The paper is devoted to the problem of analytical synthesis of control that stabilizes the position in space of an unmanned aerial vehicle (UAV) of a multi-rotor type a multicopter. An analysis of UAVs of this class has been carried out, features, place and differences among UAVs of various design schemes have been determined. The type of spatial mathematical model describing the translational and rotational motion of a multicopter is substantiated, which is considered to be  a model of a four-rotor UAV – a quadrocopter, since such UAVs are widespread and have the basic properties that are inherent in such aircraft devices. A transition was made to a linear simplified model of UAV movement by linearization and justification of the main assumptions made during the linearization of the mathematical model. The problem of determining stabilizing control is reduced to the classical form of analytical synthesis of control that minimizes a given integral quality functional. A feature of the considered quality functional is the justification of normalization coefficients, which make it possible to reduce the summable integrands of various physical natures to a dimensionless form and take into account the real  restrictions imposed by the technological and design features of a particular UAV on its maneuvering characteristics.  As a result of the analytical solution of the problem, expressions for optimal control have been obtained, which are changes  in time in the rotation speeds of the opposite quadcopter propellers, allowing to stabilize the position of the UAV in space, compensating for external undesirable effects on the UAV in the form of gusts of air flow or other factors. The executed computer simulation has confirmed the efficiency of the developed methodology. The given graphical dependences of the change in time of variables characterizing the control action and movement of the UAV in space clearly show the type of transient processes and allow us to evaluate the maneuver-ring capabilities of the UAV and formulate the basic requirements for its structural elements at the preliminary design stage.

The paper presents the results of an experimental study of the process of hot briquetting of fine-grained ferrous metal waste in a mold with a movable matrix. It has been established that in order to achieve the required density of finished briquettes of 90–95 % (one of the main quality criteria for modern metallurgical production), in the temperature range of hea-ting the charge of 700–850 °C, the pressing pressure reaches values of 470–500 MPa. The use of molds with a movable matrix ensures reduction in pressure and pressing force of ductile low- and medium-carbon steels up to 45 %, high-carbon, low ductility and difficult to deform - up to 35 %, cast iron – up to 25 %. The specific work of deformation (energy costs) when hea-ting waste ferrous metals to temperatures of incomplete hot deformation is reduced by 2.3–2.5 times. Compared to briquetting in a fixed matrix at the same temperatures, the specific work of deformation is reduced by 15–20 %. The process of deformation compaction of a discrete porous body occurs with minimal impact of lateral contact friction forces, since the compaction front (compacted chip layer) moves together with the matrix in the same direction with minimal relative displacement of the friction surfaces. The nature of deformation compaction and the level of resistance to deformation depend on the initial state of the material: the higher the plasticity of the metal, the more intense the compaction density increases; the higher the initial density and yield strength, the greater the pressing pressure must be applied to achieve the same density value. Fine additives of metallic or non-metallic origin fill the voids between larger fractions of chips and thus increase the initial compaction density and the pressure gradient as density increases.

Depending on the class in engineering practice, the problems to be solved are distinguished: static/dynamic, flat/spatial, contact/with partial or edge support, etc. The pressure of a rail on a sleeper, a column on a foundation, floor slabs on walls, a foundation on a soil foundation – all these are typical examples of practical problems that lead to the need to solve boundary value problems – mathematically and contact problems – physically. From the mathematical formulations of contact problems of structures lying on an elastic foundation, it is known that the basis for their solution is the search for the law of distribution of reactive pressures at the contact of the structure with the foundation, which depends in a complex way on the rigidity of the structure, the elastic characteristics of the foundation, external load, and the nature of the structure’s fastening. When solving many boundary-value and initial-boundary-value problems of structural mechanics and the theory of elasticity, such as solving a classical homogeneous equation by the method of eigenfunctions, under certain boundary conditions arising from the type of fastening of the beam at the ends, an important, sometimes decisive, role is played by the fundamental functions of the operator x^IV, which received their basic interpretation by Academician A. N. Krylov. However, calculations using these formulas are very difficult due to mathematical limitations and the cumbersomeness of the expressions. In the proposed work, eigenfunctions of the differential equation of bending vibrations of statically indeterminate single-span beams are used to construct the Green's function in the form of an infinite series for these eigenfunctions. Exact expressions have been constructed to determine the deflections of beams due to concentrated force. The resulting expressions are presented through elementary functions, are of a general nature and make it possible to solve various problems of statics, dynamics and stability of the beams under consideration. The authors obtained numerical results for bending moments and deflections of a clamped beam and a beam with clamped and hinged supports using the MATHEMATICA computer package.

