TY - GEN

T1 - Dynamics of a solid affected by a pulsating point source of fluid

AU - Morgulis, Andrey

AU - Vladimirov, Vladimir

PY - 2008

Y1 - 2008

N2 - This paper provides a new insight to the classical Björknes's problem. We examine a mechanical system "solid+fluid" consisted of a solid and a point source (singlet) of fluid, whose intensity is a given function of time. First we show that this system is governed by the least action (Hamilton's) principle and derive an explicit expression for the Lagrangian in terms of the Green function of the solid. The Lagrangian contains a linear in velocity term. We prove that it does not produce a gyroscopic force only in the case of a spherical solid. Then we consider the periodical high-frequency pulsations (vibrations) of the singlet. In order to construct the high-frequency asymptotic solution we employ a version of the multiple scale method that allows us to obtain the "slow" Lagrangian for the averaged motions directly from Hamilton's principle. We derive such a "slow" Lagrangian for a general solid. In details, we study the "slow" dynamics of a spherical solid, which can be either homogeneous or inhomogeneous in density. Finally, we discuss the "Björknes's dynamic buoyancy" for a solid of general form.

AB - This paper provides a new insight to the classical Björknes's problem. We examine a mechanical system "solid+fluid" consisted of a solid and a point source (singlet) of fluid, whose intensity is a given function of time. First we show that this system is governed by the least action (Hamilton's) principle and derive an explicit expression for the Lagrangian in terms of the Green function of the solid. The Lagrangian contains a linear in velocity term. We prove that it does not produce a gyroscopic force only in the case of a spherical solid. Then we consider the periodical high-frequency pulsations (vibrations) of the singlet. In order to construct the high-frequency asymptotic solution we employ a version of the multiple scale method that allows us to obtain the "slow" Lagrangian for the averaged motions directly from Hamilton's principle. We derive such a "slow" Lagrangian for a general solid. In details, we study the "slow" dynamics of a spherical solid, which can be either homogeneous or inhomogeneous in density. Finally, we discuss the "Björknes's dynamic buoyancy" for a solid of general form.

KW - Analytical dynamics

KW - Björknes's force

KW - Pulsating point source of fluid

KW - Solid body

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U2 - 10.1007/978-1-4020-6744-0_12

DO - 10.1007/978-1-4020-6744-0_12

M3 - Conference contribution

AN - SCOPUS:77957147616

SN - 9781402067433

T3 - Solid Mechanics and its Applications

SP - 135

EP - 150

BT - IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence - Proceedings of the IUTAM Symposium

PB - Springer Verlag

T2 - IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence

Y2 - 25 August 2006 through 30 August 2006

ER -