Hostname: page-component-6bf8c574d5-mggfc Total loading time: 0 Render date: 2025-02-14T15:50:08.715Z Has data issue: false hasContentIssue false
  • English
  • Français

Flow-induced periodic snap-through dynamics

Published online by Cambridge University Press:  03 March 2021

Hyeonseong Kim ,
Mohsen Lahooti Open the ORCID record for Mohsen Lahooti [Opens in a new window] ,
Junsoo Kim  and
Daegyoum Kim Open the ORCID record for Daegyoum Kim [Opens in a new window]
Hyeonseong Kim
Affiliation:
Department of Mechanical Engineering, KAIST, Daejeon34141, Republic of Korea
Mohsen Lahooti
Affiliation:
Department of Mechanical Engineering, KAIST, Daejeon34141, Republic of Korea
Junsoo Kim
Affiliation:
Department of Mechanical Engineering, KAIST, Daejeon34141, Republic of Korea
Daegyoum Kim*
Affiliation:
Department of Mechanical Engineering, KAIST, Daejeon34141, Republic of Korea
*
†Email address for correspondence: daegyoum@kaist.ac.kr
Get access Rights & Permissions [Opens in a new window]

Abstract

The stability and post-critical behaviour of periodic snapping are investigated experimentally for a buckled elastic sheet with two clamped ends under an external uniform flow. In addition to experimental investigations, low-order numerical simulations are conducted with the elastica model for the deformation of the sheet, which is coupled with the simple quasi-steady fluid force model based on Bollay's lift theory, in order to identify the deformed shape of the sheet in an equilibrium state and the critical velocity where the sheet begins to snap. Continuous exposure to fluid-dynamic loading induces snap-through oscillations from an initial equilibrium state. While the critical flow velocity for bifurcation is inversely related to the ratio of the streamwise distance of the sheet to its length, it is not significantly affected by the mass ratio of the sheet and the surrounding fluid, leading to divergence instability. In the post-equilibrium state, regular oscillations with the same dominant modes persist in the sheet for a broad range of the flow velocity. As the sheet crosses the midline in the snapping process, the bending energy stored in the sheet is released quickly, and the time for energy release is found to be lower than that required for energy storage. Because of the initial buckled shape, the minimum bending energy of the sheet over a cycle remains at least 40% of its maximum magnitude.

