No 4 (2024)

The subject of investigation is the problem on precession motions of a gyrostat with a fixed point in three homogeneous force fields. The class of precessions under consideration is characterized by the constancy of the precession angle and by the commensurability of the precession and proper rotation velocities. Equations of motion of a gyrostat are reduced to a system of three second order differential equations with respect to velocities of precession and proper rotation. Integration of these equations is conducted in the case of precessionally isoconic motions (the precession velocity equals to the proper rotation velocity) and in the case of 2:1 resonance, when the precession velocity is two times more, than the proper rotation velocity. It is proved that the obtained solutions can be described by elementary functions of time.

A program of basic tests and a method for identifying a three-dimensional model of the elastoplastic behavior of an isotropic porous or powdery consolidated medium experiencing arbitrary quasi-static loading under compressive medium stress at room temperature are proposed. The medium under consideration under compressive medium stresses is compacted with increasing effective stress, which leads to a nonlinear change in elastic modules, hardening and dilatancy (coupling of shear and volumetric components of deformations) in the yield region. To describe this behavior, the cap model of DiMaggio and Sandler, which is present in application software packages, is considered. As basic tests, the free and constrained compression of a cylindrical sample is considered according to a special program containing the stages of loading and unloading with a sequential increase in the amplitude voltage. Samples with a given porosity for free compression tests are manufactured using a tight compression test rig. According to the initial slope of the discharge curves, the values of the elastic modulus for free and constrained compression are determined in a certain range of porosity changes, according to which the Poisson’s ratio is determined. The five constants of the cap model are correctly and explicitly determined by the deformation curve of the material under constrained compression over a wide range of changes in axial deformation (and density), the flow stress under free compression of the sample at some density, and the assumption that the coefficient of transverse deformation in the yield region is equal to the Poisson’s ratio. The elastic and plastic constants were determined according to the test data of powdered paraffin grade T1 with a fraction of 0.63 mm. The corresponding model is applicable for numerical simulation of extrusion processes and mold filling for casting by melting models, processes for manufacturing blanks of non-melting polymer composites by powder technology, stamping sealing elements from flexible graphite and other pressure treatment processes of non-compact media.

The paper presents outcomes of the study of short-timed shock action of the pulse electron beam on the aluminum obstacle. Analysis of the generation of the stress wave near the loaded surface based on the experimental data is provided. It is proved that wave generation in this case in contrast to theaction of laser beam takes place inside material in the area governed by the depth of electrons invasion.Relaxationofthestress wave starts from the boarder of this area. It was established that strongly non-equilibrium processes are take place in this relaxation area causing dramatic change depending on the shock parameters of the velocity of the stress and strength waves compared theirs stationary values. It is underlined that relaxation process has solo-wave nature in spite of the high stress amplitude. Separation of the elastic and plastic stresses propagation takes place only after the end of relaxation process.

The paper examines the process of thermoelastic instability occurrence during unsteady friction of anisotropic disk samples in the presence of a third body film on the friction surface. This process takes place during the operation of highly loaded braking systems (in aviation and railway transport), specialized clutches of motor vehicles and in other mechanisms. The presence of surface film leads to a decrease in surface wear simultaneously with the emergence of significant nonlinearity in the wear rate. The finite difference method was used to simulate the mutual influence of wear, frictional heating, elastic deformations and the evolution of the film on the friction surface. The process of friction and wear of discs was studied taking into account the history of a series of braking events. The annular shape of surface pressures and temperatures distribution is considered. A comparison was made of the evolution of disc wear from braking to braking for the cases of the film presence, its absence, and experimentally measured wear.

Based on an exact analytical solution to the two-dimensional problem of a strip of orthotropic material with the main axes of the elasticity tensor directed parallel and perpendicular to its boundaries and a central semi-infinite crack, expressions for T-stresses are obtained. A balanced load system in the form of four independent active loading modes is assumed to be applied sufficiently far from the crack tip. It is shown that for two (antisemimetric) loading modes the T-stresses are equal to zero, and for the other two (symmetric) they are determined by one or two parameters composed of components of the elasticity tensor. The dependences of T-stresses for symmetric loading modes are obtained in the form of double integrals from combinations of elementary functions depending on one of the dimensionless parameters; the second of the dimensionless parameters is included in the expression for T-stresses of only one of the modes in the form of a multiplicative coefficient.

The paper considers a non-classical optimization problem associated with the development of the production of new functionally graded materials. It is proposed to optimize the first natural frequency of oscillations by choosing the law of change in elastic moduli, and not the shape, as is done in most works devoted to optimization. This formulation of the problem becomes practically justified with the development of 3D printing and the production of FGM ceramics with specified properties. As an example, the problems of oscillations of a FGM rod and a FGM beam with spring boundary conditions at one of the ends are considered.

The mechanical properties of metamaterials with different cellular internal structures were experimentally studied when perforated along the normal by a rigid spherical striker. Auxetic and non-auxetic samples of metamaterials with a chiral structure of cells, respectively, in the form of concave or convex hexagons, were produced using a 3D printer from e-PLA plastic. Based on the penetration experiments, the properties of chiral auxetic and non-auxetic samples of the same mass were compared for the cases when there was air inside the cells and when the cells were filled with gelatin. The relative loss of kinetic energy of the striker when perforating gelatin-filled samples was significantly higher for the auxetic metamaterial than for the non-auxetic one. For unfilled (“air”) samples, the relative loss of kinetic energy was slightly higher for the nonauxetic.