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Acta Mechanica Sinica

, Volume 35, Issue 1, pp 15–23 | Cite as

Study on vibration of dragon wash basin and free surface waves inside

  • Zi-Yu Guo
  • Xiao-Peng ChenEmail author
  • Lai-Bing Jia
  • Bin Xu
Research Paper
  • 26 Downloads

Abstract

We conducted experimental and numerical studies on the vibrating modes of a dragon wash basin (DWB) and the free surface waves inside the DWB. Both the vibration of the DWB and the sound produced were studied carefully. It was found that the DWB can be excited at different intrinsic modes under different excitation, including striking and rubbing it fast/slowly. However, with gentle rubbing, the DWB will be excited mainly at the first vibrating mode. We showed that the concave side wall of a DWB decreases the intrinsic frequencies (compared with a straight side wall), and the ears of a DWB lead to breaking of the vibrating-axisymmetry and cause the separation of modes I/II and IV/V as well. A theoretical model, in which the water is assumed to be incompressible and inviscid, is applied to the first order vibration and predicts the relation of vibrating frequency versus water depth in the system. The measurement shows that both the radial and azimuthal waves are produced as DWB is working. The frequency of the first component of the surface wave is twice as large as the second one induced by non-linear effects. For both the radial and azimuthal waves, the dispersion relation is presented in the framework of capillary wave theory.

Keywords

Dragon wash basin Eigen-mode vibration Surface wave 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grants 11172241 and 11472220). We are also grateful to Y. Lei at NPU for the help on sound measurements. X.P. Chen also thanks Professor J. Jiang for the valuable discussions on vibration fundamentals.

Supplementary material

10409_2018_802_MOESM1_ESM.zip (1.8 mb)
Supplementary material 1 (ZIP 1792 kb)

References

  1. 1.
    Wang, D.J.: A study on mechanical properties of cultural relic. Sci. Conserv. Archaeol. 1, 35–39 (1993). (in Chinese)Google Scholar
  2. 2.
    Wang, D.J., Liu, X.J., Huang, Q.H., et al.: “Dragon wash basin phenomenon” and its mechanism. In: Proceeding of the Second China-Japan International Conference on History of Mechanical Technology, NanKing, 1–3 November 2000Google Scholar
  3. 3.
    Ding, W.J.: Self excited vibration. TsingHua University Press, Beijing (2009). (in Chinese)Google Scholar
  4. 4.
    Liu, X.J., Wang, D.J.: Nonlinear analysis on interesting phenomenon of Chinese dragon wash basin. Chin. Sci. Bull. 41(5), 413–417 (1996). (in Chinese)Google Scholar
  5. 5.
    Jia, Q.F., Yu, W., Liu, X.J., et al.: Approximate analytical solution of the piecewise-smooth nonlinear systems of multi-degrees-of-freedom. Chin. J. Theor. Appl. Mech. 36(3), 373–378 (2004). (in Chinese)Google Scholar
  6. 6.
    Peng, H.W., Wang, D.J., Lee, C.B.: Nonlinear low frequency water waves in a cylindrical shell. Mod. Phys. Lett. B 19(28–29), 1615–1618 (2005)CrossRefGoogle Scholar
  7. 7.
    Peng, H.W., Yuan, H.J., Wang, D.J., et al.: Experimental studies on dragon wash phenomena. J. Hydrodyn. Ser. B 18(1), 496–499 (2006)CrossRefGoogle Scholar
  8. 8.
    Peng, H.W., Li, R.Q., Chen, S.Z.: Correlation dimension analysis and capillary wave turbulence in dragon-wash phenomena. Chin. Phys. B 17(2), 637 (2008)CrossRefGoogle Scholar
  9. 9.
    Lee, C.B., Peng, H.W., Yuan, H., et al.: Experimental studies of surface waves inside a cylindrical container. J. Fluid Mech. 677, 39–62 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    French, A.P.: In vino veritas: a study of wineglass acoustics. Am. J. Phys. 51(8), 688–694 (1983)CrossRefGoogle Scholar
  11. 11.
    Rossing, T.D.: Acoustics of the glass harmonica. J. Acoust. Soc. Am. 95(2), 1106–1111 (1994)CrossRefGoogle Scholar
  12. 12.
    Jundt, G., Radu, A., Fort, E., et al.: Vibrational modes of partly filled wine glasses. J. Acoust. Soc. Am. 119(6), 3793–3798 (2006)CrossRefGoogle Scholar
  13. 13.
    Van der Jeught, S., Dirckx, J.J.: Real-time structured light profilometry: a review. Opt. Lasers Eng. 87, 18–31 (2016)CrossRefGoogle Scholar
  14. 14.
    Zhou, C., Liu, T., Si, S., et al.: An improved stair phase encoding method for absolute phase retrieval. Opt. Lasers Eng. 66, 269–278 (2015)CrossRefGoogle Scholar
  15. 15.
    Nguyen, H., Nguyen, D., Wang, Z., et al.: Real-time, high-accuracy 3D imaging and shape measurement. Appl. Opt. 54(1), A9–A17 (2015)CrossRefGoogle Scholar
  16. 16.
    Harris, D.M., Quintela, J., Prost, V., et al.: Viualization of hydrodynamic pilot-wave phenomena. J. Vis. 20(1), 13–15 (2017)CrossRefGoogle Scholar
  17. 17.
    Bush, J.W.: Pilot-wave hydrodynamics. Annu. Rev. Fluid Mech. 47, 269–292 (2015)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Rao, S.S.: The finite element method in engineering. Elsevier, Amsterdam (2010)Google Scholar
  19. 19.
    Wang, X.C.: Finite element method. TsingHua University Press, Beijing (2003). (in Chinese)Google Scholar
  20. 20.
    Ansys Inc.: Ansys user’s manual. Ansys Inc., Canonsburg (2016)Google Scholar
  21. 21.
    Landau, L.D., Lifshitz, E.M.: Fluid mechanics, 2nd edn. Pergamon Press, Oxford (1987)Google Scholar
  22. 22.
    Rayleigh, J.W.S.: The theory of sound, vol. 2. Macmillan, London (1896)zbMATHGoogle Scholar
  23. 23.
    Hsieh, D.Y.: Water waves in an elastic vessel. Acta. Mech. Sin. 13(4), 289–303 (1997)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Probstein, R.F.: Physicochemical hydrodynamics. Wiley, New Jersey (1994)CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Zi-Yu Guo
    • 1
  • Xiao-Peng Chen
    • 1
    • 2
    Email author
  • Lai-Bing Jia
    • 2
  • Bin Xu
    • 1
  1. 1.School of Mechanics, Civil Engineering and ArchitectureNorthwestern Polytechnical UniversityXi’anChina
  2. 2.School of Marine Science and TechnologyNorthwestern Polytechnical UniversityXi’anChina

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