Skip to main content
Log in

Experimental study of the deflections of curved plates exposed to pulsating cross-flows

  • Original Paper
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

The deflection of thin, elastic plates with different curvatures is experimentally investigated under pulsatile cross-flow conditions. Average and maximum deflections are reported in terms of the plate’s curvature, flow frequency, and stroke fraction. The laboratory results indicate that the maximum deflections can be reduced significantly when the curvature is increased (around 50 % for low-to-intermediate curvatures and up to 80 % for high curvatures). Moreover, the comparative analysis shows that the deflection is inversely proportional to the rigidity of the plates, which depends nonlinearly on the curvature. Based on the observed behavior, a simplified Euler–Bernoulli beam model is derived to qualitatively explain the effects of geometrical factors such as the curvature, the thickness, and the length of the plates. Some traits of the flow evolving around the plate and the need to have accurate measurements of the pressure are discussed.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Andersen, A., Pasavento, U., Jane Wang, Z.: Unsteady aerodynamics of fluttering and tumbling plates. J. Fluid Mech. 541, 65–90 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  2. Arellano Castro, R.F., Guillamont, L., Cros, A., Eloy, C.: Non-linear effects on the resonant frequencies of a cantilevered plate. J. Fluids Struct. 46, 165–173 (2014)

    Article  Google Scholar 

  3. Aureli, M., Kopman, V., Porfiri, M.: Free locomotion of underwater vehicles actuated by ionic polymer metal composites. J. Appl. Phys. 109, 1–3 (2011)

    Google Scholar 

  4. Bidkar, R.A., Kimber, M., Raman, A., Bajaj, A.K., Garimella, S.V.: Nonlinear aerodynamic damping of sharp-edged flexible beams oscillating at low keulegan-carpenter numbers. J. Fluid Mech. 634, 269–289 (2009)

    Article  MATH  Google Scholar 

  5. Butcher, J.T., Mahler, G.J., Hockaday, L.A.: Aortic valve disease and treatment: the need for naturally engineered solutions. Adv. Drug Deliv. Rev. 1, 1–27 (2011)

    Google Scholar 

  6. Carra, S., Amabili, M., Garziera, R.: Experimental study of large amplitude vibrations of a thin plate in contact with sloshing liquids. J. Fluids Struct. 42, 88–111 (2013)

    Article  Google Scholar 

  7. Cook-Chennault, K.A., Thambi, N., Sastry, A.M.: Powering mems portable devices—a review of non-regenerative and regenerative power supply systems with special emphasis on piezoelectric energy harvesting systems. Smart Mater. Struct. 17, 1–33 (2008)

    Article  Google Scholar 

  8. Diourté, B., Siché, J.P., Comparat, V., Baguet, J.P., Mallion, J.M.: Study of arterial blood pressure by a windkessel-type model: influence of arterial functional properties. Comput. Methods Programs Biomed. 60, 11–12 (1999)

    Article  Google Scholar 

  9. Doaré, O., Sauzade, M., Eloy, C.: Flutter of an elastic plate in channel flow: confinement and finite-size effects. J. Fluids Struct. 27, 76–88 (2011)

    Article  Google Scholar 

  10. Eloy, C., Lagrange, R., Souilliez, C., Schouveiler, L.: Aeroelastic instability of cantileverd flexible plates in uniform flow. J. Fluid Mech. 611, 97–106 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  11. Faltinsen, O.M.: Hydroelastic slamming. J. Mar. Sci. Technol. 5, 49–65 (2000)

    Article  Google Scholar 

  12. Garitey, V., Gandelheid, T., Fusezi, J., Pelissier, R.: Ventricular flow dynamic past bileaflet prosthetic heart valves. Int. J. Artif. Organs 18, 380–391 (1995)

    Google Scholar 

  13. Gluck, M., Breuer, M., Durst, F., Halfmann, A., Rank, E.: Computation of fluid structure interaction on lightweight structures. J. Wind Eng. 89, 1351–1368 (2001)

    Google Scholar 

  14. Gosselin, F., Langre, E., Machado-Almeida, B.: Drag reduction of flexible plates by reconfiguration. J. Fluid Mech. 650, 319–341 (2010)

    Article  MATH  Google Scholar 

  15. Grigioni, M., Daniele, C., D’Avenio, G., Barbaro, V.: The influence of the leaflets’ curvature on the flow field in two bileaflet prosthetic heart valves. J. Biomech. 34, 613–621 (2001)

    Article  Google Scholar 

  16. He, G., Kashiwagi, M.: Nonlinear analysis on wave-plate interaction due to disturbed vertical elastic plate. J. Hydrodyn. 22, 507–512 (2010)

