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Impact dynamics for a floating elastic membrane

Published online by Cambridge University Press:  03 September 2014

L. Duchemin  and
N. Vandenberghe Open the ORCID record for N. Vandenberghe [Opens in a new window]
L. Duchemin*
Affiliation:
Aix Marseille Université, CNRS, Centrale Marseille, IRPHE UMR 7342, 13384, Marseille, France
N. Vandenberghe
Affiliation:
Aix Marseille Université, CNRS, Centrale Marseille, IRPHE UMR 7342, 13384, Marseille, France
*
†Email address for correspondence: [email protected]
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Abstract

We study impacts of a rigid body on a thin elastic sheet floating on a liquid. When struck by a solid object of small size, the elastic sheet deforms and waves propagate in and on the membrane. The impact triggers a longitudinal elastic wave effectively stretching the membrane. The hydroelastic transverse wave that propagates in the stretched domain is similar to capillary waves on a free surface with an equivalent ‘surface tension’ that results from the stretching of the elastic membrane. Two limiting cases, for which a self-similar solution can be computed, corresponding to short and long times are identified. Surprisingly, our study reveals that the fluid–body system behaves as a regular liquid–gas interface, but with an effective surface tension coefficient that scales linearly with the impact velocity.

JFM classification

Waves/Free-surface Flows: Capillary waves Waves/Free-surface Flows: Elastic waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 756 , 10 October 2014 , pp. 544 - 554
Copyright
© 2014 Cambridge University Press 

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References

Albrecht, A. B. & Ravi-Chandar, K. 2014 High strain rate response of rubber membranes. J. Mech. Phys. Solids 64, 377–395.Google Scholar
Courbin, L., Marchand, A., Vaziri, A., Ajdari, A. & Stone, H. A. 2006 Impact dynamics for elastic membranes. Phys. Rev. Lett. 97, 244301.CrossRefGoogle ScholarPubMed
Keller, J. B. & Miksis, M. J. 1983 Surface tension driven flows. SIAM J. Appl. Maths 43 (2), 268–277.Google Scholar
Korobkin, A. A. & Pukhnachov, V. V. 1988 Initial stage of water impact. Annu. Rev. Fluid Mech. 20, 159–185.CrossRefGoogle Scholar
Landau, L. D. & Lifshitz, E. M. 1970 Theory of Elasticity. Pergamon Press.Google Scholar
Milewski, P. A., Vanden-Broeck, J. M. & Wang, Z. 2011 Hydroelastic solitary waves in deep water. J. Fluid Mech. 679 (1), 628–640.Google Scholar
Parau, E. & Dias, F. 2002 Nonlinear effects in the response of a floating ice plate to a moving load. J. Fluid Mech. 460, 281–305.Google Scholar
Peters, I. R., Van Der Meer, D. & Gordillo, J. M. 2013 Splash wave and crown breakup after disc impact on a liquid surface. J. Fluid Mech. 724, 553–580.Google Scholar
Phoenix, S. L. & Porwal, P. K. 2003 A new membrane model for the ballistic impact response and V50 performance of multi-ply fibrous systems. Intl J. Solids Struct. 40 (24), 6723–6765.Google Scholar
Press, W. H. 1978 Mathematical theory of the waterbed. Am. J. Phys. 46 (10), 966–970.Google Scholar
Squire, V., Hosking, R. J., Kerr, A. D. & Langhorne, P. J. 1996 Moving Loads on Ice Plates. Kluwer.Google Scholar
Srinivasan, M. A. 1989 Surface deflection of primate fingertip under line load. J. Biomech. 22 (4), 343–349.Google Scholar
Thomas, T. B. & Davies, J. T. 1974 On the sudden stretching of liquid lamellae. J. Colloid Interface Sci. 48 (3), 427–436.Google Scholar
Vella, D. & Li, J. 2010 The impulsive motion of a small cylinder at an interface. Phys. Fluids 22 (5), 052104.CrossRefGoogle Scholar
Vella, D. & Metcalfe, P. D. 2007 Surface tension dominated impact. Phys. Fluids 19 (7), 072108.Google Scholar
Vermorel, R., Vandenberghe, N. & Villermaux, E. 2006 Rubber band recoil. Proc. R. Soc. Lond. A 463 (2079), 641–658.Google Scholar
Vermorel, R., Vandenberghe, N. & Villermaux, E. 2008 Impacts on thin elastic sheets. Proc. R. Soc. Lond. A 465 (2103), 823–842.Google Scholar