N., Saadatpour, M.M. and Mahzoon, M. (2012), "Using spectral element method for analyzing continuous beams and bridges subjected to a moving load", Appl. Math. Model., 36(8), 3580-3592. https://doi.org/10.1016/j.apm.2011.10.019
  5. Cai, C.W., Cheung, Y.K. and Chan, H.C. (1988), "Dynamic response of infinite continuous beams subjected to a moving force-an exact method", J. Sound Vibr., 123(3), 461-472. https://doi.org/10.1016/S0022-460X(88)80163-9
  6. Chan, T.H.T. and Ashebo, D.B. (2006), "Theoretical study of moving force identification on continuous bridges", J. Sound Vibr., 295(3), 870-883. https://doi.org/10.1016/j.jsv.2006.01.059
  7. Cheung, Y.K., Au, F.T.K., Zheng, D.Y. and Cheng, Y.S. (1999), "Vibration of multi-span non-uniform bridges under moving vehicles and trains by using modified beam vibration functions", J. Sound Vibr., 228(3), 611-628. https://doi.org/10.1006/jsvi.1999.2423
  8. De Salvo, V., Muscolino, G. and Palmeri, A. (2010), "A substructure approach tailored to the dynamic analysis of multispan continuous beams under moving loads", J. Sound Vibr., 329(15), 3101-3120. https://doi.org/10.1016/j.jsv.2010.02.016
  9. Dmitriev, A.S. (1974), "Transverse vibrations of a three-span beam under a moving load", Appl. Mech., 10(11), 1263-1266.
  10. Dmitriev, A.S. (1977), "Transverse vibrations of a two-span beam with elastic central support under the action of a moving point force", Appl. Mech., 13(11), 1160-1163.
  11. Dmitriev, A.S. (1982), "Dynamics of continuous multispan beams under a moving force", Appl. Mech., 18(2), 179-186.
  12. Dugush, Y.A. and Eisenberger, M. (2002), "Vibrations of non-uniform continuous beams under moving loads", J. Sound Vibr., 254(5), 911-926. https://doi.org/10.1006/jsvi.2001.4135
  13. Fryba, L. (1999), Vibration of Solids and Structures under Moving Loads, Thomas Telford Publishing, London.
  14. Henchi, K., Fafard, M., Dhatt, G. and Talbot, M. (1997), "Dynamic behaviour of multi-span beams under moving loads", J. Sound Vibr., 199(1), 33-50. https://doi.org/10.1006/jsvi.1996.0628
  15. Hong, S.W. and Kim, J.W. (1999), "Modal analysis of multi-span Timoshenko beams connected or supported by resilient joints with damping", J. Sound Vibr., 227(4), 787-806. https://doi.org/10.1006/jsvi.1999.2385
  16. Ichikawa, M., Miyakawa, Y. and Matuda, A. (2000), "Vibration analysis of the continuous beam subjected to a moving mass", J. Sound Vibr., 230(3), 493-506. https://doi.org/10.1006/jsvi.1999.2625
  17. Jiang, R.J., Au, F.T.K. and Cheung, Y.K. (2004), "Identification of vehicles moving on continuous bridges with rough surface", J. Sound Vibr., 274(3), 1045-1063. https://doi.org/10.1016/S0022-460X(03)00664-3
  18. Johansson, C., Pacoste, C. and Karoumi, R. (2013), "Closed-form solution for the mode superposition analysis of the vibration in multi-span beam bridges caused by concentrated moving loads", Comput. Struct., 119, 85-94. https://doi.org/10.1016/j.compstruc.2013.01.003
  19. Kiani, K., Nikkhoo, A. and Mehri, B. (2010), "Assessing dynamic response of multispan viscoelastic thin beams under a moving mass via generalized moving least square method", Acta Mech. Sin., 26(5), 721-733. https://doi.org/10.1007/s10409-010-0365-0
  20. Kim, T., Park, I. and Lee, U. (2017), "Forced vibration of a Timoshenko beam subjected to stationary and moving loads using the modal analysis method", Shock Vibr., 3924921.
  21. Krawczuk, M., Palacz, M. and Ostachowicz, W. (2003), "The dynamic analysis of a cracked Timoshenko beam by the spectral element method", J. Sound Vibr., 264(5), 1139-1153. https://doi.org/10.1016/S0022-460X(02)01387-1
  22. Kreyszig, E. (1972), Advanced Engineering Mathematics, John Wiley & Sons, New Jersey, U.S.A.
  23. Kwon, H.C., Kim, M.C. and Lee, I.W. (1998), "Vibration control of bridges under moving loads", Comput. Struct., 66(4), 473-480. https://doi.org/10.1016/S0045-7949(97)00087-4
  24. Lee, H.P. (1994), "Dynamic response of a beam with intermediate point constraints subject to a moving load", J. Sound Vibr., 171(3), 361-368. https://doi.org/10.1006/jsvi.1994.1126
  25. Lee, H.P. (1996), "Dynamic response of a beam on multiple supports with a moving mass", Struct. Eng. Mech., 4(3), 303-312. https://doi.org/10.12989/sem.1996.4.3.303
