The plane problem on vertical impact of a rotating circular cylindrical shell against the surface of a liquid

The plane nonsymmetric problem on impact against and immersion into a compressible fluid of a thin electic cylindrical shell is considered. The shell rotates about its axis with a given angular velocity. The boundary-value problem is reduced to an infinite system of integral Volterra equations of the second kind. Translated from Prikladnaya Mekhanika, Vol. 36, No. 5, pp. 103–113, May, 2000.     

Convective flows in a cylindrical fluid zone in a high-frequency vibration field

Convective flows of a nonuniformly heated fluid in a cylindrical fluid zone in a high-frequency longitudinal vibration field are studied. Vibration frequencies which are high as compared with dissipative decrements and capillary frequencies, but small as compared with acoustic frequencies are considered. The general method formulated earlier for describing the behavior of inhomogeneous fluids under the influence of high-frequency vibrations is used. The interaction between the vibrational flow mechanisms and thermocapillary effects on a free surface is analyzed.Perm'. Marseilles (France). Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 53–61, September–October, 1994.     

Thermovibrational convective instability of mechanical equilibrium of an inclined fluid layer

The convective instability of mechanical equilibrium of an inclined plane layer of fluid developing under the action of a static gravity field and high-frequency vibration is studied. Configurations corresponding to four directions of the equilibrium temperature gradient — vertical, longitudinal, horizontal, and transverse — are considered for an arbitrary orientation of the vibration axis. The stability limits and the characteristics of the critical perturbations are determined. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 8–15, January–February, 1998. This investigation was carried out with partial support form RSA-NASA (contract No. 920/18 — 5208/96).     

Effect of rotation on the vibroconvective stability of a fluid layer with internal heat release

The equilibrium stability of a horizontal fluid layer with homogeneous internal heat release is investigated theoretically for the case in which the layer simultaneously undergoes high-frequency circular vibration in a horizontal plane and rotates about a vertical axis. The rotation frequency is assumed to be small as compared with the vibration frequency. It is found that the rotation has a stabilizing effect on the vibrational-gravitational convection. At the high-frequency limit the dependence of the critical values of the controlling parameters (gravitational and vibrational Rayleigh numbers) and the wave number on the rotation frequency is obtained.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, 2005, pp. 53–61. Original Russian Text Copyright © 2005 by Ivanova, Kozlov, and Kolesnikov.     

Vibrational dynamics of a light body in a liquid-filled rotating cylinder

The behavior of a light free cylindrical body in a rapidly rotating horizontal cylinder containing a liquid under vibrational action (the vibration direction is perpendicular to the rotation axis) is investigated. An intense rotation of the body relative to the cavity is detected. Depending on the vibration frequency, the body rotation velocity in the laboratory reference system may be higher or lower than the cavity rotation velocity and in the resonance region they may differ by several times. The mechanism of motion generation is theoretically described. It is shown that the motion is related with the excitation of inertial oscillations of the body: the cause of the motion is an average vibrational force generated due to nonlinear effects in the Stokes boundary layer near the oscillating body. The formation of large-scale axisymmetric vortex structures periodic along the rotation axis, which appear under conditions of inertial oscillation of the body during its motion, both leading and lagging, is detected.     

Free vibrations of a viscoelastic noncircular cylindrical shell under homogeneous axial loading

Free low-frequency vibrations of a noncircular cylindrical shell subject to an axial static load are investigated. The case where the vibrations are localized near a certain generatrix, called the weakest, is considered. The complex WKB-method is used to determine the natural modes of vibrations that damp with time and drop down far from the weakest generatrix. An example on the vibration of a viscoelastic shell is considered with the relaxation rate function given and in the presence of a static axial force. State Polytechnic Academy of Belarus, Minsk. Translated from Prikladnaya Mekhanika, Vol. 35, No. 11, pp. 68–74, November, 1999.     

