Motion Of Solid Body Research Articles

Effect of elasticity on the dynamics of a superconducting rotor rotating in a magnetic field

A spherical shape of the outer surface of rotors of some types of noncontact gyroscopes gives rise to conditions, where the force field ensures the stability of the center of mass relative to the base and has an insignificant effect on the angular motion of the rotor. However, there are some effects (for instance, the Barnett—London effect), which lead to emergence of moments of mechanical forces even for spherical bodies. The effect of rotor elasticity on the motion of a superconducting deformable spherical solid body in a magnetic field is studies. It is shown that the moment of mechanical forces acting on the body in the magnetic field is proportional in the first approximation to the angular velocity squared. The effect of this moment on the dynamics of angular motion of the rotor is studied.

Long-time tails in the solid-body motion of a sphere immersed in a suspension

Long-time tails in the translational and rotational motion of a sphere immersed in a suspension of spherical particles are discussed on the basis of the linear, time-dependent Stokes equations of hydrodynamics. It is argued that the coefficient of the t(-3/2) long-time tail of translational motion depends only on the effective mass density and shear viscosity of the suspension. A similar expression holds for the coefficient of the t(-5/2) long-time tail of rotational motion. In particular, the long-time tails are independent of the sphere radius, and therefore the expressions hold also for a particle of the suspension. On account of the fluctuation-dissipation theorem the long-time tails of the velocity autocorrelation function and the angular velocity autocorrelation function of interacting Brownian particles are also given by these expressions.

Body motion in artificial thermal channels

The possibility of reducing the losses of kinetic energy of small bodies that fly with high velocity in the atmosphere by creating a thermal channel along the flight trajectory owing to electromagnetic-energy supply from external sources is studied. The amount of energy necessary to change the ambient-medium parameters significantly is estimated, and an expression for the distribution of the temperature and density perturbations in the thermal wake of a system of crossed Gaussian laser beams, which form a region of heat release with an intensity one order of magnitude greater than the intensity of separate beams is derived. The spatial problem of the motion of a long solid body of revolution over a thermal channel is solved. The efficiency of the proposed method of decreasing the losses of kinetic energy along the trajectory is shown.

Motion of bodies under vibration in granular media

Results obtained from experimental studies of the motion of solid bodies through a granular medium under a time-varying load are presented. Dependences of the average velocity of a body on the driving frequency are obtained, and the resonance behavior of these dependences is observed. It is established that the experimental value of the resonance frequency has a universal meaning and is fundamentally and closely related to the structure of the granular material. The structural features of a granular medium are qualitatively described, along with the correlation between them and the result of the study.

Flow of Granular Material through Rotating Cylinders: Modelling Transients

ABSTRACTGranular material, fed continuously into the top of a slowly rotating, slightly inclined cylinder, forms a moving bed. Much of the bed rotates with the cylinder in solid body motion. When particles reach the surface of the bed, they move rapidly down it, and are absorbed once more into the solid body motion. Such cylinders are used in calcining, pharmaceutical manufacture, and drying. A steady state transport model, applicable when the bed depth varies slowly along the cylinder, has existed for around 50 years. The bed surface is considered locally flat, and particles in it fall along the line of steepest descent, inclined to the horizontal at the angle of repose. There is reasonable agreement with experiment.We propose a quasi-steady state dynamical model, in which the steady state model is coupled with a volume balance across an axial element. The model takes the form of a nonlinear diffusion equation which was solved numerically. The parameters of the dynamic model are the dimensions of the cylinder and outlet dam, the inclination of the axis of the cylinder, its rotational speed, the angle of repose of the granular material and its feed volumetric flow rate: the dynamic model has no free parameters. Experiments were conducted using sand, mean particle size 490 μm, in a perspex tube of length 1 m, radius 0.0515 m, lined with sandpaper, with a feed end dam of height 0.029 m, and with no exit dam, or an exit dam of height 0.0105 m. With the system initially in steady state, step changes in feed flow rate, rotational speed or axis inclination were imposed, and the resulting discharge flow rate and bed depth axial profile measured as functions of time. Good agreement is found between model and experiment.

