Skip to main content
SpringerLink
Log in

An efficient method for vibration and stability analysis of rectangular plates axially moving in fluid

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

Abstract

An efficient method is developed to investigate the vibration and stability of moving plates immersed in fluid by applying the Kirchhoff plate theory and finite element method. The fluid is considered as an ideal fluid and is described with Bernoulli’s equation and the linear potential flow theory. Hamilton’s principle is used to acquire the dynamic equations of the immersed moving plate. The mass matrix, stiffness matrix, and gyroscopic inertia matrix are determined by the exact analytical integration. The numerical results show that the fundamental natural frequency of the submersed moving plates gradually decreases to zero with an increase in the axial speed, and consequently, the coupling phenomenon occurs between the first- and second-order modes. It is also found that the natural frequency of the submersed moving plates reduces with an increase in the fluid density or the immersion level. Moreover, the natural frequency will drop obviously if the plate is located near the rigid wall. In addition, the developed method has been verified in comparison with available results for special cases.

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. CHEN, L., ZHANG, W., and LIU, Y. Modeling of nonlinear oscillations for viscoelastic moving belt using generalized Hamilton’s principle. Journal of Vibration and Acoustics, 129(1), 128–132 (2007)

    Article  Google Scholar 

  2. DING, H. and CHEN, L. Q. Galerkin methods for natural frequencies of high-speed axially moving beams. Journal of Sound and Vibration, 329(17), 3484–3494 (2010)

    Article  Google Scholar 

  3. YAO, M., ZHANG, W., and ZU, J. W. Multi-pulse chaotic dynamics in non-planar motion of parametrically excited viscoelastic moving belt. Journal of Sound and Vibration, 331(11), 2624–2653 (2012)

    Article  Google Scholar 

  4. DING, H., HUANG, L. L., DOWELL, E., and CHEN, L. Q. Stress distribution and fatigue life of nonlinear vibration of an axially moving beam. Science China Technological Sciences, 62(7), 1123–1133 (2019)

    Article  Google Scholar 

  5. MAO, X. Y., DING, H., and CHEN, L. Q. Internal resonance of a supercritically axially moving beam subjected to the pulsating speed. Nonlinear Dynamics, 95(1), 631–651 (2019)

    Article  Google Scholar 

  6. CHEN, L. Q. Analysis and control of transverse vibrations of axially moving strings. Applied Mechanics Reviews, 58(2), 91–116 (2005)

    Article  Google Scholar 

  7. PELLICANO, F. and VESTRONI, F. Nonlinear dynamics and bifurcations of an axially moving beam. Journal of Vibration and Acoustics, 122(1), 21–30 (2000)

    Article  Google Scholar 

  8. ÖZ, H., PAKDEMIRLI, M., and BOYACI, H. Non-linear vibrations and stability of an axially moving beam with time-dependent velocity. International Journal of Non-Linear Mechanics, 36(1), 107–115 (2001)

    Article  Google Scholar 

  9. ZHANG, W., WANG, D., and YAO, M. Using Fourier differential quadrature method to analyze transverse nonlinear vibrations of an axially accelerating viscoelastic beam. Nonlinear Dynamics, 78(2), 839–856 (2014)

    Article  MathSciNet  Google Scholar 

  10. CHEN, L. Q. and YANG, X. D. Steady-state response of axially moving viscoelastic beams with pulsating speed: comparison of two nonlinear models. International Journal of Solids and Structures, 42(1), 37–50 (2005)

    Article  MathSciNet  Google Scholar 

  11. GHAYESH, M. H. and BALAR, S. Non-linear parametric vibration and stability of axially moving visco-elastic Rayleigh beams. International Journal of Solids and Structures, 45(25-26), 6451–6467 (2008)

    Article  Google Scholar 

  12. CHEN, L., ZHANG, W., and YANG, F. Nonlinear dynamics of higher-dimensional system for an axially accelerating viscoelastic beam with in-plane and out-of-plane vibrations. Journal of Sound and Vibration, 329(25), 5321–5345 (2010)

    Article  Google Scholar 

  13. YANG, X. D., TANG, Y. Q., CHEN, L. Q., and LIM, C. W. Dynamic stability of axially accelerating Timoshenko beam: averaging method. European Journal of Mechanics-A/Solids, 29(1), 81–90 (2010)

    Article  MathSciNet  Google Scholar 

  14. CHANG, J. R., LIN, W. J., HUANG, C. J., and CHOI, S. T. Vibration and stability of an axially moving Rayleigh beam. Applied Mathematical Modelling, 34(6), 1482–1497 (2010)

    Article  MathSciNet  Google Scholar 

  15. HUANG, J., SU, R., LI, W., and CHEN, S. Stability and bifurcation of an axially moving beam tuned to three-to-one internal resonances. Journal of Sound and Vibration, 330(3), 471–485 (2011)

    Article  Google Scholar 

  16. DING, H. and CHEN, L. Q. Natural frequencies of nonlinear vibration of axially moving beams. Nonlinear Dynamics, 63(1–2), 125–134 (2011)

    Article  MathSciNet  Google Scholar 

  17. ZHOU, Y. F. and WANG, Z. M. Transverse vibration characteristics of axially moving viscoelastic plate. Applied Mathematics and Mechanics (English Edition), 28(2), 209–218 (2007) https://doi.org/10.1007/s10483-007-0209-1

