Structural Engineering and Mechanics

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Effect of temperature and spring-mass systems on modal properties of Timoshenko concrete beam

  • Liu, Hanbing (College of Transportation, Jilin University) ;
  • Wang, Hua (College of Transportation, Jilin University) ;
  • Tan, Guojin (College of Transportation, Jilin University) ;
  • Wang, Wensheng (College of Transportation, Jilin University) ;
  • Liu, Ziyu (College of Transportation, Jilin University)
  • Received : 2017.07.19
  • Accepted : 2018.01.23
  • Published : 2018.02.25
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Abstract

An exact solution for the title problem was obtained in closed-form fashion considering general boundary conditions. The expressions of moment, shear and shear coefficient (or shear factor) of cross section under the effect of arbitrary temperature distribution were first derived. In view of these relationships, the differential equations of Timoshenko beam under the effect of temperature were obtained and solved. Second, the characteristic equations of Timoshenko beam carrying several spring-mass systems under the effect of temperature were derived based on the continuity and force equilibrium conditions at attaching points. Then, the correctness of proposed method was demonstrated by a Timoshenko laboratory beam and several finite element models. Finally, the influence law of different temperature distribution modes and parameters of spring-mass system on the modal characteristics of Timoshenko beam had been studied, respectively.

Keywords

Acknowledgement

Supported by : National Natural Science Foundation of China

References

  1. Abramovich, H. and Elishako, I. (1990), "Influence of shear deformation and rotary inertia on vibration frequencies via love's equations", J. Sound Vibr., 137(3), 516-522. https://doi.org/10.1016/0022-460X(90)90816-I
  2. Abramovich, H. and Hamburger, O. (1991), "Vibration of a cantilever Timoshenko beam with a tip mass", J. Sound Vibr., 148(1), 162-170. https://doi.org/10.1016/0022-460X(91)90828-8
  3. Abramovich, H. and Hamburger, O. (1992), "Vibration of a cantilever Timoshenko beam with translational and rotational springs and with tip mass", J. Sound Vibr., 154(1), 67-80. https://doi.org/10.1016/0022-460X(92)90404-L
  4. Alvandi, A. and Cremona, C. (2006), "Assessment of vibrationbased damage identification techniques", J. Sound Vibr., 292(1-2), 179-202. https://doi.org/10.1016/j.jsv.2005.07.036
  5. Askegaard, V. and Mossing, P. (1988), Long Term Observation of RC-Bridge Using Changes in Natural Frequency, Nordic concrete research, January.
  6. Baldwin, R. and North, M.A. (1973), A Stress-strain Relationship for Concrete at High Temperatures, Magazine of Concrete Research, December.
  7. Bruch, J.C. and Mitchell, T.P. (1987), "Vibrations of a mass-loaded clamped-free Timoshenko beam", J. Sound Vibr., 114(2), 341-345. https://doi.org/10.1016/S0022-460X(87)80158-X
  8. Cornwell, P., Farrar, C.R., Doebling, S.W. and Sohn, H. (1999), "Environmental variability of modal properties", Exp. Tech., 23(6), 45-48. https://doi.org/10.1111/j.1747-1567.1999.tb01320.x
  9. Cruz, P.J.S. and Salgado, R. (2009), "Performance of vibration-based damage detection methods in bridges", Comput.-Aid. Civil Inf., 24(1), 62-79. https://doi.org/10.1111/j.1467-8667.2008.00546.x
  10. De Rosa, M.A., Auciello, N.M. and Maurizi, M.J. (2003), "The use of Mathematica in the dynamics analysis of a beam with a concentrated mass and dashpot", J. Sound Vibr., 263, 219-226. https://doi.org/10.1016/S0022-460X(02)01434-7
  11. De Rosa, M.A., Franciosi, C. and Maurizi, M.J. (1995), "On the dynamics behaviour 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
  12. Doebling, S.W. and Farrar, C.R. (1997), "Using statistical analysis to enhance modal-based damage identification", Proceedings of the Structural Damage Assessment Using Advanced Signal Processing Procedures Conference, January.
  13. El-Sayed, T.A. and Farghaly, S.H. (2016), "Exact vibration of Timoshenko beam combined with multiple mass spring sub-systems", Struct. Eng. Mech., 57(6), 989-1014. https://doi.org/10.12989/sem.2016.57.6.989
