Skip to main content
SpringerLink
Log in

Free vibration of a sagged cable with attached discrete elements

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

An algorithm is presented to analyze the free vibration in a system composed of a cable with discrete elements, e.g., a concentrated mass, a translational spring, and a harmonic oscillator. The vibrations in the cable are modeled and analyzed with the Lagrange multiplier formalism. Some fragments of the investigated structure are modeled with continuously distributed parameters, while the other fragments of the structure are modeled with discrete elements. In this case, the linear model of a cable with a small sag serves as a continuous model, while the elements, e.g., a translational spring, a concentrated mass, and a harmonic oscillator, serve as the discrete elements. The method is based on the analytical solutions in relation to the constituent elements, which, when once derived, can be used to formulate the equations describing various complex systems compatible with an actual structure. The numerical analysis shows that, the method proposed in this paper can be successfully used to select the optimal parameters of a system composed of a cable with discrete elements, e.g., to detune the frequency resonance of some structures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. SERGEV, S. S. and IWAN, W. D. The natural frequencies and mode shapes of cables with attached masses. Journal of Energy Resources Technology, 3, 237–242 (1981)

    Article  Google Scholar 

  2. CHENG, S. P. and PERKINS, N. C. Free vibration of a sagged cable supporting a discrete mass. The Journal of the Acoustical Society of America, 91, 2654–2662 (1992)

    Article  Google Scholar 

  3. LIN, H. P. and PERKINS, N. C. Free vibration of complex cable/mass systems: theory and experiment. Journal of Sound and Vibration, 179, 131–149 (1995)

    Article  Google Scholar 

  4. AL-QASSAB, M. and NAIR, S. Wavelet-Galerkin method for the free vibrations of an elastic cable carrying an attached mass. Journal of Sound and Vibration, 270, 191–206 (2004)

    Article  MATH  Google Scholar 

  5. WANG, L. and REGA, G. Modelling and transient planar dynamics of suspended cables with moving mass. International Journal of Solids and Structures, 47, 2733–2744 (2010)

    Article  MATH  Google Scholar 

  6. MAIN, J. A. and JONES, N. P. Free vibrations of taut cable with attached damper, I: linear viscous damper. Journal of Engineering Mechanics, 128, 1062–1071 (2002)

    Article  Google Scholar 

  7. CU, V. H., HAN, B., PHAM, D. H., and YAN, W. T. Free vibration and damping of a taut cable with an attached viscous mass damper. KSCE Journal of Civil Engineering, 22, 1792–1802 (2018)

    Article  Google Scholar 

  8. SUN, L. H. and CHEN, L. Free vibrations of a taut cable with a general viscoelastic damper modeled by fractional derivatives. Journal of Sound and Vibration, 335, 19–33 (2015)

    Article  Google Scholar 

  9. ZHOU, H., SUN, L., and XING, F. Damping of full-scale stay cable with viscous damper: experiment and analysis. Advances in Structural Engineering, 17, 265–274 (2014)

    Article  Google Scholar 

  10. ZHOU, H., SUN, L., and XING, F. Free vibration of taut cable with a damper and a spring. Structural Control and Health Monitoring, 21, 996–1014 (2014)

    Article  Google Scholar 

  11. YU, Z. and XU, Y. L. Mitigation of three-dimensional vibration of inclined sag cable using hdiscrete oil dampers, I: formulation. Journal of Sound and Vibration, 214, 659–673 (1998)

    Article  Google Scholar 

  12. WU, W. J. and CAI, C. S. Theoretical exploration of a taut cable and a TMD system. Engineering Structures, 29, 962–972 (2007)

    Article  Google Scholar 

  13. CHEN, L., SUN, L., and NAGARAJAIAH, S. Cable vibration control with both lateral and rotational dampers attached at an intermediate location. Journal of Sound and Vibration, 377, 38–57 (2016)

    Article  Google Scholar 

  14. MEKKI, O. B. and AURICCHIO, F. Performance evaluation of shape-memory-alloy superelastic behavior to control a stay cable in cable-stayed bridges. International Journal of Non-Linear Mechanics, 46, 470–477 (2011)

    Article  Google Scholar 

  15. ZHOU, H., YANG, X., SUN, L., and XING, F. Free vibrations of a two-cable network with near-support dampers and a cross-link. Structural Control and Health Monitoring, 22, 1173–1192 (2015)

    Article  Google Scholar 

  16. GIACCU, G. F., CARACOGILA, L., and BARBIELLINI, B. Modeling unilateral response in the cross-ties of a cable network: deterministic vibration. Journal of Sound and Vibration, 333, 4427–4443 (2014)

    Article  Google Scholar 

  17. GIACCU, G. F. and CARACOGILA, L. Effects of modeling nonlinearity in cross-ties on the dynamics of simplified in-plane cable networks. Structural Control and Health Monitoring, 19, 348–369 (2012)

    Article  Google Scholar 

  18. AHMAD, J., CHENG, S., and GHRIB, F. Impact of cross-tie properties on the modal behavior of cable networks on cable-stayed bridges. Scientific World Journal, 2015, 989536 (2015)

