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

Andrey Morgulis, Vladimir Vladimirov

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationIUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence - Proceedings of the IUTAM Symposium
Pages135-150
Number of pages16
Volume6
Publication statusPublished - 2008
EventIUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence - Moscow, Russian Federation
Duration: Aug 25 2006Aug 30 2006

Publication series

NameSolid Mechanics and its Applications
Volume6
ISSN (Print)1875-3507

Other

OtherIUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence
CountryRussian Federation
CityMoscow
Period8/25/068/30/06

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Keywords

  • Analytical dynamics
  • Björknes's force
  • Pulsating point source of fluid
  • Solid body

ASJC Scopus subject areas

  • Aerospace Engineering
  • Automotive Engineering
  • Civil and Structural Engineering
  • Mechanical Engineering
  • Acoustics and Ultrasonics

Cite this

Morgulis, A., & Vladimirov, V. (2008). Dynamics of a solid affected by a pulsating point source of fluid. In IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence - Proceedings of the IUTAM Symposium (Vol. 6, pp. 135-150). (Solid Mechanics and its Applications; Vol. 6).