  26. Lee, U. (2009), Spectral Element Method in Structural Dynamics, John Wiley & Sons, Singapore.
  27. Li, W.L. and Xu H. (2009), "An exact Fourier series method for the vibration analysis of multispan beam systems", J. Comput. Nonlin. Dyn., 4(2), 021001. https://doi.org/10.1115/1.3079681
  28. Lou, P. and Au, F.T.K. (2013), "Finite element formulae for internal forces of Bernoulli-Euler beams under moving vehicles", J. Sound Vibr., 332(6), 1533-1552. https://doi.org/10.1016/j.jsv.2012.11.011
  29. Lou, P., Yu, Z.W. and Au, F.T.K. (2012), "Rail-bridge coupling element of unequal lengths for analysing train-track-bridge interaction systems", Appl. Math. Model., 36(4), 1395-1414. https://doi.org/10.1016/j.apm.2011.08.041
  30. Martinez-Castro, A.E., Museros, P. and Castillo-Linares, A. (2006), "Semi-analytic solution in the time domain for non-uniform multi-span Bernoulli-Euler beams traversed by moving loads", J. Sound Vibr., 294(1), 278-297. https://doi.org/10.1016/j.jsv.2005.11.009
  31. Newland, D.E. (1993), Random Vibrations: Spectral and Wavelet Analysis, Longman, New York, U.S.A.
  32. Petyt, M. (2010), Introduction to Finite Element Vibration Analysis, Cambridge University Press, New York, U.S.A.
  33. Sarvestan, V., Mirdamadi, H.R., Ghayour, M. and Mokhtari, A. (2015), "Spectral finite element for vibration analysis of cracked viscoelastic Euler-Bernoulli beam subjected to moving load", Acta Mech., 226(12), 4259-4280. https://doi.org/10.1007/s00707-015-1491-3
  34. Song, Y., Kim, T. and Lee, U. (2016), "Vibration of a beam subjected to a moving force: Frequency-domain spectral element modeling and analysis", J. Mech. Sci., 113, 162-174. https://doi.org/10.1016/j.ijmecsci.2016.04.020
  35. Szylko-Bigus, O. and Sniady, P. (2015), "Dynamic response of a Timoshenko beam to a continuous distributed moving load", Struct. Eng. Mech., 54(4), 771-792. https://doi.org/10.12989/sem.2015.54.4.771
  36. Tang, C.C. and Wang, Y.C. (2002), "Dynamic characteristics of elastic beams subjected to traffic loads", Struct. Eng. Mech., 13(2), 211-230. https://doi.org/10.12989/sem.2002.13.2.211
  37. Tehrani, M. and Eipakchi, H.R. (2012), "Response determination of a viscoelastic Timoshenko beam subjected to moving load using analytical and numerical methods", Struct. Eng. Mech., 44(1), 1-13. https://doi.org/10.12989/sem.2012.44.1.001
  38. Wang, J.F. and Lin, C.C. and Chen, B.L. (2003), "Vibration suppression for high-speed railway bridges using tuned mass dampers", J. Sol. Struct., 40(2), 465-491. https://doi.org/10.1016/S0020-7683(02)00589-9
  39. Wang, R.T. (1997), "Vibration of multi-span Timoshenko beams to a moving force", J. Sound Vibr., 207(5), 731-742. https://doi.org/10.1006/jsvi.1997.1188
  40. Wang, R.T. and Lin, T.Y. (1998), "Random vibration of multi-span Timoshenko beam due to a moving load", J. Sound Vibr., 213(1), 127-138. https://doi.org/10.1006/jsvi.1998.1509
  41. Wang, R.T. and Sang, Y.L. (1999), "Out-of-plane vibration of multi-span curved beam due to moving loads", Struct. Eng. Mech., 7(4), 361-375. https://doi.org/10.12989/sem.1999.7.4.361
  42. Wu, J.J., Whittaker, A.R. and Cartmell, M.P. (2000), "The use of finite element techniques for calculating the dynamic response of structures to moving loads", Comput. Struct., 78(6), 789-799. https://doi.org/10.1016/S0045-7949(00)00055-9
  43. Wu, J.S. and Dai, C.W. (1987), "Dynamic responses of multispan nonuniform beam due to movin 0.5 줄g loads", J. Struct. Eng., 113(3), 458-474. https://doi.org/10.1061/(ASCE)0733-9445(1987)113:3(458)
  44. Xu, H. and Li, W.L. (2008), "Dynamic behavior of multi-span bridges under moving loads with focusing on the effect of the coupling conditions between spans", J. Sound Vibr., 312(4), 736-753. https://doi.org/10.1016/j.jsv.2007.11.011
  45. Zheng, D.Y., Cheung, Y.K., Au, F.T.K. and Cheng, Y.S. (1998), "Vibration of multi-span non-uniform beams under moving loads by using modified beam vibration functions", J. Sound Vibr., 212(3), 455-467. https://doi.org/10.1006/jsvi.1997.1435
  46. Zhu, X.Q. and Law, S.S. (1999), "Moving forces identification on a multi-span continuous bridge", J. Sound Vibr., 228(2), 377-396. https://doi.org/10.1006/jsvi.1999.2416