Motion of a slender body made of magnetizable composite in a traveling magnetic field

The motion of a slender body made of magnetizable composite in a channel, along which coils producing a heterogeneous “traveling” magnetic field are mounted, is investigated. The coil axes are vertical and lie in the same plane. A mathematical model of a slender body made of viscoelastic magnetizable material is proposed. The magnetic force is calculated from a formula used in ferrohydrodynamics of magnetic fluids with equilibrium magnetization. The problem of the motion of this body in a channel in a vertical plane under the action of the magnetic field produced in an experimental setup is numerically solved. The dependence of the body velocity on the coil switching frequency is calculated and the effect of different problem parameters on the form of this dependence is studied. The theoretical results are compared with the experimental data.     

Integrable systems in the dynamics on the tangent bundle of a two-dimensional sphere

A mechanical system whose phase space is the tangent bundle of a two-dimensional sphere is studied. The potential nonconservative systems describing a geodesic flow are classified. A multiparameter family of systems possessing a complete set of transcendental first integrals expressed in terms of finite combinations of elementary functions is found. Some examples illustrating the spatial dynamics of a rigid body interacting with a medium are discussed.     

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.     

Vibrational hydrodynamic interaction between a sphere and the boundaries of a cavity

A new type of vibrational lift force [1] acting on a spherical body oscillating in a viscous fluid near a rigid boundary is experimentally investigated. The interaction between the body and the cavity boundary creates a repulsion force which is capable of holding a heavy body in the gravity field at a certain distance from the floor and a light body at a certain distance from the ceiling. The repulsion force appears at a distance comparable with the Stokesian boundary layer thickness and increases as the surface is approached. Outside the viscous interaction range, the repulsion force is replaced by an attraction force which decays with distance. Dimensionless parameters governing the vibrational interaction are found and threshold curves, corresponding to the transition of bodies of different densities to the “suspended” state, are plotted as functions of a dimensionless frequency. The dependence of the repulsion and attraction forces on the distance between the body and the wall is studied.     

Flutter instability of damped plates under combined conservative and nonconservative loads

The combined flutter and divergence instability of plates of arbitrary geometry subjected to any type of boundary conditions under interior and edge conservative and nonconservative loads are solved in presence of external and internal damping. In contrast to previous investigations, the membrane stress resultants are not in general uniform, since they result from plane stress problem under the given body forces (conservative and nonconservative) and the prescribed inplane boundary conditions. The differential equations of the problem are derived using Hamilton’s principle. The resulted initial boundary value problem is solved using the analog equation method (AEM), which is a BEM-based domain meshless method. The combined action of conservative and nonconservative forces is also investigated. Several plates have been studied and useful conclusions on the effect of boundary conditions and damping on flutter load have been drawn. The obtained numerical results demonstrate the accuracy of the developed method and its capability to solve realistic engineering problems.     

Plastic dynamic stability of a column under nonconservative forces

I.Introduction'Whenadeformableobjectmovinginamedium,thedirectionsofinteractiveforcessuchasfrictionalforceshouldvarywiththedeformationoftheobject.Thisisakindofnonconservativeforces.Forexample,thedirectionofgasfrictionalforceactingontherocketsandthefossiles…     

Structure and stability of the interface between magnetic and conventional fluids. Model of a three-component medium

The structure of a flat interphase boundary between a magnetic suspension and a conventional immiscible fluid is investigated within the framework of the model of a three-component medium taking the dependence of the free energy of the system on the concentration gradients into account. It is shown that for certain values of the constitutive parameters the bulk magnetic particle concentration increases significantly inside the interfacial layer, i.e., the particles are significantly adsorbed on the interface. The dependence of the surface tension on the magnetic field strength is determined. It is shown that for certain problem parameters this dependence qualitatively corresponds to that obtained experimentally and described in the phenomenological theory developed by Golubyatnikov and Subkhankulov in 1986. In the case of strong particle adsorption the dependence of the surface tension on the magnetic particle concentration on the phase interface is significantly nonlinear. A refined model of the interface as a two-dimensional continuum with surface magnetization is constructed. Constitutive equations, conditions on the interface, and necessary stability conditions are obtained.     