    Article  MathSciNet  Google Scholar 

  18. BANICHUK, N., JERONEN, J., NEITTAANMÄI, P., and TUOVINEN, T. On the instability of an axially moving elastic plate. International Journal of Solids and Structures, 47(1), 91–99 (2010)

    Article  Google Scholar 

  19. MARYNOWSKI, K. Free vibration analysis of the axially moving Levy-type viscoelastic plate. European Journal of Mechanics-A/Solids, 29(5), 879–886 (2010)

    Article  Google Scholar 

  20. YANG, X. D., ZHANG, W., CHEN, L. Q., and YAO, M. H. Dynamical analysis of axially moving plate by finite difference method. Nonlinear Dynamics, 67(2), 997–1006 (2012)

    Article  MathSciNet  Google Scholar 

  21. GHAYESH, M. H., AMABILI, M., and PAIDOUSSIS, M. P. Nonlinear dynamics of axially moving plates. Journal of Sound and Vibration, 332(2), 391–406 (2013)

    Article  Google Scholar 

  22. ZHANG, D. B., TANG, Y. Q., and CHEN, L. Q. Internal resonance in parametric vibrations of axially accelerating viscoelastic plates. European Journal of Mechanics-A/Solids, 75, 142–155 (2019)

    Article  MathSciNet  Google Scholar 

  23. ZHANG, W., LU, S., and YANG, X. Analysis on nonlinear dynamics of a deploying composite laminated cantilever plate. Nonlinear Dynamics, 76(1), 69–93 (2014)

    Article  MathSciNet  Google Scholar 

  24. WANG, L. and NI, Q. Vibration and stability of an axially moving beam immersed in fluid. International Journal of Solids and Structures, 45(5), 1445–1457 (2008)

    Article  Google Scholar 

  25. NI, Q., LI, M., TANG, M., and WANG, L. Free vibration and stability of a cantilever beam attached to an axially moving base immersed in fluid. Journal of Sound and Vibration, 333(9), 2543–2555 (2014)

    Article  Google Scholar 

  26. WANG, Y. Q., HUANG, X. B., and LI, J. Hydroelastic dynamic analysis of axially moving plates in continuous hot-dip galvanizing process. International Journal of Mechanical Sciences, 110, 201–216 (2016)

    Article  Google Scholar 

  27. WANG, Y. Q. and ZU, J. W. Instability of viscoelastic plates with longitudinally variable speed and immersed in ideal liquid. International Journal of Applied Mechanics, 9(1), 1750005 (2017)

    Article  Google Scholar 

  28. REDDY, J. N. Theory and Analysis of Elastic Plates and Shells, CRC Press, Florida (2006)

    Book  Google Scholar 

  29. CHARBONNEAU, E. and LAKIS, A. A. Semi-analytical shape functions in the finite element analysis of rectangular plates. Journal of Sound and Vibration, 242(3), 427–443 (2001)

    Article  Google Scholar 

  30. ELGER, D. F., ROBERSON, J. A., WILLIAMS, B. C., and CROWE, C. T. Engineering Fluid Mechanics, Wiley, New Jersey (2016)

    Google Scholar 

  31. AMABILI, M. Nonlinear Vibrations and Stability of Shells and Plates, Cambridge University Press, London (2008)

    Book  Google Scholar 

  32. KERBOUA, Y., LAKIS, A., THOMAS, M., and MARCOUILLER, L. Vibration analysis of rectangular plates coupled with fluid. Applied Mathematical Modelling, 32(12), 2570–2586 (2008)

    Article  Google Scholar 

  33. FU, Y. and PRICE, W. Interactions between a partially or totally immersed vibrating cantilever plate and the surrounding fluid. Journal of Sound and Vibration, 118(3), 495–513 (1987)

    Article  Google Scholar 

  34. LINDHOLM, U. S., KANA, D. D., CHU, W. H., and ABRAMSON, H. N. Elastic vibration characteristics of cantilever plates in water. Journal of Ship Research, 9(2), 11–36 (1965)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanics, College of Sciences, Northeastern University, Shenyang, 110819, China

    Yanqing Wang, Han Wu & Fengliu Yang

  2. Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, Northeastern University, Shenyang, 110819, China

    Yanqing Wang

  3. Department of Civil and Environmental Engineering, Shantou University, Shantou, Guangdong Province, 515063, China

    Quan Wang

Authors
  1. Yanqing Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Han Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fengliu Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Quan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yanqing Wang.

Additional information

Citation: WANG, Y. Q., WU, H., YANG, F. L., and WANG, Q. An efficient method for vibration and stability analysis of rectangular plates axially moving in fluid. Applied Mathematics and Mechanics (English Edition) (2021) https://doi.org/10.1007/s10483-021-2701-5

Project supported by the National Natural Science Foundation of China (Nos. 11922205 and 11672071), the Liaoning Revitalization Talents Program (No. XLYC1807026), and the Fundamental Research Funds for the Central Universities (No. N2005019)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Y., Wu, H., Yang, F. et al. An efficient method for vibration and stability analysis of rectangular plates axially moving in fluid. Appl. Math. Mech.-Engl. Ed. 42, 291–308 (2021). https://doi.org/10.1007/s10483-021-2701-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-021-2701-5

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Search

Navigation