Steel and Composite Structures

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Exact and approximate solutions for free vibrations of continuous partial-interaction composite beams

  • Sun, Kai Q. (School of Civil Engineering, Beijing Jiaotong University) ;
  • Zhang, Nan (School of Civil Engineering, Beijing Jiaotong University) ;
  • Zhu, Qun X. (School of Civil and Environmental Engineering, University of Technology Sydney (UTS)) ;
  • Liu, Xiao (School of Civil Engineering, Beijing Jiaotong University)
  • Received : 2021.05.19
  • Accepted : 2022.08.10
  • Published : 2022.08.25
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Abstract

An exact dynamic analytical method for free vibrations of continuous partial-interaction composite beams is proposed based on the Timoshenko beam theory. The main advantage of this method is that the independent shear deformations and rotary inertia of sub-beams are considered, which is more in line with the reality. Therefore, the accuracy of eigenfrequencies obtained by this method is significantly improved, especially for higher order modes, compared to the existing methods where the rotary angles of both sub-beams are assumed to be equal irrespective of the differences in the shear stiffness of each sub-beam. Furthermore, the solutions obtained by the proposed method are exact owing to no introduction of approximated displacement and force fields in the derivation. In addition, an exact analytical solution for the case of simply supported is obtained. Based on this, an approximate expression for the fundamental frequency of continuous partial-interaction composite beams is also proposed, which is useful for practical engineering applications. Finally, the practicability and effectiveness of the proposed method and the approximate expression are explored using numerical and experimental examples; The influence factors including the interfacial interaction, shear modulus ratio, span-to-depth ratio, and side-to-main span length ratio on the eigenfrequencies are presented and discussed in detail.

Keywords

Acknowledgement

The research described in this paper was financially supported by the National Natural Science Foundation of China (52178101). In addition, the authors would like to express their gratitude to EditSprings (https://www.editsprings.com/) for the expert linguistic services provided.