On Some Features of Solid-Body Motion under Combined Vibrowave and Static Actions

Results are presented for modeling of the effect of anomalously low friction during solid body motion due to vibrowave and static actions. Cases are examined for the motion with different coefficients of static friction between the surfaces of the solid bodies. The stand, and the measurement and control system used are described.

Lattice Boltzmann computations and applications to physics

We discuss the lattice Boltzmann computing approach, its connection with cellular automata and present a new model for simulating wave propagation in complex environments. We illustrate the behavior of our model on several applications like radio wave propagation in a city, solid body motion and fracture phenomena.

Scale relativity and quantization of planet obliquities

We apply the theory of scale relativity to the equations of rotational motion of solid bodies. We predict in the new framework that the obliquities and inclinations of planets and satellites in the solar system must be quantized. Namely, we expect their distribution to be no longer uniform between 0 and π, but instead to display well-defined peaks of probability density at angles θ k = kπ/ n. We show in the present paper that the observational data agree very well with our prediction for n = 7, including the retrograde bodies and those which are heeled over the ecliptic plane. In particular, the value 23″ 27′ of the obliquity of the Earth, which partly determines its climate, is not a random one, but lies in one of the main probability peaks at θ = π/7.

Analysis of flow in a square cavity with an oscillating top wall

The flow induced by the oscillatory motion of a solid body is important in a number of practical problems. As the solid boundary oscillates harmonically, there is steady streaming motion invoked by the Reynolds stresses, which could cause extensive migration of the fluid during a period of fluid motion. We here analyzed the flow in a square cavity with an oscillating top wall for the parameters which make the time derivatives and the convective terms equally important in the entire cavity flow. The full Navier-Stokes equations are solved by the second-order time accurate Momentum Coupling Method which is devised by the authors. The particular numerical scheme does not need subiteration at each time step which is usually a required process to calculate the incompressible Navier-Stokes equations. The effect of two parameters, the Reynolds number and the frequency parameter, on the oscillatory flow has been investigated.

The unsteady motion of solid bodies in creeping flows

In treating unsteady particle motions in creeping flows, a quasi-steady approximation is often used, which assumes that the particle's motion is so slow that it is composed of a series of steady states. In each of these states, the fluid is in a steady Stokes flow and the total force and torque on the particle are zero. This paper examines the validity of the quasi-steady method. For simple cases of sedimenting spheres, previous work has shown that neglecting the unsteady forces causes a cumulative error in the trajectory of the spheres. Here we will study the unsteady motion of solid bodies in several more complex flows: the rotation of an ellipsoid in a simple shear flow, the sedimentation of two elliptic cylinders and four circular cylinders in a quiescent fluid and the motion of an elliptic cylinder in a Poiseuille flow in a two-dimensional channel. The motion of the fluid is obtained by direct numerical simulation and the motion of the particles is determined by solving their equations of motion with solid inertia taken into account. Solutions with the unsteady inertia of the fluid included or neglected are compared with the quasi-steady solutions. For some flows, the effects of the solid inertia and the unsteady inertia of the fluid are importanty quantitatively but not qualitatively. In other cases, the character of the particles' motion is changed. In particular, the unsteady effects tend to suppress the periodic oscillations generated by the quasi-steady approximation. Thus, the results of quasi-steady calculatioins are never uniformly valid and can be completely misleading. The conditions under which the unsteady effects at small Reynolds numbers are important are explored and the implications for modelling of suspension flows are addressed.

Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid. Part 2. Couette and Poiseuille flows

This paper reports the results of a two-dimensional finite element simulation of the motion of a circular particle in a Couette and a Poiseuille flow. The size of the particle and the Reynolds number are large enough to include fully nonlinear inertial effects and wall effects. Both neutrally buoyant and non-neutrally buoyant particles are studied, and the results are compared with pertinent experimental data and perturbation theories. A neutrally buoyant particle is shown to migrate to the centreline in a Couette flow, and exhibits the Segré-Silberberg effect in a Poiseuille flow. Non-neutrally buoyant particles have more complicated patterns of migration, depending upon the density difference between the fluid and the particle. The driving forces of the migration have been identified as a wall repulsion due to lubrication, an inertial lift related to shear slip, a lift due to particle rotation and, in the case of Poiseuille flow, a lift caused by the velocity profile curvature. These forces are analysed by examining the distributions of pressure and shear stress on the particle. The stagnation pressure on the particle surface are particularly important in determining the direction of migration.

Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid Part 1. Sedimentation

This paper reports the result of direct simulations of fluid–particle motions in two dimensions. We solve the initial value problem for the sedimentation of circular and elliptical particles in a vertical channel. The fluid motion is computed from the Navier–Stokes equations for moderate Reynolds numbers in the hundreds. The particles are moved according to the equations of motion of a rigid body under the action of gravity and hydrodynamic forces arising from the motion of the fluid. The solutions are as exact as our finite-element calculations will allow. As the Reynolds number is increased to 600, a circular particle can be said to experience five different regimes of motion: steady motion with and without overshoot and weak, strong and irregular oscillations. An elliptic particle always turn its long axis perpendicular to the fall, and drifts to the centreline of the channel during sedimentation. Steady drift, damped oscillation and periodic oscillation of the particle are observed for different ranges of the Reynolds number. For two particles which interact while settling, a steady staggered structure, a periodic wake-action regime and an active drafting–kissing–tumbling scenario are realized at increasing Reynolds numbers. The non-linear effects of particle–fluid, particle–wall and interparticle interactions are analysed, and the mechanisms controlling the simulated flows are shown to be lubrication, turning couples on long bodies, steady and unsteady wakes and wake interactions. The results are compared to experimental and theoretical results previously published.

Transformation properties of certain characteristics of the motion of a deformable solid body in different forms of relativistic dynamics

We establish the transformation properties of certain characteristics of the motion of a deformable solid body (velocities, strains, stresses) with respect to a realization of the Poincare group by nonpoint infinitesimal transformations of the configuration space—a three-dimensional Riemannian manifold with the metric induced by the imbedding in the Minkowski space for an arbitrary form of relativistic dynamics.

Predominantly unidirectional motion of a compressible solid body in a vibrating liquid

Predominantly unidirectional motion of a compressible solid body in a vibrating liquid

A mixed finite element formulation for non-linear analysis of plane problems

Based on the incremental non-linear theory of solid bodies and the Hellinger-Reissncr principle, a mixed updated Lagrangian formulation of the large displacement motion of solid bodies is derived, and an associated mixed finite element model is developed. The model contains the displacements and stresses as the nodal degrees of freedom. The model is used for the large deformation elasto-plastic analysis of plane problems. In solving non-linear problems, the Newton-Raphson method with arc-length control is adopted to trace the post-buckling response. The computational steps to calculate the elasto-plastic stress increments at Gauss points in the elasto-plastic analysis by the present mixed model are described in detail. Numerical results are presented and compared with those of the displacement model and existing solutions to show the accuracy of the present mixed model in the large deformation elasto-plastic analysis of plane problems.

An Elastic Model for Lagrangian Turbulence and Diffusion

In contrast to the evolution of the velocity field of a fluid which is governed by Navier-Stokes partial differential equation, the trajectory of a fluid particle is governed by an ordinary differential equation. Consequently in a Lagrangian description of a fluid, the results of dynamical system theory of autonomous O.D.E. may be used directly. This way the observed randomness of a Lagrangian turbulence might be interpreted as deterministic chaos [1]. In the present work we give simple arguments 'based upon a classical elastic model to confirm the existence of chaotic diffusion-like particle paths in the presence of deterministic wave-like fluctuation. There are numerous analogies between elastomechanical and hydrodynamical problems such as that holding between the shape of a free fluid surface under surface tension and the bending of an elastic wire. In what follows, we use another analogy relating to the Euler elastica [2-6] and the lateral displacement of a fluid particle due to the motion of a circular cylindrical solid body in a two-dimensional flow [7, 8]. , Subsequently we modify our elastica model in such a way that allows us to mimic to some reasonable extent the well-known Karman vortices street created

Visualization Studies in Rotating Disk Cavity Flows

An experimental study was performed in a simplified turbine disk cavity consisting of a single disk rotating near a stationary flat plate, bounded radially by an axial seal fixed to the plate. The disk Reynolds number was 6.2 × 105. Cooling flow was supplied axially at a dimensionless radius of 0.33. Flow visualization showed boundary layers on both the rotating and stationary disks with the core between the layers rotating in solid body motion. At intermediate cooling flow rates, large vortical structures aligned with the disk spin axis and spanning the core were observed.

