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Nonlinear responses of a cable-beam coupled system under parametric and external excitations

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Abstract

This paper analytically investigates the nonlinear responses of a cable-beam coupled system under the combined effects of internal and external resonance. The cable is considered a geometric nonlinearity, and the beam is considered as Euler–Bernoulli model, but it is coupled by fixing it at one end. The coupled nonlinear differential equations are formulated by using the Hamilton principle. The spatial problem is solved by using Galerkin’s method to simplify the governing equations to a set of ordinary differential equations. Applying the multiple time scales method to the ordinary differential equations, the first approximate solutions and solvability condition are derived. The effects of the cable sag to span ratio, mass ratio, and stiffness ratio on the nonlinear responses are investigated. The results show good agreement between the analytical and numerical solutions especially near the external resonance frequency.

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References

  1. Yu W.Q., Chen F.Q.: Multi-pulse orbits and chaotic dynamics in a nonlinear forced dynamics of suspended cables. Arch. Appl. Mech. 81, 1231–1252 (2011)

    Article  Google Scholar 

  2. Nayfeh A.H., Arafat H.N., Chin C.M., Lacarbonara W.: Multi-mode interactions in suspended cables. J. Vib. Control 8, 337–387 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  3. Younesian D., Esmailzadeh E.: Non-linear vibration of variable speed rotating viscoelastic beams. Nonlinear Dyn. 60, 193–205 (2010)

    Article  MATH  Google Scholar 

  4. Ghayesh M.H.: Subharmonic dynamics of an axially accelerating beam. Arch. Appl. Mech. 82, 1169–1181 (2012)

    Article  Google Scholar 

  5. Wang L., Ni Q., Huang Y.Y.: Bifurcations and chaos in a forced cantilever system with impacts. J. Sound Vib. 296(4-5), 1068–1078 (2006)

    Article  Google Scholar 

  6. Mamandi A., Kargarnovin M.H., Farsi S.: An investigation on effects of traveling mass with variable velocity on nonlinear dynamic response of an inclined Timoshenko beam with different boundary conditions. Int. J. Mech. Sci. 52, 1694–1708 (2010)

    Article  Google Scholar 

  7. Mamandi A., Kargarnovin M.H.: Dynamic analysis of an inclined Timoshenko beam traveled by successive moving masses/forces with inclusion of geometric nonlinearities. Acta Mech. 218, 9–29 (2011)

    Article  MATH  Google Scholar 

  8. Holubová G., Matas A.: Initial-boundary value problem for the nonlinear string-beam system. J. Math. Anal. Appl. 288, 784–802 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  9. Yau J.D., Yang Y.B.: Vibration reduction for cable-stayed bridges traveled by high-speed trains. Finite Elem. Anal. Des. 40, 341–359 (2004)

    Article  Google Scholar 

  10. Xia Y., Fujino Y.: Auto-parametric vibration of a cable-stayed-beam structure under random excitation. ASCE J. Eng. Mech. 132, 279–286 (2006)

    Article  Google Scholar 

  11. Zhang W., Cao D.X.: Studies on bifurcation and chaos of a string-beam coupled system with two degrees-of-freedom. Nonlinear Dyn. 45, 131–147 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  12. Cao D.X., Zhang W.: Global bifurcations and chaotic dynamics for a string-beam coupled system. Chaos Solitons Fractals 37, 858–875 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  13. Gattulli V., Lepidi M.: Nonlinear interactions in the planar dynamics of cable-stayed beam. Int. J. Solids Struct. 40, 4729–4748 (2003)

    Article  MATH  Google Scholar 

  14. Gattulli V., Lepidi M., Macdonald J.H.G., Taylor C.A.: One-to-two global-local interaction in a cable-stayed beam observed through analytical, finite element and experimental models. Int. J. Nonlinear Mech. 40, 571–588 (2005)

    Article  MATH  Google Scholar 

  15. Zu J.W., Cheng G.: Dynamic analysis of an optical fiber coupler in telecommunications. J. Sound Vib. 268, 15–31 (2003)

    Article  Google Scholar 

  16. Wu Q., Takahashi K., Okabayashi T., Nakamura S.: Response characteristics of local vibrations in stay cables on an existing cable-stayed bridge. J. Sound Vib. 261, 403–420 (2003)

    Article  Google Scholar 

  17. Brownjohn J.M.W., Cheong B., Lee J.: Dynamic performance of a curved cable-stayed bridge. Eng. Struct. 21, 1015–1027 (1999)

    Article  Google Scholar 

  18. Caetano E., Cunha A., Taylor C.A.: Investigation of dynamic cable—deck interaction in a physical model of a cable-stayed bridge. Part II: seismic response. Earthq. Eng. Struct. 29, 499–521 (2000)

    Article  Google Scholar 

  19. Au F.T.K., Cheng Y.S., Cheung Y.K., Zheng D.Y.: On the determination of natural frequencies and mode shapes of cable-stayed bridges. Appl. Math. Model. 25, 1099–1115 (2001)

    Article  MATH  Google Scholar 

  20. Nayfeh A.H., Mook D.T.: Nonlinear oscillations. Wiley, New York (1979)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Construction and Engineering Management, Shenyang Jianzhu University, Shenyang, 110168, China

    Ming Hai Wei

  2. Department of Civil and Environment Engineering, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, 518055, China

    Yi Qing Xiao, Hai Tao Liu & Kun Lin

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  1. Ming Hai Wei
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  2. Yi Qing Xiao
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  3. Hai Tao Liu
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  4. Kun Lin
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Correspondence to Ming Hai Wei.

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Wei, M.H., Xiao, Y.Q., Liu, H.T. et al. Nonlinear responses of a cable-beam coupled system under parametric and external excitations. Arch Appl Mech 84, 173–185 (2014). https://doi.org/10.1007/s00419-013-0792-z

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  • DOI: https://doi.org/10.1007/s00419-013-0792-z

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