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Passive locomotion via normal-mode coupling in a submerged spring–mass system

  • EVA KANSO (a1) and PAUL K NEWTON (a1) (a2)

Abstract

The oscillations of a class of submerged mass–spring systems are examined. An inviscid fluid model is employed to show that the hydrodynamic effects couple the normal modes of these systems. This coupling of normal modes can excite the displacement mode – yielding passive locomotion of the system – even when starting with zero displacement velocity. This is in contrast with the fact that under similar initial conditions but without the hydrodynamic coupling, such systems cannot achieve a net displacement. These ideas are illustrated via two examples of a two-mass and a three-mass system.

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Email address for correspondence: kanso@usc.edu

References

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Beal, D. N., Hover, F. S., Triantafyllou, M. S., Liao, J. C. & Lauder, G. V. 2006 Passive propulsion in vortex wakes. J. Fluid Mech. 54 (9), 385402.
Brennen, C. E. 1982, A review of added mass and fluid inertial forces. Tech Rep. CR 82.010. Contract no. N62583-81-MR-554. Naval Civil Engineering Laboratory.
Burton, D. A., Gratus, J. & Tucker, R.W. 2004 Hydrodynamic forces on two moving disks. Theoret. Appl. Mech. 31, 153188.
Crowdy, D. G., Surana, A. & Yick, K.-Y. 2007 The irrotational flow generated by two planar stirrers in inviscid fluid. Phys. Fluids 19, 018103.
Ford, J. 1992 The Fermi–Pasta–Ulam problem: paradox turns discovery. Phys. Rep. 213 (5), 271310.
Kanso, E. 2009 Swimming due to transverse shape deformations. J. Fluid Mech. 631, 127148.
Kanso, E., Marsden, J. E., Rowley, C. W. & Melli-Huber, J. 2005 Locomotion of articulated bodies in a perfect fluid. J. Nonlin. Sci., 15, 255289.
Lamb, H. 1932 Hydrodynamics, 6th edn. Dover.
Lighthill, J. 1975 Mathematical Biofluiddynamics. Society for Industrial and Applied Mathematics.
Nair, S. & Kanso, E. 2007 Hydrodynamically-coupled rigid bodies. J. Fluid Mech. 592, 393411.
Najafi, A. & Golestanian, R. 2004 Simple swimmer at low Reynolds number: three linked spheres. Phys. Rev. E 69 (6), 062901.
Nayfeh, A. H. 1973 Perturbation Methods. Wiley-Interscience.
Purcell, E. M. 1977 Life at low Reynolds number. Am. J. Phys. 45 (1), 311.
Shapere, A. & Wilczek, F. 1987 Self-propulsion at low Reynolds number. Phys. Rev. Lett. 58 (2), 20512054.
Videler, J. J. & Weihs, D. 1982 Energetic advantages of burst-and-coast swimming of fish at high speeds. J. Exp. Biol. 97, 169178.
Wang, Q. X. 2004 Interaction of two circular cylinders in inviscid UID. Phys Fluids 16, 44124425.
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