Skip to main content
SpringerLink
Log in

Vibration absorption of a rectangular plate supporting a DC motor with a TLCD

  • Original paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

In this paper, a tuned liquid column damper (TLCD) device is used to reduce the amplitude of vibration of a rectangular plate supporting a DC motor acting on a specific area. The motor induces transversal vibrations to the plate, and the liquid inside the TLCD moves vertically in both directions in order to influence the transversal displacement of the plate. The harmonic balance method coupled to the bisection method and the fourth-order Runge–Kutta method are used to find, respectively, an analytical solution and a numerical solution for the resulting equations of motion of the model. Previous works on the vibration control of non-ideal systems consist of the use firstly some electric transducers and secondly to the use of the synchronization phenomenon appearing between the DC motors to reduce the amplitude of vibrations. Here, we use a TLCD to reduce vibrations in the non-ideal system studied. In addition, here it is the liquid inside the U tube which moves vertically because of the position of the opening in the U tube which is responsible of the vibrations attenuation. It was found that the amplitude of vibration of the plate is considerably reduced. In addition, the effects of some parameters such as vertical length of the column, cross sectional of the vertical column, dimensions of the space occupied by the column on the plate, densities of the plate and the fluid, the coefficient of head loss of the orifice have a positive impact in reducing the amplitude of vibration of the plate.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Samanta, A., Banerji, P.: Structural control using modified tuned liquid dampers. In: The 14th world conference on earthquake engineering, Beijing, China (2008)

  2. Sakai, F.: Tuned liquid column damper-new type device for suppression of building vibration. In: Proceedings of \(1^{\hat{}}\text{st}\) International Conference on High-rise Buildings, pp. 926–931 (1989)

  3. Bauer, H.F.: Oscillations of immiscible liquids in a rectangular container: a new damper for excited structures. J. Sound Vib. 93(1), 117–133 (1984)

    Article  Google Scholar 

  4. Chaiviriyawong, P., Limkatanyu, S., Pinkaew, T.: Simulations of characteristics of tuned liquid column damper using an elliptical flow path estimation method. In: The 14th World Conference on Earthquake Engineering, China (2008)

  5. Chang, Y.: Analytical and experimental investigations of modified tuned liquid dampers (mtlds). Ph.D. thesis (2015)

  6. Ross, A.S., El Damatty, A.A., El Ansary, A.M.: Application of tuned liquid dampers in controlling the torsional vibration of high rise buildings. Wind Struct. 21(5), 537–564 (2015)

    Article  Google Scholar 

  7. Di Matteo, A., Furtmüller, T., Adam, C., Pirrotta, A.: Optimal design of tuned liquid column dampers for seismic response control of base-isolated structures. Acta Mechanica 229(2), 437–454 (2018)

    Article  MathSciNet  Google Scholar 

  8. Felix, J.L.P., Balthazar, J.M., BRASIL, R.M.L.R.: On tuned liquid column dampers mounted on a structural frame under a non-ideal excitation. J. Sound Vib 282(3-5), 1285–1292 (2005)

  9. Djanan, A.A.N., Nbendjo, B.R.N., Woafo, P.: Effect of self-synchronization of dc motors on the amplitude of vibration of a rectangular plate. Eur. Phys. J. Spec. Top. 223(4), 813–825 (2014)

    Article  Google Scholar 

  10. Djanan, A.A.N., Nbendjo, B.R.N., Woafo, P.: Self-synchronization of two motors on a rectangular plate and reduction of vibration. J. Vib. Control 21(11), 2114–2123 (2015)

    Article  Google Scholar 

  11. Djanan, A.A.N., Nbendjo, B.R.N.: Effect of two moving non-ideal sources on the dynamic of a rectangular plate. Nonlinear Dyn. 92(2), 645–657 (2018)

    Article  Google Scholar 

  12. Kong, X., Jiang, J., Zhou, C., Xu, Q., Chen, C.: Sommerfeld effect and synchronization analysis in a simply supported beam system excited by two non-ideal induction motors. Nonlinear Dynam. 100(3), 2047–2070 (2020)

    Article  Google Scholar 

  13. Eiger, A., Sikorski, K., Stenger, F.: A bisection method for systems of nonlinear equations. ACM Trans. Math. Softw. 10(4), 367–377 (1984)

    Article  MathSciNet  Google Scholar 

  14. Mickens, R.E.: Truly nonlinear oscillations: harmonic balance, parameter expansions, iteration, and averaging methods. World Scientific, (2010)

  15. Lanczos, C.: The variational principles of mechanics. Courier Corporation (2012)

  16. Wu, J.C., Chang, C.H., Lin, Y.Y.: Optimal designs for non-uniform tuned liquid column dampers in horizontal motion. J. Sound Vibration 326(1–2), 104–122 (2009)

    Article  Google Scholar 

  17. De Lagrange, J.L.: Mécanique analytique, vol. 1. Mallet-Bachelier (1853)

  18. Cortell, R.: Application of the fourth-order runge-kutta method for the solution of high-order general initial value problems. Comp. struct. 49(5), 897–900 (1993)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The second author is grateful to the DAAD (German Academic Exchange Service) (Grant No. 1) for the financial support during this work.

Author information

Authors and Affiliations

  1. Department of Civil Engineering, University of Cape Town, Rondebosch, 7700, Cape Town, South Africa

    E. Feulefack Songong

  2. Laboratory of Modeling and Simulation in Engineering, Biomimetics and Prototypes, Faculty of Science, University of Yaounde 1, Ngoa-Ekele 812, Yaounde, Cameroon

    A. A. Nanha Djanan & B. R. Nana Nbendjo

Authors
  1. E. Feulefack Songong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. A. Nanha Djanan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. B. R. Nana Nbendjo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. A. Nanha Djanan.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Songong, E.F., Djanan, A.A.N. & Nbendjo, B.R.N. Vibration absorption of a rectangular plate supporting a DC motor with a TLCD. Nonlinear Dyn 105, 1357–1372 (2021). https://doi.org/10.1007/s11071-021-06671-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-021-06671-1

Keywords

Search

Navigation