This paper investigates a finite-dimensional model of a beam pendulum with an arbitrary number of degrees of freedom, which is used to simulate the motion of a loading crane wire rope. The model represents a system of rods connected by cylindrical joints and elastic torsions. Based on analytical calculations, dependency diagrams are plotted showing how the oscillation frequencies of the beam pendulum depend on the number of wire rope segments, and their convergence to the oscillation frequencies of the distributed model is demonstrated. It was found that the three lowest oscillation frequencies of the finitedimensional model converge to those of the distributed model with the number of segments equal to 10-20. A set of crane models is developed using the application software packages. These computer models are employed to verify the convergence of the wire rope trajectories with an increasing number of segments. Considering the two operating modes of the crane-with platform oscillation and with wire rope extension during large-amplitude load swinging-it was shown that 20 segments are sufficient for accurate wire rope modeling.
In this paper, the incompressible fluid flow in a plane channel with a heated upper wall under pressure drop conditions is studied. A 45% aqueous solution of propylene glycol is considered as a real fluid. The numerical study is performed using a spectral method based on the expansion of functions in terms of Chebyshev polynomials of the first kind. The results show a significant dependence on the selected model of the viscosity-temperature dependence. In analyzing the behavior of the real fluid, two characteristic temperature ranges are identified. In the first range, the critical flow parameters calculated using exponential and linear approximations are close in value. In the second range, however, the critical parameters differ significantly for the exponential and linear approximations. This highlights the importance of selecting an appropriate rheological model for the temperature dependence of viscosity under given conditions. Notably, for fixed Reynolds number and wavenumber values, optimal conditions for the transition regime can be identified for fluids with either exponential or linear viscosity-temperature relationships, since their instability regions overlap.
This paper presents the results of a study on detonation wave suppression in a pipeline partially filled with an inert particle layer. The numerical simulation is carried out using the large-particle method. The main purpose of this study is to analyze the impact of transverse spatial inhomogeneity in particle concentration on detonation attenuation at different particle and pipeline parameters. Integral computational dependencies were obtained to determine the minimum initial mass fraction of solid particles required to suppress detonation at various initial mass contents of the unitary fuel. The results show that an increase in the pipeline diameter causes notable differences in the gas and particle parameters along the symmetry axis and near the wallAas the detonation wave passes through the particle layer. The study also examines the effect of the inhomogeneous region thickness, as well as the diameter and length of the particle layer, on detonation suppression. It is demonstrated that smaller particle diameters and a longer particle layer reduce the minimum mass content required for suppression. Additionally, the critical relative mass content of the inert particles monotonically increases with increasing initial mass content of the unitary fuel mixture.
This paper presents a mathematical model for constructing the elastic state of a finite transversely isotropic body of revolution exposed to axisymmetric body forces varying with time according to aAcyclic law. The solution method is based on expanding the sought elastic state into a Fourier series by elements of an orthonormal basis of body-force vectors. Basic elements represent particular solutions to the three-dimensional axisymmetric stationary-dynamic problem of elasticity theory for a transversely isotropic body of revolution. A solution is presented for the case of a circular cylinder made of rock material.
A scheme and a methodology are proposed for modeling the operation of multistage ballistic launchers in conjunction with synchronization devices for activating the additional model acceleration stages as the projectile passes through predefined cross-sections of the channel. The sensing element of the device is an in-bore inductive velocity sensor operating via the deformation of magnetic barriers of measuring frames by passing a conductive projectile. Using a two-stage light-gas launcher with a synchronizer for an electrodynamic acceleration stage as a case study, the effect of various algorithms for determining the moments when the projectile passes through the sensor frames and its accelerated motion beyond the second frame on the trigger timing of the rail accelerator is analyzed. It is assumed that the projectile position during passage is not measured, and the velocity is derived from the base distance between the frames. A refined algorithm for determining the trigger for the electrodynamic acceleration stage is developed based on coupled simulations of the model’s gas-dynamic acceleration and the operation of the measuring frames of the velocity sensor.
This study investigates the structure and mechanical properties of consolidated TiC-Al materials produced using PET plastic and aluminum waste. The composites consist of an aluminum matrix and TiC particles. The hardness and compressive strength of the samples are comparable to those of composite materials produced from high-quality commercial powders and exceed those of traditional alloys. The results demonstrate the potential of using recycled materials to produce materials with prospective applications in various industrial sectors.
In this paper, we describe the class of all two-dimensional endo-commutative algebras over any base field. Thereby, we extend recent results of Takahasi, Shirayanagi, and Tsukada on description of the class of two-dimensional endo-commutative algebras to the case of an arbitrary field. The concept of an endo-commutative algebra was first introduced by aforementioned authors; in the same works, the motivations to study this class of algebras also were presented. In this paper, we present the canonical representatives of the isomorphism classes of two-dimensional endo-commutative algebras over an arbitrary field.