The paper considers a method for calculating the natural frequencies of vibrations of unequal-thickness rings, based on application of Hamilton’s variational principle and theories of vibrations of curved beams of the Euler-Bernoulli and Timoshenko type. Solutions of the problem are represented as Fourier series providing possibility of its reduction to the system of linear algebraic equations. The problem of determining natural frequencies is reduced to a generalized problem for the eigenvalues of matrices. Based on a comparison of the numerical results obtained for an eccentric ring with the results of calculations by the finite element method, the advantages of using the Timoshenko theory are shown, including increased calculation accuracy and the possibility to identify radial and radial-flexural eigenmodes. The possibility of reducing computational costs when using the Timoshenko theory is explored by representing the determinant of the block matrix describing the problem as a product of lower-order determinants. It is shown that the relations obtained on the basis of the Euler-Bernoulli theory, in the particular case of equal-thickness ring, lead to the well-known analytical formulas for the natural frequencies of the ring oscillations. The obtained results can be used to calculate ring concentrators of ultrasonic vibrations. The advantage of the proposed method in comparison with other known approaches, for example, the harmonic balance me-thod, consists in no need for the work with differential or integral-differential equations of vibrations, which are a rather complex structure for the case of unequal-thickness rings and require the use of computationally expensive operations, for example, discrete convolution, for their solution.

The material in the paper reflects the main stages and results of the development of low-energy-intensive technology for producing cellular aerated concrete without autoclave hardening using a micro-filler based on granite screenings for prefabricated and monolithic construction, including its application in 3D concreting technology [1–10]. The paper has made it possible to develop and experimentally to substantiate: methods for calculating the composition of aerated concrete according to the criteria of density and compressive strength in the range of grades D350–D900 and classes B0.5–B7.5 for structural and thermal insulation purposes, as well as grades D100–D300 (compressive strength 0.04–1.5 MPa) for thermal insulation purposes in conjunction with the dispersion of the applied micro-fillers from ground granite screening with a specific surface area, respectively: S_sp ~ 3000–500 cm²/g for structural and thermal insulation, and for thermal insulation aerated concrete: S_sp ~ 30000 cm²/g (micro-silica) and S_sp ~ 20000 cm²/g (ultra-disperse fractions of granite screenings) – for thermal insulating aerated concrete; methodology for monitoring the rheological (technological) properties of aerated concrete mixtures that provide the required conditions for the structure formation of aerated concrete of calculated compositions, a method for evaluating the lateral pressure of a mixture when laying in formwork (molds), as well as a method and device for non-destructive testing of both the kinetics of strength growth of hardening and the strength of hardened or used cellular concrete, obtained according to the developed or other technology. Modes of non-heating and low-energy (including steaming at  atmospheric pressure) technology of cellular aerated concrete of non-autoclave hardening have been developed, which makes it possible to abandon energy-consuming, technically complex and expensive autoclave equipment in the manufacture of prefabricated products and provides the possibility of using the developed technology of thermal insulating aerated concrete  in monolithic construction, including heat and sound insulation of the walls of buildings made using 3D concreting technology, as well as the construction (installation) in removable and non-removable formwork of building structures using aerated concrete for structural and thermal insulation purposes.

The optimization of mechanical performance through the use of fiber-reinforced polymer composites is achieved via META simulated experimental design, with a primary emphasis on enhancing the mechanical characteristics. Incorporating reeds and coconut shells, this approach aims for an optimal design that minimizes polymer usage while ensuring specified mechanical performance and economic efficiency. The research, anchored in a probabilistic framework, prioritizes a reliability-based optimization methodology. To assess mechanical performance, nonlinear pushover analyses at the system level  are conducted, with META simulations playing a key role in exploring uncertainties. Within the META framework, inelastic interstory drift ratios are treated as indeterministic variables, while the thickness of the polymer jacket–featuring reeds  and coconut shells–is considered a deterministic design variable. This refined design process not only reduces polymer costs but also systematically evaluates the cost-effectiveness of incorporating reeds and coconut shells, all while adhering to stringent structural reliability constraints. Explicit reliability index constraints, honed through META simulations, ensure the robustness and adaptability of the design optimization process. The numerical optimality criteria method within the META framework provides an efficient solution to the nonlinear retrofit design optimization problem. Illustrating the application,  a design example showcases the seamless integration of reeds and coconut shells, resulting in a significant enhancement  of mechanical performance within the context of retrofitting.