Coupled vibration of a partially fluid-filled cylindrical container with a cylindrical internal body

In the present paper a method is proposed to investigate the effects of a rigid internal body on the coupled vibration of a partially fluid-filled cylindrical container. The internal body is a thin-walled and open-ended cylindrical shell. The internal body is concentrically and partially submerged inside a container. The radial and axial distances between the internal body and the container are filled with fluid. Along the contact surface between the container and the fluid, the compatibility requirement for the fluid–structure interactions is applied and the Rayleigh–Ritz method is used to calculate the natural frequencies and modes of a partially fluid-filled cylindrical container. The fluid domain is continuous, simply connected, and non-convex. The fluid is assumed to be incompressible and inviscid. The velocity potential for fluid motion is formulated in terms of eigenfunction expansions for two distinct fluid regions. The resulting equations are solved by using the Galerkin method. The results from the proposed method are in good agreement with experimental and numerical solutions available in the literature for the partially water-filled cylindrical container without internal body. A finite element analysis is also used to check the validity of the present method for the partially water-filled cylindrical container with internal body. The effects of the fluid level, internal body radius, and internal body length on the natural frequencies of the coupled system are also investigated.     

Studying the forced vibrations of fluid-filled cylindrical shells with regard to the nonlinear interaction of different flexural modes

The paper is concerned with the forced nonlinear multimode vibrations of thin cylindrical shells fully filled with a perfect incompressible fluid. The frequency response characteristics of shells undergoing steady-state vibration as simple (standing wave) and compound (traveling wave) deformation modes are plotted and examined __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 8, pp. 97–106, August 2006.     

Experimental study of the drag of the forebody and the cylindrical part of the HB-1 model with an upstream injection of a fluid in a supersonic flow

Values of the gas-dynamic drag of the forebody and the cylindrical part of the HB-1 test model in a supersonic flow have been separately measured using an internal strain-gauge balance. It is shown that an upstream injection of a fluid jet from the model forebody decreases the drag of both the forebody and the cylindrical part. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 110–112, November–December, 1998.     

Supersonic flow past a cylindrical body with transverse jets at large angles of attack

Supersonic flow past a cylindrical body with a system of transverse jets ejected from its surface at angles of attack α=60–120^o is characterized by a complicated gasdynamic flow pattern [1]. The body surface is affected by both the oncoming flow and the ejected jets which shield a portion of the surface from the external flow. This results in considerable transverse and longitudinal pressure gradients appearing on the body surface. The experimental pressure distributions over a cylindrical model with four transverse jets at a Mach number M=4 and α=60°, 90°, and 120° make it possible to study the specific features of the flowfield and derive correlations for the "jet obstacle" dimensions. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 179–183, January–February, 1998.     

Stationary cylindrical vortex in a viscous electrically conducting fluid

An exact solution of the magnetohydrodynamic equations is constructed which describes steady vortex flow in a stationary cylinder on the axis of which a conductor carrying a known current is located. The solution is obtained under the assumption that the fluid is viscous and has finite electrical conductivity and that the magnetic field has only the axial and azimuthal components in a cylindrical coordinate system. It is found that the action of the Lorentz force is compensated by changing the pressure. Fluid flow occurs from the periphery to the axis of the cylinder under a pressure gradient, with flow rotation and swirling. The fluid flow causes a concentration of the magnetic lines near the axis of the cylinder, providing an exponential decrease in the magnetic field strength with distance from the axis. This flow can be considered as a model of a local increase in the magnetic field strength due to the transfer of its force lines by the flow of the electrically conducting fluid.     

Convective instability of a fluid in a vibration field under conditions of weightlessness

The problem of the convection and convective instability of a fluid in a high-frequency vibration field under conditions of weightlessness was formulated in an earlier paper of the authors [1]. In the present paper, the conditions of equilibrium are discussed and the boundaries of vibration instability are determined for some equilibrium states: a plane layer of fluid with transverse temperature gradient and arbitrary direction of the vibration, a cylindrical layer with radial gradient and longitudinal direction of the vibration, and an infinite circular cylinder with transverse and mutually perpendicular directions of the temperature gradient and the vibration axis.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 12–19, July–August, 1981.We thank G. I. Petrov for helpful discussions.     