  14. Faires, J.D. and Burden, R.L. (2002), Numerical Methods, 3rd Edition, Brooks Cole, U.S.A.
  15. Faravelli, L., Ubertini, F. and Fuggini, C. (2011), "System identification of a super high-rise building via a stochastic subspace approach", Smart Struct. Syst., 7(2), 133-152. https://doi.org/10.12989/sss.2011.7.2.133
  16. Farghaly, S.H. and El-Sayed, T.A. (2016), "Exact free vibration of multi-step Timoshenko beam system with several attachments", Mech. Syst. Sign. Pr., 72-73, 525-546. https://doi.org/10.1016/j.ymssp.2015.11.025
  17. Farrar, C.R., Doebling, S.W., Cornwell, P.J. and Straser, E.G. (1997), "Variability of modal parameters measured on the Alamosa Canyon Bridge", Proceedings of the 15th International Modal Analytical Conf. Bethel (CT): Society for Experimental Mechanics, Washington, U.S.A., December.
  18. GB 50010-2010 (2010), Code for Design of Concrete Structures, Ministry of Housing and Urban-Rural Construction of the People's Republic of China; Beijing, China.
  19. Gurgoze, M. (1985), "On the vibration of restrained beams and rods with heavy masses", J. Sound Vibr., 100(4), 588-589. https://doi.org/10.1016/S0022-460X(85)80009-2
  20. Gurgoze, M. (1996), "On the eigenfrequencies of cantilevered beams carrying tip mass and a spring mass in span", J. Mech. Sci., 38(12), 1295-1306. https://doi.org/10.1016/0020-7403(96)00015-X
  21. He, X., Conte, J.P.M. and Fraser, A. (2009), "Long-term monitoring of a highway bridge", Proceedings of the 3rd International Operational Modal Analysis Conference, Italy.
  22. Huang, T.C. (1961), "The effect of rotatory inertia and of shear deformation on the frequency and normal mode equations of uniform beams with simple end conditions", J. Appl. Mech., 28(4), 579-584. https://doi.org/10.1115/1.3641787
  23. Kim, J.T., Park, J.H. and Lee, B.J. (2007), "Vibration-based damage monitoring in model plate-girder bridges under uncertain temperature conditions", Eng. Struct., 29(7), 1354-1365. https://doi.org/10.1016/j.engstruct.2006.07.024
  24. Kukla, S. and Posiadala, B. (1994), "Free vibrations of beams with elastically mounted masses", J. Sound Vibr., 175(4), 557-564. https://doi.org/10.1006/jsvi.1994.1345
  25. Li, H., Li, S., Ou, J. and Li, H. (2010), "Modal identification of bridges under varying environmental conditions: Temperature and wind effects", Struct. Contr. Hlth., 17(5), 495-512.
  26. Liu, H., Wang, X. and Jiao, Y. (2016), "Effect of temperature variation on modal frequency of reinforced concrete slab and beam in cold regions", Shock Vibr., 2016(6), 1-17.
  27. Liu, W.H., Wu, J.R. and Huang, C.C. (1988), "Free vibrations of beams with elastically restrained edges and intermediate concentrated masses", J. Sound Vibr., 122(2), 193-207. https://doi.org/10.1016/S0022-460X(88)80348-1
  28. Love, A.E.H. (1927), A Treatise on the Mathematical Theory of Elasticity, 4th Edition, Cambridge University Press, U.K.
  29. Maeck, J., Peeters, B. and De Roeck, G. (2001), "Damage identification on the Z24-bridge using vibration monitoring analysis", Smart Mater. Struct., 10(3), 512-517. https://doi.org/10.1088/0964-1726/10/3/313
  30. Ni, Y.Q., Hua, X.G., Fan, K.Q. and Ko, J.M. (2005), "Correlating modal properties with temperature using long-term monitoring data and support vector machine technique", Eng. Struct., 27(12), 1762-1773. https://doi.org/10.1016/j.engstruct.2005.02.020
  31. Peeters, B. and De Roeck, G. (2000), "One year monitoring of the Z24-Bridge: environmental influences versus damage events, #268", Proceedings of the SPIE-The International Society for Optical Engineering Conference, Texas, U.S.A.
  32. Peeters, B., Maeck, J. and De Roeck, G. (2001), "Vibration-based damage detection in civil engineering: Excitation sources and temperature effects", Smart Mater. Struct., 10(3), 518-527. https://doi.org/10.1088/0964-1726/10/3/314
  33. Rayleigh, L. (1945), Theory of Sound, 2nd Edition, The Macmillan Company, New York, U.S.A.