This paper presents a methodology for constructing the stress-strain state of transversely isotropic bodies of revolution under the conditions of the first fundamental problem of elasticity theory, where the forces specified on the body surface vary harmonically in time. The applied forces are also non-axisymmetric. The disturbance propagates with a constant velocity along one axis of the elastic symmetry of the material. The approach is based on the relationship between the three-dimensional stress-strain state of an elastic transversely isotropic body and a set of auxiliary two-dimensional states. The auxiliary states are constructed using the general solution to the stationary-dynamic problem of plane strain and deplanation. The solution is then obtained using the method of boundary states. A set of plane auxiliary states is formed, and using transition formulas, a corresponding set of three-dimensional states is constructed. Sets of such states form bases for the spaces of internal and boundary states. After orthogonalization, these bases are used when the desired state is expanded into Fourier series with the same coefficients. Thus, a solution to the first fundamental dynamic problem of elasticity theory is presented for a transversely isotropic circular cylinder subjected to time-harmonic (sinusoidal) forces applied to its lateral surface.
This paper investigates a finite-dimensional model of aAbeam pendulum with an arbitrary number of degrees of freedom, which is used to simulate the motion of a loading crane wire rope. The model represents a system of rods connected by cylindrical joints and elastic torsions. Based on analytical calculations, dependency diagrams are plotted showing how the oscillation frequencies of the beam pendulum depend on the number of wire rope segments, and their convergence to the oscillation frequencies of the distributed model is demonstrated. It was found that the three lowest oscillation frequencies of the finite-dimensional model converge to those of the distributed model with the number of segments equal to 10-20. A set of crane models is developed using the application software packages. These computer models are employed to verify the convergence of the wire rope trajectories with an increasing number of segments. Considering the two operating modes of the crane-with platform oscillation and with wire rope extension during large-amplitude load swinging-it was shown that 20 segments are sufficient for accurate wire rope modeling.
This paper indicates the feasibility of using the resonance method of ice cover destruction by amphibious air-cushion vehicles. The essence of flexural-gravity resonance is explained, as well as the possibility of applying this method to solve a number of ice engineering problems: breaking ice cover in shallow waters, where the water depth is inaccessible to icebreakers due to their draft; breaking ice jams and ice gorges during spring break-up to prevent destructive floods; breaking ice over large areas when servicing hydroelectric power plants and opening the ice cover of reservoirs and river bays to enable earlier navigation on inland waterways, etc. Based on the theoretical dependencies developed for calculating the stress-strain state of the ice cover under a moving load, the results are obtained for determining the ice-breaking capacity of vessels with account for variations in water depth and the presence of a snow cover on the ice under resonant conditions. When describing the relations between stresses and strains in ice, the Voigt model of viscoelastic deformation is used. The snow cover is modeled as a viscous layer. It is found that such ice conditions as water depth and snow-covered ice significantly affect the ice-breaking capability, i.e., Athe efficiency of ice cover destruction by the resonance method. Dependencies are presented for determining the main vessel parameters that ensure complete destruction of the ice cover with a given ice thickness and specified ice conditions. It is concluded that, to increase efficiency, icebreaking operations should be initiated in snow-free ice areas, near the shore, and in shallow waters.
This study presents a numerical investigation of unsteady gas-dynamic processes in axisymmetric solid-propellant rocket motors equipped with a movable central body for thrust regulation. Three motor configurations with identical burning-surface areas but different chamber volumes and grain geometries were analyzed, including a design with a recessed nozzle. The nonstationary Euler equations were solved using the control-volume Godunov scheme on moving meshes incorporating a hybrid algorithm combining grid smoothing and local remeshing to track the motion of the flow-control element. Calculations were performed for two propellants with different burning-rate characteristics at varying velocity of the throttling mechanism. The results show that rapid changes in the throat area induce strong transient restructuring of the flow in the transonic and supersonic zones, leading to short-term thrust overshoots or undershoots caused by the mismatch between chamber-pressure evolution and instantaneous critical-area variation. The magnitude of these thrust excursions increases with the throttling rate, whereas the duration of the transient process decreases. Transients during throttling from the maximum to the minimum thrust were 2-2.5 times shorter than in the reverse mode. For all configurations, the maximum difference in thrust-overshoot amplitude at a fixed rate reached 5.5-7% of the initial thrust.