    Google Scholar 

  19. YAMAGUCHI, H. and ALAUDDIN, M. Control of cable vibrations using secondary cable with special reference to nonlinearity and interaction. Engineering Structures, 25, 801–816 (2003)

    Article  Google Scholar 

  20. DOWELL, E. H. Free vibrations of a linear structure with arbitrary support conditions. Journal of Applied Mechanics, 38, 595–600 (1971)

    Article  MATH  Google Scholar 

  21. DOWELL, E. H. Free vibrations of an arbitrary structure in terms of component modes. Journal of Applied Mechanics, 39, 727–732 (1972)

    Article  Google Scholar 

  22. DOWELL, E. H. On some general properties of combined dynamical systems. Journal of Applied Mechanics, 46, 206–209 (1979)

    Article  MATH  Google Scholar 

  23. GÜRGÖZE, M. On the eigenfrequencies of a cantilever beam with attached tip mass and a spring-mass system. Journal of Sound and Vibration, 190, 149–162 (1996)

    Article  Google Scholar 

  24. GÜRGÖZE, M. On the alternative formulations of the frequency equation of a Bernoulli-Euler beam to which several spring-mass systems are attached in-span. Journal of Sound and Vibration, 217, 585–595 (1998)

    Article  Google Scholar 

  25. GÜRGÖZE, M. Mechanical systems with a single viscous damper subject to a constraint equation. Computers and Structures, 70, 299–303 (1999)

    Article  MATH  Google Scholar 

  26. GÜRGÖZE, M. and Erol, H. On the eigencharacteristics of longitudinally vibrating rods carrying a tip mass and viscously damped spring-mass in-span. Journal of Sound and Vibration, 225, 573–580 (1999)

    Article  Google Scholar 

  27. POSIADAŁA, B. Use of Lagrange multiplier formalism to analyze free vibrations of combined dynamical systems. Journal of Sound and Vibration, 176, 563–572 (1994)

    Article  MATH  Google Scholar 

  28. POSIADAŁA, B. Free vibrations of uniform Timoshenko beams with attachments. Journal of Sound and Vibration, 204, 359–369 (1997)

    Article  MATH  Google Scholar 

  29. POSIADAŁA, B. and CEKUS, D. Discrete model of vibration of truck crane telescopic boom with consideration of the hydraulic cylinder of crane radius change in the rotary plane. Automation in Construction, 17, 245–250 (2008)

    Article  Google Scholar 

  30. POSIADAŁA, B., CEKUS, D., and WARYS, P. Algorithm for automatic analysis of free vibrations of uniform Bernoulli-Euler beams with attachments. Proceedings of the World Congress on Engineering and Computer Science 2012, San Francisco (2012)

    Google Scholar 

  31. CEKUS, D. Use of Lagrange multiplier formalism to solve transverse vibrations problem of stepped beams according to Timoshenko theory. Scientific Research of the Institute of Mathematics and Computer Science, 10, 49–56 (2011)

    Google Scholar 

  32. KUKLA, S. and POSIADAŁA, B. Free vibrations of beams with elastically mounted masses. Journal of Sound and Vibration, 175, 557–564 (1994)

    Article  MATH  Google Scholar 

  33. KUKLA, S. Application of Green functions in frequency analysis of Timoshenko beams with oscillators. Journal of Sound and Vibration, 205, 355–363 (1997)

    Article  MATH  Google Scholar 

  34. CHA, P. D. Eigenvalues of a linear elastic a carrying lumped masses, springs and viscous dampers. Journal of Sound and Vibration, 257, 798–808 (2002)

    Article  Google Scholar 

  35. CHA, P. D. and PIERRE, C. Free vibrations of uniform Timoshenko beams with lumped attachments. Journal of Sound and Vibration, 211, 273–176 (1998)

    Article  Google Scholar 

  36. CHA, P. D. Specifying nodes at multiple locations for any normal mode of a linear elastic structure. Journal of Sound and Vibration, 250, 923–934 (2002)

    Article  Google Scholar 

  37. IRVINE, H. M. and CAUGHEY, T. K. The linear theory of free vibrations of a suspended cable. Proceedings of The Royal Society A, 341, 299–315 (1974)

    Article  Google Scholar 

  38. IRVINE, H. M. Cable Structures, The MIT Press, Cambridge (1981)

    Google Scholar 

  39. CAETANO, E. Cable Vibration in Cable-Stayed Bridges, IABSE-AIPC-IVBH ETH Hönggerberg, Zürich (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Civil Engineering, Wrocław University of Science and Technology, Wrocław, 50-370, Poland

    W. Pakos

Authors
  1. W. Pakos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to W. Pakos.

Additional information

Citation: PAKOS, W. Free vibration of a sagged cable with attached discrete elements. Applied Mathematics and Mechanics (English Edition) (2019) https://doi.org/10.1007/s10483-019-2479-6

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pakos, W. Free vibration of a sagged cable with attached discrete elements. Appl. Math. Mech.-Engl. Ed. 40, 631–648 (2019). https://doi.org/10.1007/s10483-019-2479-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-019-2479-6

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Search

Navigation