Natural vibrations of a cantilever thin elastic orthotropic cylindrical shell

The natural vibrations of a cantilever thin elastic orthotropic circular cylindrical shell are studied. Dispersion equations for the determination of possible natural frequencies of cantilever closed shells and open shells with Navier hinged boundary conditions at the longitudinal edges are derived from the classical dynamic theory of orthotropic cylindrical shells. It is proved that there are asymptotic relationships between these problems and the problems for a cantilever orthotropic strip plate and for a cantilever rectangular plate and the eigenvalue problem for a semi-infinite closed orthotropic cylindrical shell with free end and for the same but open shell with Navier hinged boundary conditions at the longitudinal edges. A procedure to identify types of vibrations is presented. Orthotropic cylindrical shells with different radii and lengths are used as an example to find approximate values of the dimensionless natural frequency and damping factor for vibration modes __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 5, pp. 68–91, May 2008.     

Free vibrations of ribbed cylindrical shells with local axisymmetric deflections

The paper proposes a method to calculate the natural frequencies of ribbed cylindrical shells with local axisymmetric deflections. The influence of initial imperfections of two types on the minimum frequencies of vibration is analyzed Translated from Prikladnaya Mekhanika, Vol. 44, No. 9, pp. 63–72, September 2008.     

Vibrational convection in a saturated porous medium in the absence of thermal equilibrium between the solid and liquid phases

Thermal vibrational convection in a saturated porous medium is theoretically studied on the basis of a thermal nonequilibrium model, in accordance with which the temperatures of the porous medium and the saturating liquid can be different. In the high-frequency vibration approximation the averaged equations of convection are derived. The dependence of the vibration force direction on the interphase heat transfer coefficient and the vibration frequency is established. Vibrational convection in a cylindrical layer is studied. It is shown that, depending on the interphase heat transfer coefficient, the flows of two types differing in the liquid circulation direction can exist.     

Experimental study of the instability of convective boundary layers under the action of vibration

The wave instability of convective boundary layers in a horizontal cylindrical layer of ethanol under the action of vertical hamonic high-frequency vibration is studied. A strong destabilizing effect of the vibration on the stability of the convective boundary layers is detected. In the plane of the gravity and vibration Rayleigh numbers (Ra and R _V ), the excitation limit of the wave instability is determined. The periods of the temperature oscillations caused by the waves in the boundary layers near the inner and outer cavity boundaries are studied as functions of the Rayleigh numbers. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 32–40, May–June, 1998.     

Experimental investigation of the nonlinear resonance properties of cylindrical shells

The nonlinear resonance properties of cylindrical shells filled with a fluid are experimentally studied. It is proved that travelling waves appear under resonance conditions due to the effect of the gyroscopic moment on the shell. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 2, pp. 111–114, February, 2000.     

Shape of the free surface of a magnetic fluid containing a cylindrical concentrator of the magnetic field

The shape of the surface of a magnetic fluid containing a cylindrical body made of a well-magnetizable material (magnetic field concentrator) in a uniform applied magnetic field is studied experimentally and theoretically. Various static shapes of the surface are calculated numerically taking into account the gravity forces, the surface tension, and the dependence of the magnetic fluid magnetization on the magnetic field strength. It is found that there exists several equilibrium shapes of the magnetic fluid surface. Abrupt changes in the magnetic fluid surface and its hysteresis are predicted theoretically and observed experimentally. The theoretical and experimental results are compared.     

Dynamics of a Spherical Body in a Liquid with Rotational Vibration of the Cavity

The average dynamics of a single solid sphere in a liquid-filled cylindrical cavity in the presence of high-frequency rotational oscillation about the axis of symmetry is studied experimentally. In the cavity there is an impermeable membrane which forces the liquid as a whole to vibrates together with the cavity. Various orientations of the vessel in the gravity force field are considered. The action of an average force of vibrational nature on the sphere and the dependence of this force on the vibration parameters and the body dimensions and density are studied. The force is measured with respect to the floating threshold for the heavy body, when the average vibrational force balances or exceeds the action of the gravity force.