References

  1. Berczynski, S. and Wroblewski, T. (2005), "Vibration of steel- concrete composite beams using the Timoshenko beam model", J. Vib. Control 11(6), 829-848. http://10.1177/1077546305054678.
  2. Cas, B., Planinc, I. and Schnabl, S. (2018), "Analytical solution of three-dimensional two-layer composite beam with interlayer slips", Eng. Struct. 173(2018), 269-282. https://doi.org/10.1016/j.engstruct.2018.06.108.
  3. Chakrabarti, A., Sheikh, A.H., Griffith, M. and Oehlers, D.J. (2012), "Analysis of composite beams with longitudinal and transverse partial interactions using higher order beam theory", Int. J. Mech. Sci., 59(2012), 115-125. http://dx.doi.org/10.1016/j.ijmecsci.2012.03.012.
  4. Chakrabarti, A., Sheikh, A.H., Griffith, M. and Oehlers, D.J. (2013), "Dynamic response of composite beams with partial shear interaction using a higher-order beam theory", J. Struct. Eng., 139(1) 47-56. http://10.1061/(ASCE)ST.1943-541X.0000603.
  5. Fang, G., Wang, J., Li, S. and Zhang, S. (2016), "Dynamic characteristics analysis of partial-interaction composite continuous beams", Steel Compos. Struct., 21(1), 195-216. https://doi.org/10.12989/scs.2016.21.1.195.
  6. Girhammar, U.A. and Pan, D.H. (1993), "Dynamic analysis of composite members with interlayer slip", Int. J. Solids Struct. 30(6), 797-823. https://doi.org/10.1016/0020-7683(93)90041-5.
  7. Girhammar, U.A., Pan, D.H. and Gustafsson, A. (2009), "Exact dynamic analysis of composite beams with partial interaction", Int. J. Mech. Sci., 51(8), 565-582. https://doi.org/10.1016/j.ijmecsci.2009.06.004.
  8. He, G.H. and Yang, X. (2015), "Dynamic analysis of two-layer composite beams with partial interaction using a higher order beam theory", Int. J. Mech. Sci., 90(2015), 102-112. http://dx.doi.org/10.1016/j.ijmecsci.2014.10.020.
  9. Hou, Z.M., Xia, H. and Zhang, Y.L. (2012), "Dynamic analysis and shear connector damage identification of steel-concrete composite beams", Steel Compos. Struct., 13(4), 327-341. https://doi.org/10.12989/scs.2012.13.4.327.
  10. Huang, C.W. and Su, Y.H. (2008), "Dynamic characteristics of partial composite beams", Int. J. Struct. Stab. Dyn., 8(4), 665-685. https://doi.org/10.1142/S0219455408002946.
  11. Jin, L.J. (2011), Natural Vibration Characteristic Analysis and Practical Calculator Research of Fundamental Frequency of the Continuous System Bridge with High-Pier and Long-Span, Ph.D. Dissertation, Zhejiang University of Technology, Zhejiang.
  12. Li, J., Huo, Q.J., Li, X.B., Shao, K.X. and Wu, W.G. (2014), "Dynamic stiffness analysis of steel-concrete composite beams", Steel Compos. Struct., 16(6), 577-593. https://doi.org/10.12989/scs.2014.16.6.577.
  13. Newmark, N.M., Siess, C.P. and Viest, I.M. (1951), "Test and analysis of composite beams with incomplete interaction", Proc. Soc. Exp. Stress Anal. 9(1), 75-92.
  14. Nguyen, Q.H., Hjiaj, M. and Grognec, P.L. (2012), "Analytical approach for free vibration analysis of two-layer Timoshenko beams with interlayer slip", J. Sound Vib. 331(12), 2949-2961. https://doi.org/10.1016/j.jsv.2012.01.034.
  15. Nie, J.G., Tao, M.X., Cai, C.S. and Li, S.J. (2009), "Deformation analysis of prestressed continuous steel-concrete composite beams", J. Struct. Eng., 135(11), 1377-1389. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000067.
  16. Schnabl, S., Saje, M., Turk, G. and Planinc, I. (2007), "Analytical solution of two-layer beam taking into account interlayer slip and shear deformation", J. Struc.t Eng.-ASCE 133(6), 886-894. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:6(886).
  17. Schnabl, S., Saje, M., Turk, G. and Planinc, I. (2007), "Lockingfree two-layer Timoshenko beam element with interlayer slip", Finite Elem. Anal. Des. 43(9), 705-714. https://doi.org/10.1016/j.finel.2007.03.002.
  18. Shen, X.D., Chen, W.Q., Wu, Y.F. and Xu, R.Q. (2011), "Dynamic analysis of partial-interaction composite beam", Compos. Sci. Technol. 71(10), 1286-1294. https://doi.org/10.1016/j.compscitech.2011.04.013.
  19. Sun, Q.K., Zhang, N., Liu, X. and Tao, X.Y. (2021), "Free vibrations of steel-concrete composite beams by the dynamic direct stiffness method", Int. J. Struct. Stab. Dyn., 21(4), 2150049. https://doi.org/10.1142/S0219455421500498.
  20. Sun, Q.K., Zhang, N., Liu, X. and Tao, X.Y. (2021), "An equivalent single-layer theory for free vibration analysis of steel-concrete composite beams", Steel Compos. Struct., 38(3), 281-291. http://dx.doi.org/10.12989/scs.2021.38.3.281.
  21. Wang, J.F., Zhang, J.T., Xu, R.Q. and Yang, Z.X. (2019), "A numerically stable dynamic coefficient method and its application in free vibration of partial-interaction continuous composite beams", J. Sound Vib., 457(2019), 314-332. https://doi.org/10.1016/j.jsv.2019.06.012.
  22. Wu, Y.F., Xu, R.Q. and Chen, W.Q. (2007), "Free vibrations of the partial-interaction composite members with axial force", J. Sound Vib. 299(4), 1074-1093. https://doi.org/10.1016/j.jsv.2006.08.008.
  23. Xu, R. and Wu, Y. (2007), "Static dynamic and buckling analysis of partial interaction composite members using Timoshenko's beam theory", Int. J. Mech. Sci., 49(10), 1139-1155. https://doi.org/10.1016/j.ijmecsci.2007.02.006.