Effect of external radiation on the distortion of a vitreous body in a flow of gas

The semitransparency of a material, which determines the penetration of external radiation into the inside layers, affects significantly the temperature profile in the body [1, 2]. Since the viscosity of a melt of viscous materials depends strongly on the temperature, deformation of the temperature profile close to the surface leads to considerable change of the rate of spread of the liquid film, which has a significant effect on the rate of distortion of the body. In the present paper, the problem of distortion is formulated taking into account the transfer of radiation inside the body. The dependence of the distortion parameters and the degree of blackness of the body on the fraction of radiation in the external thermal flux and the mean free path of the radiation inside the material is determined. A sufficient condition is also obtained for the presence of a temperature maximum inside the body in a more general case than in [3].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 127–134, July–August, 1976.The author thanks G. A. Tirskii for a discussion of the posing of the problem.     

A numerical study of flows driven by a rotating magnetic field in a square container

The magnetically induced fluid flow in a square container is investigated by means of numerical simulations. Low frequency/ low induction conditions are assumed. The effect of the rotating magnetic field gives rise to a time-independent magnetic body force, computed via the electrical potential equation and Ohm's law and a time-dependent part that is neglected due to the low-interaction parameter. The magnetic body force calculation is verified successfully by comparison with the exact solution. The behavior of the fluid flow in the square container reveals similar features to the flow in the cylindrical container, for instance, in the dependence on the intensities of the magnetic field. However, we did find differences in the velocity field distribution. Particularly, in the finite as well as infinite geometry, the velocity field is influenced by the corner of the container and remains non-axisymmetric in a wide range of Taylor numbers.     

Variational methods for the problems of nonconservative force fields in the micropolar elastodynamics

Based on the properties of the convolution and the convolute commutation, some quasi-variational principles for the problems of nonconservative force field in the micropolar elastodynamics are given and verified in this paper. The theorem given in this paper can be applied to the theories of the nonlocal elastic mediums and the nonlocal micropolar elastic mediums.     

PIV analysis of merging flow in a simplified model of a rotary kiln

Rotary kilns are used in a variety of industrial applications. The focus in this work is on characterizing the non-reacting, isothermal flow field in a rotary kiln used for iron ore pelletization. A downscaled, simplified model of the kiln is experimentally investigated using particle image velocimetry. Five different momentum flux ratios of the two inlet ducts to the kiln are investigated in order to evaluate its effect on the flow field in general and the recirculation zone in particular. Time-averaged and phase-averaged analyses are reported, and it is found that the flow field resembles that of two parallel merging jets, with the same characteristic flow zones. The back plate separating the inlet ducts acts as a bluff body to the flow and creates a region of reversed flow behind it. Due to the semicircular cross-section of the jets, the wake is elongated along the walls. Conclusions are that the flow field shows a dependence on momentum flux ratio of the jets; as the momentum flux ratio approaches unity, there is an increasing presence of von Kármán-type coherent structures with a Strouhal number of between 0.16 and 0.18. These large-scale structures enhance the mixing of the jets and also affect the size of the recirculation zone. It is also shown that the inclination of the upper inlet duct leads to a decrease in length of the recirculation zone in certain cases.     

On the problem of free deceleration of a rigid body in a resisting medium

A mathematical model of the influence of a medium on a rigid body with some part of its external surface being flat is considered with due allowance for an additional dependence of the moment of the medium action force on the angular velocity of the body. A full system of equations of motion is given under quasi-steady conditions; the dynamic part of this system forms an independent third-order system, and an independent second-order subsystem is split from the full system. A new family of phase portraits on a phase cylinder of quasi-velocities is obtained. It is demonstrated that the results obtained allow one to design hollow circular cylinders (“shell cases”), which can ensure necessary stability in conducting additional full-scale experiments.     

