### 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 language | English |
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Title of host publication | IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence - Proceedings of the IUTAM Symposium |

Pages | 135-150 |

Number of pages | 16 |

Volume | 6 |

Publication status | Published - 2008 |

Event | IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence - Moscow, Russian Federation Duration: Aug 25 2006 → Aug 30 2006 |

### Publication series

Name | Solid Mechanics and its Applications |
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Volume | 6 |

ISSN (Print) | 1875-3507 |

### Other

Other | IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence |
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Country | Russian Federation |

City | Moscow |

Period | 8/25/06 → 8/30/06 |

### Fingerprint

### 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

*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).

**Dynamics of a solid affected by a pulsating point source of fluid.** / Morgulis, Andrey; Vladimirov, Vladimir.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence - Proceedings of the IUTAM Symposium.*vol. 6, Solid Mechanics and its Applications, vol. 6, pp. 135-150, IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence, Moscow, Russian Federation, 8/25/06.

}

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

UR - http://www.scopus.com/inward/record.url?scp=77957147616&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77957147616&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9781402067433

VL - 6

T3 - Solid Mechanics and its Applications

SP - 135

EP - 150

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

ER -