 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
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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
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| 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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