In this paper, the porous TiNi alloys produced by self-propagating high-temperature synthesis at reaction onset temperatures ranging from 395 degrees C to 515 degrees C were studied. Porosity, average pore size, and wall thickness were determined using optical coherence tomography. The porosity decreased from 63% to 58-59%; the pore size reached a minimum of 5.9 mu m at 495 degrees C and increased to 27.1 mu m at 515 degrees C. Wall thickness varied from 78.1 mu m at 395 degrees C to a minimum value of 28.4 mu m at 495 degrees C. The compressive mechanical response of the alloys was governed by the structural parameters of the porous framework. With decreasing porosity and average pore size, the elastic modulus increased from 1200-1300 MPa to 2400 MPa, the ultimate strength from similar to 65 MPa to 128 MPa, and the strain to failure from similar to 7% to similar to 14%. The most favorable combination of high strength and ductility was achieved at a temperature of 435 degrees C. The dependence of the ultimate strength sigma B on porosity was approximated by the Gibson-Ashby model with n = 3.2 (R-2 = 0.98).
This paper presents the results of a numerical study of the body launching at an angle to the horizon under external gas-dynamic forces. The motion of the body is determined considering its geometric dimensions, mass, and mass-centering characteristics. A mathematical model and a computational methodology are proposed for determining the forces acting on the body and their points of application, the body torque relative to its center of mass, as well as the angular velocities and angular accelerations of the body. Based on this methodology, an original user-defined code has been developed for the ANSYS Fluent software package using the C programming language. This paper presents the results of numerical simulation of the symmetric rectangular body motion in a two-dimensional unsteady formulation for various initial launch angles and different mass-center configurations of the body.
During manufacturing, a residual pressure of up to 0.1 Pa is provided inside the housing of the reaction wheel (RW) assemblies. Under these conditions, the assumption of continuity of the medium ceases to be true. To calculate the aerodynamic component of the drag torque of the RW rotor, a mathematical model is adopted that describes the behavior of the gas medium in a non-equilibrium thermodynamic state near the walls using the concepts of rarefaction degree and tangential momentum accommodation coefficient. This model does not use the solution of the Boltzmann equation for statistical mechanics which requires significant computational resources. Modification of the no-slip boundary condition at the walls to account for the partial slip made it possible to determine the effect of the pressure inside the sealed chamber of the RW and the rotor rotational speed on the aerodynamic component of the drag torque. The computed and experimental dependences for the aerodynamic component of the rotor drag torque demonstrate similar behavior.
This study focuses on modeling the apparent brightness of orbital objects using physically-based rendering. The authors developed a Python software that employed the Skyfield library to calculate the positions of the Sun, orbital objects, and observer, as well as the physically-based rendering system Mitsuba3 to calculate the reflected radiance. The software components allow accounting for the realistic geometry of the studied orbital object, optical properties of its surfaces, lighting conditions, and relative positions of the Sun, observer, and target. The simulation procedure involves the calculation of the required direction vectors, construction of a 3D model containing the object under study, virtual camera, light source, and rendering and integration of the resulting radiance to determine the irradiance at the observer and apparent magnitudes. A series of test calculations was conducted for simple geometric shapes (sphere, cylinder, and plate) with diffuse and specular surfaces. The results showed good agreement with analytical solutions: the relative error was less than 0.002% for diffuse surfaces and less than 1.2% for specular surfaces. This paper also presents preliminary simulations of the apparent brightness of the geostationary satellite SIRIO-1, demonstrating that representing the satellite by a simple geometric shape, such as a cylinder, is insufficient to capture all features of its brightness variation. In future work, the developed software will be used to analyze the observed light curves of orbital objects.
It is known that the derivative of higher order is an analogue of the first-order derivative. Although the second-order subdifferential is a generalization of the second order derivative, the second-order subdifferential is not closely related to the first-order subdifferential. AThe article considers modifications of the concept of the second-order sub differential. Like the first-order subdifferential, the second-order directional derivative plays an essential role in the study of the second-order subdifferential. The paper considers the second-order directional derivative which is a generalization of the first-order derivative in Penot's direction. It is proved that if a function satisfies the 2-Lipschitz condition in a neighborhood of a point, then the second-order directional derivative is a bisublinear continuous symmetric function, i.e. it is a bipositively homogeneous biconvex continuous function. Using the tensor product, extensions of a bisublinear function on the space of the tensor product are considered. It is shown that the extension of a bisublinear even function on the space of the tensor product is a sublinear function. It is proved that if a bisublinear even function is continuous, then the sublinear function is also continuous. In this paper, it is shown that a bisublinear symmetric continuous function is an upper bound for a sym-metric continuous bilinear function. In this paper, we study the second-order derivative in the direction of the maximum of a finite number of functions. We consider the subdif-ferential of the of continuous even bisublinear functions. We also consider a class of 2-Lipschitz functions in a neighborhood of a point. A number of properties of 2-Lip-schitz functions are studied. The paper considers the square of the distance function of a set and studies when the square of the distance function of a set satisfies the 2-Lipschitz condition in a neighborhood of a point. It is shown that in a Hilbert space the square of the distance function of a convex closed set satisfies the global 2-Lipschitz condition with a coefficient of 6. The paper defines the bitangent bicone and the binormal cone. A number of their properties are studied. We consider the second-order subdifferential of the sum of a function that satisfies the 2-Lipschitz condition in the neighborhood of a point.