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 913 , 25 April 2021 , A52
Check for updates
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Alben, S. 2009 Wake-mediated synchronization and drafting in coupled flags. J.Fluid Mech. 641, 489.CrossRefGoogle Scholar
Alben, S. & Shelley, M.J. 2008 Flapping states of a flag in an inviscid fluid: bistability and the transition to chaos. Phys. Rev. Lett. 100 (7), 074301.CrossRefGoogle Scholar
Alben, S., Shelley, M. & Zhang, J. 2002 Drag reduction through self-similar bending of a flexible body. Nature 420 (6915), 479–481.CrossRefGoogle ScholarPubMed
Alexander, R.M. 2003 Principles of Animal Locomotion. Princeton University Press.CrossRefGoogle Scholar
Arena, G., Groh, R.M.J., Brinkmeyer, A., Theunissen, R., Weaver, P.M. & Pirrera, A. 2017 Adaptive compliant structures for flow regulation. Proc. R. Soc. A 473 (2204), 20170334.CrossRefGoogle ScholarPubMed
Argentina, M. & Mahadevan, L. 2005 Fluid-flow-induced flutter of a flag. Proc. Natl Acad. Sci. USA 102 (6), 1829–1834.CrossRefGoogle ScholarPubMed
Audoly, B. & Pomeau, Y. 2010 Elasticity and Geometry: From Hair Curls to the Non-Linear Response of Shells. Oxford University Press.Google Scholar
Beharic, J., Lucas, T.M. & Harnett, C.K. 2014 Analysis of a compressed bistable buckled beam on a flexible support. J.Appl. Mech. 81 (8), 081011.CrossRefGoogle Scholar
Berkooz, G., Holmes, P. & Lumley, J.L. 1993 The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25 (1), 539–575.CrossRefGoogle Scholar
Boisseau, S., Despesse, G., Monfray, S., Puscasu, O. & Skotnicki, T. 2013 Semi-flexible bimetal-based thermal energy harvesters. Smart Mater. Struct. 22 (2), 025021.CrossRefGoogle Scholar
Bollay, W. 1939 A non-linear wing theory and its application to rectangular wings of small aspect ratio. Z. Angew. Math. Mech. 19 (1), 21–35.CrossRefGoogle Scholar
Buchak, P., Eloy, C. & Reis, P.M. 2010 The clapping book: wind-driven oscillations in a stack of elastic sheets. Phys. Rev. Lett. 105 (19), 194301.CrossRefGoogle Scholar
Chen, J.S. & Hung, S.Y. 2011 Snapping of an elastica under various loading mechanisms. Eur. J. Mech. A Solids 30 (4), 525–531.CrossRefGoogle Scholar
Cleary, J. & Su, H.J. 2015 Modeling and experimental validation of actuating a bistable buckled beam via moment input. J.Appl. Mech. 82 (5), 051005.CrossRefGoogle Scholar
Connell, B.S. & Yue, D.K. 2007 Flapping dynamics of a flag in a uniform stream. J.Fluid Mech. 581, 33–67.CrossRefGoogle Scholar
Eloy, C., Lagrange, R., Souilliez, C. & Schouveiler, L. 2008 Aeroelastic instability of cantilevered flexible plates in uniform flow. J.Fluid Mech. 611, 97–106.CrossRefGoogle Scholar
Eloy, C., Souilliez, C. & Schouveiler, L. 2007 Flutter of a rectangular plate. J.Fluids Struct. 23 (6), 904–919.CrossRefGoogle Scholar
Fargette, A., Neukirch, S. & Antkowiak, A. 2014 Elastocapillary snapping: capillarity induces snap-through instabilities in small elastic beams. Phys. Rev. Lett. 112 (13), 137802.CrossRefGoogle ScholarPubMed
Forterre, Y., Skotheim, J.M., Dumais, J. & Mahadevan, L. 2005 How the venus flytrap snaps. Nature 433 (7024), 421.CrossRefGoogle ScholarPubMed
Gomez, M., Moulton, D.E. & Vella, D. 2017 a Critical slowing down in purely elastic ‘snap-through’ instabilities. Nat. Phys. 13 (2), 142.CrossRefGoogle Scholar
Gomez, M., Moulton, D.E. & Vella, D. 2017 b Passive control of viscous flow via elastic snap-through. Phys. Rev. Lett. 119 (14), 144502.CrossRefGoogle ScholarPubMed
Gonçalves, P.B., Pamplona, D., Teixeira, P.B., Jerusalmi, R.L., Cestari, I.A. & Leirner, A.A. 2003 Dynamic non-linear behavior and stability of a ventricular assist device. Intl J. Solids Struct. 40 (19), 5017–5035.CrossRefGoogle Scholar
Gosselin, F., de Langre, E. & Machado-Almeida, B.A. 2010 Drag reduction of flexible plates by reconfiguration. J.Fluid Mech. 650, 319–341.CrossRefGoogle Scholar
Guo, C.Q. & Païdoussis, M.P. 2000 Stability of rectangular plates with free side-edges in two-dimensional inviscid channel flow. J.Appl. Mech. 67 (1), 171–176.CrossRefGoogle Scholar
Gurugubelli, P.S. & Jaiman, R.K. 2015 Self-induced flapping dynamics of a flexible inverted foil in a uniform flow. J.Fluid Mech. 781, 657–694.CrossRefGoogle Scholar
Han, J.S., Ko, J.S. & Korvink, J.G. 2004 Structural optimization of a large-displacement electromagnetic lorentz force microactuator for optical switching applications. J.Micromech. Microengng 14 (11), 1585.CrossRefGoogle Scholar
Huang, W.X. & Sung, H.J. 2010 Three-dimensional simulation of a flapping flag in a uniform flow. J.Fluid Mech. 653, 301–336.CrossRefGoogle Scholar
