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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2008, Volume 49, Issue 4, Pages 174–191
(Mi pmtf1938)
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This article is cited in 1 scientific paper (total in 1 paper)
On equations of motion of a nonlinear hydroelastic structure
P. I. Plotnikov, I. V. Kuznetsov Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Abstract:
Formal derivation of equations of a nonlinear hydroelastic structure, which is a volume of an ideal incompressible fluid covered by a shell, is proposed. The study is based on two assumptions. The first assumption implies that the energy stored in the shell is completely determined by the mean curvature and by the elementary area. In a three-dimensional case, the energy stored in the shell is chosen in the form of the Willmore functional. In a two-dimensional case, a more generic form of the functional can be considered. The second assumption implies that the equations of motionhave a Hamiltonian structure and can be obtained from the Lagrangian variational principle. In a two-dimensional case, a condition for the hydroelastic structure is derived, which relates the external pressure and the curvature of the elastic shell.
Keywords:
free boundary, variational principle, ideal fluid, hydroelasticity, constraint forces, Antman equation, Bernoulli law.
Received: 30.07.2007 Accepted: 03.10.2007
Citation:
P. I. Plotnikov, I. V. Kuznetsov, “On equations of motion of a nonlinear hydroelastic structure”, Prikl. Mekh. Tekh. Fiz., 49:4 (2008), 174–191; J. Appl. Mech. Tech. Phys., 49:4 (2008), 666–680
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https://www.mathnet.ru/eng/pmtf1938 https://www.mathnet.ru/eng/pmtf/v49/i4/p174
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