  34. Register, A.H. (1994), "A note on the vibration of generally restrained end loaded beams", J. Sound Vibr., 172(4), 561-571. https://doi.org/10.1006/jsvi.1994.1198
  35. Roberts, G.P. and Pearson, A.J. (1996), "Dynamic monitoring as a tool for long span bridges", Proceedings of the Bridge Management 3: Inspection, Maintenance, Assessment and Repair, London, U.K., April.
  36. Rossi, R.E., Laura, P.A.A., Avalos, D.R. and Larrondo, H. (1993), "Free vibration of Timoshenko beams carrying elastically mounted, concentrated masses", J. Sound Vibr., 165(2), 209-223. https://doi.org/10.1006/jsvi.1993.1254
  37. Rossit, C.A. and Laura, P.A.A. (2001a), "Transverse vibrations of a cantilever beam with a spring mass system attached on the free end", Ocean Eng., 28, 933-939. https://doi.org/10.1016/S0029-8018(00)00055-X
  38. Rossit, C.A. and Laura, P.A.A. (2001b), "Transverse normal modes of vibration of a cantilever Timoshenko beam with a mass elastically mounted at the free end", J. Acoust. Soc. Am., 110(6), 2837-2840. https://doi.org/10.1121/1.1416908
  39. Salawu, O.S. (1997), "Detection of structural damage through changes in frequency: A review", Eng. Struct., 19(9), 718-723. https://doi.org/10.1016/S0141-0296(96)00149-6
  40. Shoukry, S.N., William, G.W., Downie, B. and Riad, M.Y. (2011), "Effect of moisture and temperature on the mechanical properties of concrete", Constr. Build. Mater., 25(2), 688-696. https://doi.org/10.1016/j.conbuildmat.2010.07.020
  41. Sohn, H., Dzwonczyk, M., Straser, E.G., Kiremidjian, A.S., Law, K.H. and Meng, T. (1999), "An experimental study of temperature effect on modal parameters of the Alamos Canyon Bridge", Earthq. Eng. Struct. Dyn., 28(8), 879-897. https://doi.org/10.1002/(SICI)1096-9845(199908)28:8<879::AID-EQE845>3.0.CO;2-V
  42. Su, H. and Banerjee, J.R. (2005), "Exact natural frequencies of structures consisting of two part beam-mass systems", Struct. Eng. Mech., 19(5), 551-566. https://doi.org/10.12989/sem.2005.19.5.551
  43. Talebinejad, I., Fischer, C. and Ansari, F. (2011), "Numerical evaluation of vibration-based methods for damage assessment of cablestayed bridges", Comput.-Aid. Civil Inf., 26(3), 239-251. https://doi.org/10.1111/j.1467-8667.2010.00684.x
  44. Timoshenko, S.P. (1921), On the Correction for Shear of the Differential Equation for Transverse Vibrations of Prismatic Bars, Philosophical Magazine, April.
  45. Timoshenko, S.P. (1922), On the Transverse Vibrations of Bars of Uniform Cross Sections, Philosophical Magazine, April.
  46. Wahab, M.A. and De Roeck, G. (1997), "Effect of temperature on dynamic system parameters of a highway bridge", Struct. Eng. Int., 7(4), 266-270. https://doi.org/10.2749/101686697780494563
  47. Xia, Y., Chen, B., Weng, S., Ni, Y.Q. and Xu, Y.L. (2012), "Temperature effect on vibration properties of civil structures: A literature review and case studies", J. Civil Struct. Health Monitor., 2(1), 29-46. https://doi.org/10.1007/s13349-011-0015-7
  48. Xia, Y., Hao, H., Zanardo, G. and Deeks A. (2006), "Long term vibration monitoring of a RC slab: Temperature and humidity effect", Eng. Struct., 28(3), 441-452. https://doi.org/10.1016/j.engstruct.2005.09.001
  49. Xia, Y., Xu, Y.L., Wei, Z.L., Zhu, H.P. and Zhou, X.Q. (2011), "Variation of structural vibration characteristics versus non-uniform temperature distribution", Eng. Struct., 33(1), 146-153. https://doi.org/10.1016/j.engstruct.2010.09.027
  50. Yan, A.M., Kerschen, G., De Boe, P. and Golinval, J.C. (2005a), "Structural damage diagnosis under changing environmental conditions-part 1: Linear analysis", Mech. Syst. Sign. Pr., 19(4), 847-864. https://doi.org/10.1016/j.ymssp.2004.12.002
  51. Yan, A.M., Kerschen, G., De Boe, P. and Golinval, J.C. (2005b), "Structural damage diagnosis under changing environmental conditions-part 2: Local PCA for nonlinear cases", Mech. Syst. Sign. Pr., 19(4), 865-880. https://doi.org/10.1016/j.ymssp.2004.12.003
  52. Zhou, G.D. and Yi, T.H. (2014), "A summary review of correlations between temperatures and vibration properties of long-span bridges", Math. Probl. Eng., 2014(1), 1-19.

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