Inamdar, T.C., Wang, X. & Christov, I.C. 2020 Unsteady fluid-structure interactions in a soft-walled microchannel: a one-dimensional lubrication model for finite reynolds number. Phys. Rev. Fluids 5 (6), 064101.CrossRefGoogle Scholar
Jensen, O.E. & Heil, M. 2003 High-frequency self-excited oscillations in a collapsible-channel flow. J.Fluid Mech. 481, 235–268.CrossRefGoogle Scholar
Jia, L.B., Li, F., Yin, X.Z. & Yin, X.Y. 2007 Coupling modes between two flapping filaments. J.Fluid Mech. 581, 199.CrossRefGoogle Scholar
Kim, D., Cossé, J., Cerdeira, C.H. & Gharib, M. 2013 Flapping dynamics of an inverted flag. J.Fluid Mech. 736, R1.CrossRefGoogle Scholar
Kim, H. & Kim, D. 2019 Stability and coupled dynamics of three-dimensional dual inverted flags. J.Fluids Struct. 84, 18–35.CrossRefGoogle Scholar
Kim, H., Zhou, Q., Kim, D. & Oh, I.K. 2020 Flow-induced snap-through triboelectric nanogenerator. Nano Energy 68, 104379.CrossRefGoogle Scholar
Krylov, S., Ilic, B.R. & Lulinsky, S. 2011 Bistability of curved microbeams actuated by fringing electrostatic fields. Nonlinear Dyn. 66 (3), 403.CrossRefGoogle Scholar
Lighthill, M.J. 1960 Note on the swimming of slender fish. J.Fluid Mech. 9 (2), 305–317.CrossRefGoogle Scholar
Luhar, M. & Nepf, H.M. 2011 Flow-induced reconfiguration of buoyant and flexible aquatic vegetation. Limnol. Oceanogr. 56 (6), 2003–2017.CrossRefGoogle Scholar
Michelin, S. & Doaré, O. 2013 Energy harvesting efficiency of piezoelectric flags in axial flows. J.Fluid Mech. 714, 489–504.CrossRefGoogle Scholar
Michelin, S., Llewellyn Smith, S.G. & Glover, B.J. 2008 Vortex shedding model of a flapping flag. J.Fluid Mech. 617, 1–10.CrossRefGoogle Scholar
Païdoussis, M.P., Price, S.J. & de Langre, E. 2010 Fluid-Structure Interactions: Cross-Flow-Induced Instabilities. Cambridge University Press.CrossRefGoogle Scholar
Pandey, A., Moulton, D.E., Vella, D. & Holmes, D.P. 2014 Dynamics of snapping beams and jumping poppers. Europhys. Lett. 105 (2), 24001.CrossRefGoogle Scholar
Peretz, O., Mishra, A.K., Shepherd, R.F. & Gat, A.D. 2020 Underactuated fluidic control of a continuous multistable membrane. Proc. Natl Acad. Sci. USA 117 (10), 5217–5221.CrossRefGoogle ScholarPubMed
Polhamus, E.C. 1966 A concept of the vortex lift of sharp-edge delta wings based on a leading-edge-suction analogy. NASA Tech. Note, pp. TN D–3767.Google Scholar
Poppinga, S. & Joyeux, M. 2011 Different mechanics of snap-trapping in the two closely related carnivorous plants dionaea muscipula and aldrovanda vesiculosa. Phys. Rev. E 84 (4), 041928.CrossRefGoogle ScholarPubMed
Sader, J.E., Cossé, J., Kim, D., Fan, B. & Gharib, M. 2016 a Large-amplitude flapping of an inverted flag in a uniform steady flow–a vortex-induced vibration. J.Fluid Mech. 793, 524–555.CrossRefGoogle Scholar
Sader, J.E, Huertas-Cerdeira, C. & Gharib, M. 2016 b Stability of slender inverted flags and rods in uniform steady flow. J.Fluid Mech. 809, 873–894.CrossRefGoogle Scholar
Shankar, M.R., Smith, M.L., Tondiglia, V.P., Lee, K.M., McConney, M.E., Wang, D.H., Tan, L.S. & White, T.J. 2013 Contactless, photoinitiated snap-through in azobenzene-functionalized polymers. Proc. Natl Acad. Sci. USA 110 (47), 18792–18797.CrossRefGoogle ScholarPubMed
Shelley, M., Vandenberghe, N. & Zhang, J. 2005 Heavy flags undergo spontaneous oscillations in flowing water. Phys. Rev. Lett. 94 (9), 094302.CrossRefGoogle ScholarPubMed
Taira, K., Brunton, S.L., Dawson, S.T., Rowley, C.W., Colonius, T., McKeon, B.J., Schmidt, O.T., Gordeyev, S., Theofilis, V. & Ukeiley, L.S. 2017 Modal analysis of fluid flows: an overview. AIAA J. 55 (12), 4013–4041.CrossRefGoogle Scholar
Tang, L. & Païdoussis, M.P. 2007 On the instability and the post-critical behaviour of two-dimensional cantilevered flexible plates in axial flow. J.Sound Vib. 305 (1–2), 97–115.CrossRefGoogle Scholar
Tavallaeinejad, M., Païdoussis, M.P. & Legrand, M. 2018 Nonlinear static response of low-aspect-ratio inverted flags subjected to a steady flow. J.Fluids Struct. 83, 413–428.CrossRefGoogle Scholar
Timoshenko, S.P. & Gere, J.M. 2009 Theory of Elastic Stability. Courier Corporation.Google Scholar
Wagner, T.J.W. & Vella, D. 2013 The ‘sticky elastica’: delamination blisters beyond small deformations. Soft Matt. 9 (4), 1025–1030.CrossRefGoogle Scholar
Williamson, C.H.K. 1996 Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28 (1), 477–539.CrossRefGoogle Scholar
Xia, C., Lee, H. & Fang, N. 2010 Solvent-driven polymeric micro beam device. J.Micromech. Microengng 20 (8), 085030.CrossRefGoogle Scholar
Zhu, Y. & Zu, J.W. 2013 Enhanced buckled-beam piezoelectric energy harvesting using midpoint magnetic force. Appl. Phys. Lett. 103 (4), 041905.CrossRefGoogle Scholar

Kim et al. supplementary movie

Movie for Figure 5(a)

Download Kim et al. supplementary movie(Video)
Video 1 MB