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Vol 88, No 5 (2024)
Articles
Non-Regular Precession of a Gyrostat in Three Uniform Fields
Abstract
This article presents a solution to the problem of the conditions of gyrostat non-regular precession in three homogeneous fields, in which the ratio of precession and proper rotation velocities is constant. The case of a gyrostat with axial dynamic symmetry, the axis of its proper rotation coinciding with the axis of symmetry of the gyrostat, is highlighted. It is shown that the precession is possible only at a precession rate twice the rate of its proper rotation, and the gyrostatic moment deflected from the axis of symmetry by some angle ε. An expression for each of the rates is obtained through elementary functions of time. At 0 < ε < ε*, the motion is periodic, at ε ≥ ε*, the velocity tends to zero and the solid makes no more than one revolution around the axis of its proper rotation, the angle ε* is expressed through the constant nutation angle θ. A relationship has been found between the nutation angle and the ratio of the axial and equatorial moments of inertia, under spherical symmetry cosθ = 1/4. The set of permissible positions of the centers of force at arbitrary given angles between the lines of force of homogeneous fields and for the special case of orthogonal fields is indicated.
649-664
Synthesis of Time-Optimal Control for One Fourth-Order Linear System
Abstract
A linear fourth-order control system is studied, describing in the first approximation the dynamics of an inverted pendulum with an active dynamic damper. Based on Pontryagin’s maximum principle and the method proposed by A.A. Feldbaum for constructing sets on which control switching occurs, the problem of synthesizing optimal control that brings the system to a state of rest in minimal time is solved. The properties of the system under consideration make it possible to reduce the solution of the optimal response problem to the solution of a similar problem for a system of lower dimension.
665-679
The Fine Structure of the Density Field in Two-Dimensional Periodic Flows on the Surface of a Viscous Stratified Liquid
Abstract
In the linear approximation, the propagation of a periodic disturbance along the free surface of a viscous stratified fluid in a uniform gravitational field is considered, taking into account the action of surface tension. Complete solutions of the linearized system of fundamental equations of the mechanics of heterogeneous fluids, which determine the regular wave and singular ligament components, are obtained. The fine spatial structure of the fields of next physical variables: fluid velocity, momentum, density and density gradient are calculated.
679-691
Effect of Charge Relaxation Effect on Electromagnetic Radiation Intensity of Oscillating Viscous Liquid Drop
Abstract
Theoretical asymptotic methods have shown that the electric charge relaxation effect affects the physical characteristics of the electromagnetic radiation of the oscillating charged droplet. Analytical expressions are obtained for frequencies, decrements of attenuation of capillary oscillations of droplets due to viscous attenuation and energy losses on radiation. It has been shown that the frequencies of electromagnetic radiation of cloud droplets, realized in the ranges of hundreds of kilohertz and megahertz units, decrease with an increase in the radius and charge parameter of the emitting droplet, as well as attenuation decrements associated with radiation. Intensity of emission of electromagnetic waves decreases with decrease of electrical conductivity and mobility of charges in liquid.
692-721
Analytical Solution of the Problem on Bi-Linear Flow in a Formation with a Finite Auto-Fracture
Abstract
The problem of unsteady bilinear flow of a single-phase Newtonian fluid in a formation with a finite auto-fracture connecting an injection and production well is considered. The wells simultaneously begin to operate at constant pressures in an initially undisturbed infinite formation with a vertical main fracture of constant width. Using the Laplace transform method, analytical solutions were obtained for the pressure fields in the fracture and formation, as well as the flow velocity in the fracture. An approximate model is considered that uses a self-similar solution to the problem of filtration of an incompressible fluid in an elastic half-space with constant pressure at the boundary to simulate filtration leaks. It was found that for a number of model parameters a simple analytical solution of the approximate model gives acceptable results.
722-737
Body Waves Induced by a Concentrated Force
Abstract
Body waves in an isotropic elastic space propagating along the line of action of a concentrated force singularity are analyzed. It is shown that along the line of action of the force singularity, in addition to the P-wave, the S-wave also propagates. The erroneous statements found in a number of publications about the absence of S-waves on the line of action of the force singularity are noted.
