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IssuesArchive of Issues2001-2pp.148-162

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D. A. Galitsyn and V. A. Trotsenko, "On the determination of frequencies and virtual masses of a fluid in a moving rectangular cavity with baffles," Mech. Solids. 36 (2), 148-162 (2001)
Year 2001 Volume 36 Number 2 Pages 148-162
Title On the determination of frequencies and virtual masses of a fluid in a moving rectangular cavity with baffles
Author(s) D. A. Galitsyn (Kiev)
V. A. Trotsenko (Kiev)
Abstract In engineering practice, in order to restrict the mobility of a fluid in a container, one often resorts to baffles or ribs attached to the surface of the container. The action of such vibration damping devices is based on the property of the walls to exhibit strong resistance to the flow.

The presence of baffled structures in a container leads to a substantial change in the hydrodynamic coefficients in the equations describing the motion of the "container-fluid" system. A comparison of theoretical and experimental results for various types of baffled cavities has shown that within the linear theory of wave motion of a fluid, the influence of viscosity on the fluid inertial characteristics is inessential. Therefore, in the majority of practical situations when one has to calculate frequencies and virtual masses of fluids, it is possible to apply the ideal fluid model. It is a common practice now to take into account the effect of viscosity forces by introducing linear dissipative terms into the equations that describe the motion of a rigid body with a fluid. The damping coefficients of these terms are determined experimentally.

Theoretical problems of finding frequencies and virtual masses of ideal fluids in moving cavities formed by a body of revolution with longitudinal and transverse baffles are considered in [1-5]. In [6-8], the method of perturbations is used for finding the inertial characteristics of fluids in cavities with transverse and longitudinal ribs of a relatively small width. Comprehensive experimental results regarding the dynamical characteristics of fluids in various types of baffled cavities are described in [9, 10].

On the basis of the approach developed in [4, 5], a method is proposed below for the determination of the coefficients of the equation that describes the motion of a rigid body with a baffled rectangular cavity. The solutions obtained for the basic boundary value problems are analyzed as regards their efficiency. The effect of the baffles on the dynamical characteristics of the fluid is described.
References
1.  V. I. Ermakov, G. A. Moiseev, and V. G. Shershenev, "Perturbed motion of a body with a cylindrical cavity with ribs," Izv. AN. MTT [Mechanics of Solids]old, No. 2, pp. 52-61, 1970.
2.  L. V. Dokuchaev, "On the virtual moment of inertia of a fluid in a baffled cylinder rotating about its longitudinal axis," Izv. AN SSSR. Mekh. i Mashinostr., No. 2, pp. 168-171, 1964.
3.  V. N. Morozov, "A finite-difference method for boundary value problems describing the perturbed motion of a rigid body with a fluid," in Vibrations of Elastic Structures with a Fluid [in Russian], pp. 161-165, Novosibirsk. Elektrotekhn. In-t, Novosibirsk, 1974.
4.  V. A. Trotsenko, "Perturbed motion of a body containing a cavity with an elastic ring-shaped plate," Izv. AN. MTT [Mechanics of Solids]old, No. 4, pp. 78-88, 1974.
5.  V. A. Trotsenko, "On coefficients in the equations describing the perturbed motion of a body containing a cylindrical cavity with transverse ribs," Prikl. Mekh., Vol. 5, No. 10, pp. 50-57, 1969.
6.  F. Bauer, "Zur Trägheitsmoment Erhöhung und Schwappmassenreduktion durch Dämpfungsringe in Treibstofftank," Raumfahrforschung, Bd. 11, H. 4, S. 163-171, 1967.
7.  B. I. Rabinovich, "On the influence of internal ribs on the dynamic characteristics of fluids in moving containers," Prikl. Mekh., Vol. 6, No. 8, pp. 103-111, 1970.
8.  V. L. Shchetukhin, "Vibrations of a fluid in axially symmetric containers with annular ribs," Prikl. Mekh., Vol. 11, No. 8, pp. 89-95, 1975.
9.  G. N. Mikishev and B. I. Rabinovich, Dynamics of Thin-Walled Structures with Compartments Containing Fluid [in Russian], Mashinostroenie, Moscow, 1971.
10.  G. N. Mikishev, Experimental Methods in the Dynamics of Space Vehicles [in Russian], Mashinostroenie, Moscow, 1978.
11.  I. A. Lukovskii, M. Ya. Barnyak, and A. N. Komarenko, Approximate Methods for Problems of Hydrodynamics of Finite Volumes [in Russian], Naukova Dumka, Kiev, 1984.
12.  N. N. Moiseev, "Motion of a rigid body with a cavity partially filled with an ideal dropping liquid," Doklady AN SSSR, Vol. 85, No. 4, pp. 719-722, 1952.
13.  G. S. Narimanov, "On the motion of a rigid body with a cavity partially filled with a fluid," PMM [Applied Mathematics and Mechanics], Vol. 20, No. 1, pp. 21-38, 1956.
14.  G. S. Narimanov, L. V. Dokuchaev, and I. A. Lukovskii, Nonlinear Dynamics of Flying Vehicles With Liquid [in Russian], Mashinostroenie, Moscow, 1977.
15.  G. N. Mikishev and B. I. Rabinovich, Dynamics of a Rigid Body Containing Cavities Partially Filled With Liquid [in Russian], Mashinostroenie, Moscow, 1968.
16.  N. E. Zhukovskii, "On the motion of a rigid body containing cavities filled with a homogeneous dropping liquid," Complete Works [in Russian], Vol. 2, pp. 152-309, Gostekhteorizdat, Moscow, Leningrad, 1949.
17.  L. V. Kantorovich and V. I. Krylov, Approximate Methods of Higher Analysis [in Russian], Gostekhizdat, Moscow, Leningrad, 1950.
18.  I. I. Vorovich, V. M. Alexandrov, and V. A. Babeshko, Nonclassical Mixed Problems in Elasticity [in Russian], Nauka, Moscow, 1974.
19.  G. Ya. Popov, "Some properties of classical polynomials and their application to contact problems," PMM [Applied Mathematics and Mechanics], Vol. 27, No. 5, pp. 821-832, 1963.
20.  G. N. Watson, Theory of Bessel Functions. Part 1 [Russian translation], Izd-vo Inostr. Lit-ry, Moscow, 1949.
21.  R. V. Hemming, Numerical Methods for Scientists and Engineers [Russian translation], Nauka, Moscow, 1972.
22.  L. I. Sedov, Plane Problems in Hydrodynamics and Aerodynamics [in Russian], Nauka, Moscow, 1966.
Received 09 April 1999
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