  17. Hernańdez-Badillo, C., Guzmán, J., Zenit, R.: Effect of the curvature of elastic plates on the evolution of pulsatile flow fields. J. Fluids Struct. 56, 177–189 (2015)

    Article  Google Scholar 

  18. Holman, J.P.: Experimental Methods for Engineers. McGraw-Hill Book Company, New York (2012)

    Google Scholar 

  19. Howell, R.M., Lucey, A.D., Pitman, M.W.: The effect of inertial inhomogeneity on the flutter of a cantilevered flexible plate. J. Fluids Struct. 27, 383–393 (2011)

    Article  Google Scholar 

  20. Ihara, A., Watanabe, H.: On the flow around flexible plates oscillating with large amplitude. J. Fluids Struct. 8, 601–619 (1994)

    Article  Google Scholar 

  21. Landau, L., Lifshitz, E.M.: Theroy of Elasticity: Course on Theoretical Physics Volume 7, 3rd edn. Butterworth Heinemann, Oxford (1986)

    Google Scholar 

  22. Lauga, E., Powers, T.R.: The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72, 1–36 (2009)

    Article  MathSciNet  Google Scholar 

  23. Ledesma-Alonso, R., Guzmán, J.E.V., Zenit, R.: Experimental study of a model valve with flexible leaflets in a pulsatile flow. J. Fluid Mech. 739, 338–362 (2014)

    Article  Google Scholar 

  24. Lee, J., Lee, S.: Fluid-structure interaction analysis on a flexible plate normal to a free stream at low reynolds numbers. J. Fluids Struct. 29, 18–34 (2012)

    Article  Google Scholar 

  25. Li, S., Yuang, J., Lipson, H.: Ambient wind energy harvesting using cross-flow fluttering. J. Appl. Phys. 109, 1–3 (2011)

    Google Scholar 

  26. López-Zazueta, A., Ledesma-Alonso, R., Guzmán, J.E.V., Zenit, R.: Study of the velocity and strain fields in the flow through prosthetic heart valves. J. Biomech. Eng. 133, 003–10 (2011)

  27. Meirovitch, L.: Elements of Vibration Analysis. McGraw-Hill Book Company, New York (1986)

    MATH  Google Scholar 

  28. Nielsen, A.H., Rasmussen, J.J.: Formation and temporal evolution of the Lamb-dipole. Phys. Fluids 9, 982–991 (1997)

  29. Peterson, S.D., Porfiri, M., Rovardi, A.: A particle image velocimetry study of vibrating ionic polymer metal composites in acqueous environments. IEEE/ASME Trans. Mechatron. 14, 474–483 (2009)

    Article  Google Scholar 

  30. Porfiri, M., Peterson, S.: Advances in Energy Harvesting Methods, 1st edn. Springer, New York (2013)

    Google Scholar 

  31. Prince, C., Lin, W., Lin, J., Peterson, S.D., Porfiri, M.: Temporally-resolved hydrodynamics in the vicinity of a vibrating ionic polymer metal. J. Appl. Phys. 107, 1–12 (2010)

    Article  Google Scholar 

  32. Sipcic, S.R.: The chaotic response of a fluttering panel: the influence of maneuvering. Nonlinear Dyn. 1, 243–264 (1990)

    Article  Google Scholar 

  33. Taylor, R.E., Ohkusu, M.: Green functions for hydroelastic analysis of vibrating free-free beams and plates. Appl. Ocean Res. 22, 295–314 (2000)

    Article  Google Scholar 

  34. Thiriet, M.: Biology and Mechanics of Blood Flows, Part II: Mechanics and Medical Aspects, 1st edn. Springer, New York (2008)

    Book  MATH  Google Scholar 

  35. Tubaldi, E., Amabili, M.: Vibrations and stability of a periodically supported rectangular plate immersed in axial flow. J. Fluids Struct. 39, 391–407 (2013)

    Article  Google Scholar 

  36. Yamaguchi, N., Yokota, K., Tsujimoto, Y.: Flutter limits and behaviors of a flexible thin sheet in high-speed flow-I: analytical method for prediction of the sheet behavior. J. Fuids Eng. 122, 65–73 (2000)

    Google Scholar 

  37. Yoganathan, A.P., He, Z., Casey-Jones, S.: Fluid mechanics of heart valves. Annu. Rev. Biomed. Eng. 6, 331–362 (2004)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to J. E. V. Guzmán.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Guzmán, J.E.V., Hernández-Badillo, C. & Zenit, R. Experimental study of the deflections of curved plates exposed to pulsating cross-flows. Acta Mech 227, 3621–3637 (2016). https://doi.org/10.1007/s00707-016-1687-1

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-016-1687-1

Navigation