Lift Force Acting on a Heavy Solid in a Rotating Liquid-Filled Cavity with a Time-Varying Rotation Rate

The dynamics of a heavy cylindrical body in a liquid-filled horizontal cylindrical cavity with a time-varying rotation rate is experimentally investigated. The body is near the cavity boundary under a centrifugal force and undergoes solid-body rotation together with the liquid and the cavity at a fixed rotation rate. The dependence of the body dynamics on the amplitude and frequency of modulation of the rotation rate is investigated. It is found that at a critical amplitude of modulation (at definite frequency), the heavy body repulses from the cavity boundary and comes into a steady state at some distance from the wall. It is found that the average lift force (repulsive one) is generated by the azimuthal oscillation of the body in the rotating frame of reference and manifests itself at a distance comparable to the thickness of the viscous boundary layer. In the experiments, we observed azimuthal drift of the body due to asymmetric azimuthal oscillations of the body. In the limit of high frequency of the rotation rate modulation, the dependence of the lift force coefficient on the gap between the body and the wall is determined.     

Dynamic stability of uncertain laminated beams subjected to subtangential loads

Because of the inherent complexity of fiber-reinforced laminated composites, it can be challenging to manufacture composite structures according to their exact design specifications, resulting in unwanted material and geometric uncertainties. Thus the understanding of the effect of uncertainties in laminated structures on their static and dynamic responses is highly important for a reliable design of such structures. In this research, we focus on the probabilistic stability analysis of laminated structures subject to subtangential loading, a combination of conservative and nonconservative tangential loads, using the dynamic criterion. In order to study the dynamic behavior by including uncertainties into the problem, three models were developed: exact Monte Carlo simulation, sensitivity-based Monte Carlo simulation, and probabilistic FEA. These methods were integrated into the existing finite element analysis. Also, perturbation and sensitivity analysis have been used to study nonconservative problems to study the stability analysis using the dynamic criterion.     

Stability of a rigid body translating in a resisting medium

The paper discusses a nonlinear model that describes the interaction of a rigid body with a medium and takes into account (based on experimental data on the motion of circular cylinders in water) the dependence of the arm of the force on the normalized angular velocity of the body and the dependence of the moment of the force on the angle of attack. An analysis of plane and spatial models (in the presence or absence of an additional follower force) leads to sufficient stability conditions for translational motion, as one of the key types of motions. Either stable or unstable self-oscillation can be observed under certain conditions     

Instability of elastic bodies

The study of the equilibrium of systems constitutes an important chapter of applied mechanics. Since Euler’s works on beam buckling, in 1774, many eminent specialists studied the problem of the elastic instability of structures.An examination of many works published in this field shows a large number of approaches or criteria adopted by various authors. The objective of this study is to show through a classical example the link between the different approaches to provide a multi-level basis and to propose a valid global approach for conservative as well as nonconservative systems.     

Diffusion in multicomponent gaseous mixtures in a model of local thermodynamic equilibrium

Diffusion of chemical elements into an ionized multicomponent gaseous mixture is considered in a model of local thermodynamic equilibrium. A linear dependence of the mass flows of chemical elements and the heat flow on the temperature gradient, mass fractions of the chemical elements, and the electric field is obtained. An example is given of a calculation of the effective diffusion coefficients for a hydrogen-helium mixture.     

A Slender Chisel-Like Body in a Supersonic Stream

The wave drag of a chisel-tike slender ruled body in a supersonic stream is considered. The dependence of the drag on the body geometry is studied. A comparison with axisymmetric bodies and the von Karman ogive is drawn.     

Parametric equations of nonholonomic nonconservative systems in the event space and the method of their integration

In this paper, the parametric equations with multipliers of nonholonomic nonconservative systems in the event space are established, their properties are studied, and their explicit formulation is obtained. And then the field method for integrating these equations is given. Finally, an example illustrating the application of the integration method is given. The Project is supported by the National Natural Science Foundation of China.