A study on lateral impact of Timoshenko beam

The impact of solid bodies occurs in machines and it is the primary reason of noise and vibration. To understand the quantitative characteristics of noise and vibration, it is necessary to understand the motion of solid bodies, especially the deformation of the surface. In this study the authors analyze theoretically and numerically the impact phenomena on a falling body of a Timoshenko beam. Also we have compared a Bernoulli-Euler hinged-hinged beam and a Timoshenko hinged-hinged beam with regard to the impact of a cylindrical body on each of them. The conclusions are as follows: (1) the impact force, the deflection and the bending moment of the Timoshenko beam, and the displacement of the falling body can be calculated precisely according to the equations derived from this study, (2) the examination of the Timoshenko beam are compared with that of the Bernoulli-Euler beam, (3) the Timoshenko beam deflections with the passage of time are illustrated.

Hydromagnetic screw dynamo

We solve the problem of magnetic field generation by a laminar flow of conducting fluid with helical (screw-like) streamlines for large magnetic Reynolds numbers, Rm. Asymptotic solutions are obtained with help of the singular perturbation theory. The generated field concentrates within cylindrical layers whose position, the magnetic field configuration and the growth rate are determined by the distribution of the angular, Ω, and longitudinal, Vz, velocities along the radius. The growth rate is proportional to Rm−½. When Ω and Vz are identically distributed along the radius, the asymptotic forms are of the WKB type; for different distributions, singular-layer asymptotics of the Prandtl type arise. The solutions are qualitatively different from those obtained for solid-body screw motion. The generation threshold strongly depends on the velocity profiles.

Predicting the storage life of lubricating oils

One of the most important requirements imposed on lubricating oils is stability of their properties in extended storage. However, lubricating oils, the same as any other products of organic origin, are subject to natural aging over an extended period of exposure to various actions such as temperature variations, oxygen, air, moisture, and gravitation. These products are complex multicomponent systems; and during extended storage they may undergo various physical and chemical conversions such as oxidation, polymerization, hydrolysis, and layer separation. The rates of these conversions are determined by the intensities of the indicated actions and also by the composition, structure, and properties of the oil components. The relationships are complex because of the diversity of external factors and also the great variation in composition and properties of the oil components [I]. In the USSR and in other countries, the storage stability of oils is usually evaluated by long-term natural storage of the oils in different climatic zones, with periodic evaluation of the oil quality to determine conformance to the requirements imposed by technical standardization documents [2, 3]. In order to improve the reliability of results, two or three batches of commercial oll are usually subjected to test. The results of such studies are used to establish the allowable storage periods for each particular oil. This method is quite simple, but it has serious disadvantages, in that the test time is excessive (5-10 years), considerable expenditure of labor is involved, and large quantities of oil are required. Because of these shortcomings, the technique cannot be used to determine the storage stability of oil properties in the stage of product development, where it would be desirable~to make the appropriate changes to improve these properties. We have proposed a laboratory method for predicting the storage life of mineral and synthetic oils for aircraft gas turbine engines. This method was developed on the basis that oils, as complex multicomponent systems, may separate into layers, form sludge, and change in physical homogeneity during extended storage under the influence of the above-indicated factors; and under the influence of oxidation and other processes, the oils may change in chemical composition. With this background, we took as the basis of the method an evaluation of the physical and chemical stability of oils with due regard for the action of different factors. As a criterion for rating the physical stability we took the length of the storage period during which, with no layer separation or turbidity, the content of precipitated sludge would reach the maximum allowable value of 0.005%. As a criterion for rating the allowable storage period of the oil with respect to chemical stability we took the acid number, the property index that is the most subject to change during storage under real conditions. In finely dispersed systems, processes of enlargement and precipitation of particles under the influence of the gravitational field are very slow and extend overlong periods of time. The acceleration of oil layering with precipitation of sludge can be achieved by centrifuging. The ratio of rates of motion of a small solid body in a liquid under the influence of a centrifugal field (Vc) and a gravitational field (vo) is equal to the separa