Vibrations of a body in a bounded volume of viscous fluid
type: Item
instance of: scholarly article
title: Vibrations of a body in a bounded volume of viscous fluid
zbMATH Open document ID: 0581.76050
DOI: 10.1007/BF01090502
author: G. N. Mikishev
author: V. I. Stolbetsov
published in: Fluid Dynamics
publication date: 1983-01-01T00:00:00Z
review text: The problem of the vibrations of a body in a bounded volume of viscous fluid has been studied on a number of occasions. The main attention has been devoted to determining the hydrodynamic characteristics of elements in the form of rods. Analytic solution of the problem is possible only in the simplest cases. In the present paper, in which large Reynolds numbers are considered, the asymptotic method of Vishik and Lyusternik and Chernous'ko is used to consider the general problem of translational vibrations of an axisymmetric body in an axisymmetric volume of fluid. Equations of motion of the body and expressions for the coefficients due to the viscosity of the fluid are obtained. It is shown that in the first approximation these coefficients differ only by a constant factor and are completely determined if the solution to the problem for an ideal fluid is known. Examples are given of the determination of the ''viscous'' added mass and the damping coefficient for some bodies and cavities. In the case of an ideal fluid, general estimates are obtained for the added mass and also for the influence of nonlinearity.
Mathematics Subject Classification ID: 76D99
Mathematics Subject Classification ID: 70E15
Mathematics Subject Classification ID: 70J99
zbMATH DE Number: 3930583
zbMATH Keywords: viscous added mass computations
zbMATH Keywords: rods
zbMATH Keywords: Analytic solution
zbMATH Keywords: asymptotic method
zbMATH Keywords: translational vibrations of an axisymmetric body in an axisymmetric volume
zbMATH Keywords: first approximation
zbMATH Keywords: determination of the ''viscous'' added mass
zbMATH Keywords: damping coefficient
MaRDI profile type: Publication
cites work: Q3259838
cites work: Q3249645
cites work: Q3241404
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description: scientific article; zbMATH DE number 3930583