This paper presents the results of experimental studies on the mechanical properties of M600 heavyweight concrete (compliance with EU classification c35/45) under various loading conditions. Massive cylindrical specimens with a diameter of 105 mm and lengths of 500, 200, and 100 mm were tested. The main results include the determination of quasi-static tensile strength obtained from Brazilian tests in the splitting scheme of cylindrical specimens under radial compression, as well as the dynamic tensile strength obtained from spall fracture using shock-wave loading methods applied to the massive specimens. In processing the quasi-static experimental data, a correction factor recommended for concretes of similar composition containing fly ash was applied. After correction, the uniaxial tensile strength of 4.8 MPa was found, which correlated with available theoretical estimates. Compressive and tensile fracture zones were determined on the remaining fragments of the specimens after shock-wave loading. The average dynamic tensile strength, determined from the free-surface velocity profiles of three specimens of different lengths, was 30 MPa. The calculated dynamic hardening coefficient for the concrete grade under study was 6.3 MPa. The obtained results are consistent with published data for similar concrete grades, complement existing studies, and provide a better understanding of the mechanisms governing the resistance of concrete to deformation under dynamic tensile loading. These findings can be used to more accurately predict the behavior of concrete structures under extreme loading conditions.
A group G is called orderable if it is possible to introduce on it a linear order relation that is stable under two-way multiplication. Obviously, if a group admits a finite number of orderings, then it is even. It is still unknown whether for every natural n there is a group admitting exactly 2n orderings. For solvable groups, this issue was solved by V.M. Kopytov. Namely, it was shown that if a nonabelian solvable group admits a finite number of orders, then it is a multiple of 4, and for each natural number n an example of a solvable group with 4n orders is given. However, all these groups had a solvability class of 2. Therefore, the question of the existence (description) of solvable groups with a finite number of orderings and the solvability class greater than 2 seems natural. The study of such groups was started by V.V. Bludov and L.E. Badmaeva. They gave examples of solvable groups of class 3 with a finite number of orderings. In the proposed work, we construct solvable groups with a finite number of orderings the solvability class of which is 4, 5, and 6. These groups are constructed as a semidirect product of a free nilpotent group with two generators using an infinite cyclic group. We also note that calculations in a free nilpotent group are based on the standard calculus of basic commutators.
This paper presents the results of the finite element modeling of the milling of AISI 304 SS stainless steel and Grade 5 titanium alloy. The mathematical formulation of the problem is outlined along with the assumptions and simplifications adopted to enable efficient computation. The results of the numerical simulations are reported, taking into account variations in the cutting conditions, including the cutting regimes and edge microgeometry. A multilevel model is proposed in which functional relations between the tool design parameters, cutting edge sharpness, cutting modes, characteristics of the processed material, and the arising equivalent von Mises stresses in the cutting wedge of the milling tooth are specified. The study results make it possible to obtain a cutting part with improved geometrical parameters of a new generation tool, to increase its rigidity and strength, and to improve the tool performance.
A number of studies have examined the influence of electromagnetic fields (EMFs) on petroleum liquids. An interesting problem is to investigate the behavior of these liquids in porous media due to the presence of complex hydrocarbons. This paper investigates the features of the viscous oil flow in porous-medium models under EMF exposure. The main component of the experimental setup was a cell with electrodes positioned both across and along the flow direction. It was found that the maximum value of the dielectric loss tangent was reached at a frequency of 5 MHz. The dynamic viscosity coefficient increased after EMF exposure, indicating structural changes in the oil. The fluid flow rate was measured as a function of temperature at different pressure levels. The application of the field led to a decrease in the flow rate compared to filtration without exposure. Considering the design features of the micromodel and the measured dynamic viscosity coefficient, it was assumed that the effect was caused by the dielectrophoretic forces acting on the polar components of the oil and their structural transformation. Such a reduction of the flow rate can be explained by the increased dynamic viscosity and deterioration of the filtration characteristics of the porous medium, which results in a blocking effect in the local areas closest to the electrodes, where the highest electric-field-strength gradient is formed.
