No 3 (2025)

For a three-axis satellite with a ball damper, resonant rotations in the central gravitational field are studied. The equations of the rotational motion of a satellite in an elliptical orbit are obtained. For the case of a circular orbit, spatial resonance rotations of 1 : 1 and 2 : 1 were investigated using the averaging method.

A complex model of pore annihilation during hot isostatic pressing (HIP), which takes into account the simultaneous action of the mechanisms of material plastic flow and diffusive pore dissolution due to the emission of vacancies by the pore surface, has been proposed. The obtained mathematical equations are applied to analyze the kinetics of pore annihilation in single crystals of the nickel-based superalloy CMSX-4 during HIP used for this alloy in industry. It follows from the analysis that both mechanisms (plastic flow and vacancy diffusion) make comparable contributions to the reduction of pore volume under these conditions. As the HIP pressure increases, the contribution of plastic flow increases, while the contribution of vacancy diffusion decreases. Large pores shrink in volume mainly due to the mechanism of plastic flow, however, at the final stage of pore closure, the mechanism of vacancy diffusion is more active. To ensure reliable pore healing by the vacancy mechanism, HIP should be carried out at a moderate argon pressure in the HIP plant.

The article considers the nonlinear dynamics of a cylindrical resonator of a wave solid-state gyroscope with electromagnetic control sensors. A mathematical model that describes nonlinear resonator oscillations and electrical processes of the oscillation control circuit in an interconnected form is deduced. The resulting mathematical model represents a nonlinear system of differential equations, which contains singularly perturbed equations, and the equations of electrical processes are singularly perturbed. The nonlinearity caused by the finite ratio of the small deflection to the small gap of the control sensor is taken into account. The methods of constructing approximate solutions are proposed. The fundamental difference between the nonlinear terms of the equations of resonator dynamics using eight and sixteen control sensors is shown. It is shown that by using electromagnetic control sensors it is necessary to take into account a small parameter singularly included in the differential equations of electrical processes. According to the estimation of the angular drift velocity, it is concluded that the gyroscope circuit with eight electromagnetic control sensors is inapplicable due to the obtained value of the uncompensated angular drift velocity. In the case of a gyroscope with sixteen control sensors, a formula for the angular drift velocity which can be compensated is derived and a method for calculating the displacement of the resonant peak of the amplitude-frequency response is proposed.

A planar equilibrium problem of a heavy homogeneous thin wire triangle suspended on a thin horizontal nail is considered. The existence of equilibrium positions and their dependence on the coefficient of friction and the lengths of the sides of the triangle are studied under the assumption of the presence of a dry friction force acting between the triangle and the nail. The problem is solved in barycentric coordinates associated with the vertex system of the triangle in question. The equilibrium condition is written in a form that allows a cyclic shift of the indices of the quantities included in it to obtain an equilibrium condition for any of the sides of the triangle with which it contacts the nail.

The work presents the experimental study results of the titanium alloy Ti–6Al–4V fatigue life obtained during additive manufacturing by wire-arc surfacing using the cold metal transfer welding. This additive manufacturing technology is used for fusing large-sized products in the Laboratory of methods for creating and designing systems “material-technology-construction” PNRPU. The quality of the resulting blank is confirmed by the results of chemical analysis, microstructural research and static tensile tests. Samples were cut from the deposited plate in the longitudinal and transverse direction with respect to the formation plane of the layers. Experimental studies of fatigue life were conducted in the Center of Experimental Mechanics PNRPU using Instron testing equipment. According to the test results, the dependences of cyclic durability on the level of applied stresses are obtained. It is noted that the direction of cutting samples from the deposited fragment significantly affect to the resistance characteristics of the low- and high-cycle fatigue of the additive titanium alloy VT6. It is concluded that there is a significant anisotropy of cyclic properties, which must be taken into account when designing and manufacturing products from additive materials.

Using the example of four-dimensional equilibrium equations for kinetic stresses in Eulerian rectangular coordinates, it is shown that the operator of the four-dimensional Cauchy strain tensor is conjugate (transposed) to the operator of the equilibrium equations. The same connection between the operators of the equilibrium equations and the Cauchy strain tensor also holds in the three-dimensional case. Three variants of the derivation of the conditions for the compatibility of Cauchy deformations are given. In the four-dimensional case, there are 21 compatibility conditions, and in the three-dimensional case, there are six Saint-Venant compatibility conditions. It is shown that the Cauchy strain tensor, both in Eulerian and Lagrangian variables, completely determines the deformed state of a continuous medium. At the same time, no restrictions on the amount of displacements, deformations or rotations are required. The Lagrange-Green and Euler-Almancy tensors, the so-called large or nite deformations, and the displacements are expressed using Cesaro formulas in terms of the Cauchy strain tensor. The de ning equations of an elastic continuous medium relate the Cauchy true stress tensor and the Cauchy strain tensor one to another. Using proper bases in the spaces of symmetric stress and strain tensors, the de ning relations can be written as six separate independent equations containing functions of only one argument. For continuous media with crystallographic symmetries, we can use the bases obtained on the basis of the generalized Hooke’s law.

The long-term destruction of a long thin-walled cylindrical shell during creep under conditions of a non-stationary complex stress state is studied, taking into account the influence of the active medium. The influence of the active medium on the creep and long-term strength of the shell is determined by the diffusion penetration of medium elements into the shell material. Using the kinetic theory of Yu.N. Rabotnov determined the times to fracture of such a shell under unsteady loading. A singular linear fractional model of creep and long-term strength is used, in which the ultimate strength of the material at the appropriate temperature plays the role of the ultimate stress. To take into account the accumulation of damage during creep and determine the criterion before failure, scalar and vector damage parameters are used, while the components of the vector damage parameter are related to the space of principal stresses. To estimate the rate of the diffusion process, an approximate method for solving the diffusion equation is used, based on the introduction of a diffusion front. Taking into account the influence of the medium on the time to fracture is carried out by introducing a function of the integral average concentration into the constitutive and kinetic linear fractional relations. A comparison of times to fracture using scalar and vector damage parameters was carried out. The features of using a linear fractional model to describe processes of long-term destruction are determined.

The properties of metamaterials with negative Poisson’s ratio (with an auxetic structure based on a cell in the form of a concave hexagon) to resist penetration by a rigid spherical striker along the normal were experimentally studied. Using a 3D printer, samples of the same mass with a chiral and non-chiral structure were made from flexible thermoplastic polyurethane (TPU 95A plastic) and rigid e-PLA plastic, which were compared by the ability to reduce the kinetic energy of strikers at a speed of about 190 m /s. It was found that the chirality of the sample structure (for both TPU and PLA plastics) leads to an increase in their protective properties. However, when the sample structure was rotated by 90 degrees, the samples without chirality showed the best resistance to penetration. Based on the results of a series of experiments with TPU and PLA samples, the most effective in terms of resistance to penetration by a striker were auxetics made of thermoplastic polyurethane, with a non-chiral structure turned by 90 degrees.