It must be noted that the construction industry of the Republic of Belarus is forced to use fine aggregate for low-quality concrete due to the lack of high-quality natural sand in many regions of the country. When using this aggregate in the preparation of concrete mixtures and mortars, an increase in cement consumption is required to confirm the quality of the concrete. The research results of this work can be used to improve the quality of fine aggregate when used in concrete. The technology for producing normalized (enriched) sand of the required granulometry has theoretically and experimentally proven itself positively due to the introduction into natural (fine, medium) sand of fractions of granite screenings ≥(0.5–0.6) mm in size, formed at the RUPP “Granit” of the Brest region Belarus in the production of coarse aggregate for concrete. A computer program “Normalization” (registration number 022 dated 03/07/2024) has been developed to calculate the required ratio of the starting material – natural sand (characterized by a fineness modulus: 0.9 < Mk < 2.5) and processed (prepared) granite screenings of size ≥(0.5–0.6) mm to ensure the required granulometry of enriched sand with Mk = 3.25–3.50. All conditions have been identified for obtaining a material of any granulometric composition, characterized (if there is such a need) by a particle size modulus within the limits recommended by the current technical regulatory legal acts (TNPA): 2.0 < Mk < 3.5. The effectiveness of the technology for normalizing the granulometry of fine-grained natural sands has been experimentally confirmed and is determined by an increase in concrete compressive strength up to 25–40 %, axial tensile and shear strength up to 35–45 %, a decrease in the delamination rate (solution separation and water separation) by 30–47 %, as well as increasing the elastic-deformation characteristics and operational properties (waterproofing, water, salt and frost resistance) and the protective ability of concrete in relation to steel reinforcement, with an assessment of the degree of its corrosion damage. Industrial testing has confirmed the possibility of reducing the cement content in concrete by 10–20 % without deteriorating its physical and mechanical properties. Based on the totality of research results, it was determined that the method of enriching natural sand with large fractions of granite screenings can be used for concrete for various purposes without restrictions.

. The paper discusses issues of urban mobility of the population. In recent decades, Russia and Belarus has seen active urbanization and an increase in the proportion of residents in large cities. This process is accompanied by motorization. The municipal authorities are introducing the concept of priority to public transport, developing metro, trams and bicycle infrastructure. The above studies also note the difficulty of changing people's attitudes towards personal transport and the need to develop public transport. The hypothesis of the impact of measures to stimulate and demotivate the use of personal cars when traveling and the effectiveness of measures, including the organization of paid parking and reduction of parking spaces, is confirmed in the paper. A mathematical model has been developed for the effect of the cost of travel along 1 km of a highway on the number of movements by type of transport and the total travel time. A two-factor mathematical model has been developed for the effect of the cost of travel along 1 km of a highway and the cost of travel in public transport on the share of movements by type of transport and types of movement. The analysis of changes in the structure of population mobility and traffic parameters calculated using the macro model of the city of Tyumen, built in the PTV VISUM program for the morning time of day, is presented. With the introduction of tolls on the city's street and road network with a tariff of 30 rubles per 1 km, the share of movement by passenger cars decreases from 40 to 16 %. Further research is aimed at taking into account the influence of other socio-economic and technological factors on the structure of population mobility, as well as at developing a methodology for determining balanced tariffs for the urban transport system.

The reliability of the results of sensory analysis depends on a number of factors that affect the objectivity of the tests carried out. Today, the credibility of subjective measurements is primarily achieved through standardization. However, the issue of the credibility of subjective measurements remains, furthermore, it moves to a new level. Special attention must be paid to subjective measures related to the measurement of sensations to ensure credibility of results. The dynamics of increasing credibility through factor standardization lags behind the dynamics of stakeholder demand for increasing the credibility of subjective measurements. The purpose of the paper is to consider subjective measurements from the point of view of the development of the theory of quantitative measurements and to substantiate a process model for measurement that ensures the meaningfulness of the results in relation to expert assessments that ensure the subjectivity of measurements when conducting sensory tests, the results of which form decisions on compliance or non-compliance. The object of research is expert assessment methods used in sensory measurements, specifically in the evaluation of participating experts. The research methods used in this work include system analysis of measurement theories, method of alternatives, and standardized methods of expert assessment. A model of quantitative measurements is proposed to ensure meaningful measurement results, based on an analysis of the evolution of measurement theories. The problem of ensuring the meaningfulness of subjective measurements is formulated, which manifests itself in the form of risks of making incorrect decisions about characteristics of food products and processes based on expert assessments that lack reliability. An algorithm for quantitative measurements has been defined and tested on a specific example of expert assessment, demonstrating the importance of the identified problem of ensuring the reliability of expert assessments.