738-744
Simulation of the Flow Velocity Field on the Free Surface of a Stratified Fluid
Abstract
The paper considers the problem of simulation of the velocity field on the free surface of an ideal stratified fluid generated by internal gravitational waves that reached the surface. The buoyancy frequency may vary with depth. The computer program has been written that allows calculating all components of the velocity field on the surface. It is shown that the calculation results for the vertical velocity component are consistent with the known asymptotics obtained in the far-field approximation for the cases of uniform and rectilinear motion of a point mass source horizontally (by B. Voisin) or at a fixed angle to the horizon (by M.M. Scase and S.B. Dalziel) in a uniformly stratified fluid.
745-757
Numerical Simulation of Edge Noise Using a Method Based on Synthetic Turbulence
Abstract
An approach to the numerical modeling of broadband noise excited by turbulent fluid pulsations in the presence of an elastic body using a method based on synthetic turbulence is presented. The most common methods aimed at solving this problem involve determining noise emission as a result of solving the Helmholtz equation with sources in the form of the Lighthill tensor, previously determined in the hydrodynamic part of the problem using eddy-resolving turbulence models. These methods require a large amount of computation, which in the case of real technical applications leads to almost impossible requirements for computing resources. A reduction in the amount of calculations can be achieved for the class of problems in which continuous flow is implemented. In this case, hydrodynamic fields determined using a relatively simple Reynolds averaging of the Navier–Stokes equations can be used as initial data instead of directly determining velocity fluctuations in the computational domain using eddy-resolving methods.
In the presented method, velocity pulsations are generated based on information about averaged hydrodynamic fields, by spatial filtering of white noise with given correlation characteristics. As a result, an express assessment of the noise flow around a body is reduced to finding the radiation power density of elementary streams of current near the inhomogeneity of the streamlined surface, using data on the velocity vectors obtained as a result of solving a hydrodynamic problem, in the approximation of an incompressible fluid, as well as the transfer coefficient “source of volumetric acceleration – pressure”, which is determined by the reciprocity method. The transmission coefficient characterizes the geometry of the streamlined body, its mechanical properties and the properties of the medium in which acoustic radiation propagates. The method allows you to localize areas with the most intense noise emission, as well as interpret the results obtained by analyzing the features of the hydrodynamic flow and the properties of the elastic structure. A verification of the method is presented using the example of the problem of noise emission from a fragment of a real technical structure flowing around a fluid flow.
758-777
Geomechanical Markers of the Stress and Strain State and Interaction of Structures in Inhomogeneous Geoenvironments
Abstract
Geodynamics in an inhomogeneous 3D-geoenvironment, due to gravitational processes, is characterized by fields of displacement, rotations and deformations. The quantitative and dimensional characteristics of the distribution of these fields are provided by the corresponding stress fields. The results of computational experiments modeling the stress and strain state of two profiles are presented. The distribution of fields in depth is due to density inhomogeneity, one of the internal sources of tectonic stresses. The generalization of the component analysis showed the general properties of the stress and strain state, which is characterized by stretching against the background of prevailing compression. The stress intensity parameter is used to model the interaction features of inhomogeneous profile structures. The degree of plasticity of the geoenvironment is modeled by the deformation intensity parameter.
778-796
Three-Field FEM in Shell Calculations with Options for Interpolation of the Sought Values
Abstract
A three-field finite element of a quadrangular shape of a thin shell with nodal unknowns in the form of: displacements and their first derivatives has been developed; deformations and curvatures of the median surface; forces and moments of the middle surface.
The approximation of the required quantities was carried out in two versions. In the first version, the components of the displacement vector and the components of the strain and curvature tensors, as well as the force and moment tensors, were approximated using traditional shape functions as components of scalar fields. In the second version, tensor quantities were approximated through the corresponding tensors of nodal points, and only after coordinate transformations based on the relations of the used curvilinear coordinate system were approximating expressions for the components of the corresponding tensors obtained.
Specific examples show the effectiveness of using the second version of approximating expressions in shell calculations.
797-820