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The object of the study is concrete bridge beams strengthened with external reinforcement adhered with methyl methacrylate compositions. A method for strengthening defective concrete bridge beams using methyl methacrylate based compositions is presented. A mathematical model has been improved for evaluating the temperature field and temperature stresses in a multilayer structure formed during the strengthening of defective beams with external reinforcement adhered with methyl methacrylate compositions. The distribution of temperatures and stresses in a strengthened concrete bridge beam under the influence of climatic temperature changes in the environment was investigated. A temperature gradient was found to occur at the interfaces between structural layers. At the same time, thermal stresses are also distributed unevenly in the vertical direction of the strengthened bridge beam: a discontinuity in thermal stresses occurs at the boundaries of contact between the structural layers. It has been established that under positive ambient temperatures, the magnitude of the temperature stress discontinuity in the vicinity of the contact plane between the upper edge of the polymer concrete layer and the lower edge of the reinforced concrete beam was 14.64 MPa, under the influence of negative temperatures it was 9.09 MPa, and under the influence of positive and negative temperatures on different surfaces of the beam, the maximum value of the discontinuity in thermal stresses was 1.74 MPa.

The deformable derivative is a recently proposed mathematical tool that interpolates between a function and its classical derivative using a parameterized limit. Initially introduced for single-variable functions, the concept is inherently fractional and has shown promise in various analytical applications. While fractional calculus is a fundamental tool for modeling non-linear, non-local and memory-based systems, it lacks the algebraic simplicity of higher-order derivatives when applied to multivariate calculus. To address this gap, a significant extension of the deformable derivative to multivariable functions is introduced by defining partial deformable derivatives in each coordinate direction while maintaining analytic consistency with classical calculus, and the validation is conducted through several test functions. To further address the lack of higher-order generalizations, the formulation is extended to include second-order deformable derivatives, yielding a higher-order Euler-type theorem. Unlike fractional calculus that relies on complex kernel, the novel method provides a local, computationally efficient identity that preserves the structural elegance of classical homogeneity. Several examples are provided to demonstrate the theoretical results and confirm the smooth convergence of the deformable Euler theorem to its classical counterpart. The proposed framework offers new tools for analysing homogeneous functions and provides a foundation for further extensions in partial differential equations and geometric analysis.

In this study, a straight-line underground section of a pipeline of finite length is considered, one (right) end of which is rigidly sealed, which excludes the possibility of its movement. The differential equations of equilibrium in displacements, based on the application of the principles of linear elasticity theory and the finite displacement method, have been formulated and derived. In this case, it is assumed that the geometric and physical-mechanical characteristics of the pipeline, as well as the temperature gradient and internal pressure, are constant throughout the entire length of the considered section. The mathematical model takes into account the temperature deformations caused by the thermal expansion of the material and the internal forces arising from the pressure of the working medium. Numerical calculations of the pipeline’s stress-strain state were performed using appropriate boundary conditions and assumptions. The results of the calculation analysis are presented in the form of graphical dependencies of displacements, stresses, and forces along the length of the pipeline section, which allows visualizing the influence of the main factors on its mechanical behavior. The obtained dependencies can be used for engineering assessment of the pipeline’s operability under long-term operation conditions.

The working elements of agricultural and road construction machinery operating in abrasive environments often fail prematurely due to intense wear. Enhancing their wear resistance is therefore a pressing challenge. This scientific article presents the results of laboratory, bench, and field tests of undercarriage components of tracked machines, whose working surfaces were strengthened with wear-resistant coatings. Borided and boro-titanized coatings were formed on the working surfaces of the support and drive rollers, while composite bimetallic coatings based on PG-S27 “Sormite” with the addition of boron carbide were applied to the running surfaces of track links directly during casting. Numerous tests have demonstrated that the developed technologies for forming wear-resistant coatings on the friction surfaces of tracked machine undercarriage parts increase their wear resistance by a factor of 5 to 7. This represents an effective solution to one of the most critical operational challenges for machinery working under conditions of severe abrasive wear.

The article presents the results of the development and improvement of the theoretical foundations of mathematical modeling of controlled vibration mechanisms of the following three types: a scanner, a reversible mechanism, and mechanisms based on external physical fields – the electrorheological and magnetorheological effects. An analysis and generalization of existing studies and designs of vibration systems with controlled parameters and kinematic relations are carried out, and an updated classification of control methods is proposed. A unified mathematical model is formulated based on the principles of precision vibromechanics and modern vibration theory. Numerical calculations and qualitative analysis of the differential equations were performed using modern computational methods. The reliability of the results is confirmed by experimental tests of a new vibration mechanism design, demonstrating improved dynamic accuracy and control efficiency.

Forecasting the occurrence of cracks in asphalt-concrete highway pavements worldwide - while considering natural and climatic influences - is essential for ensuring high-quality road maintenance, preserving pavement value at standard levels, guaranteeing traffic safety, and improving both transportation services and overall societal mobility. In this context, special emphasis is placed on identifying the underlying causes of crack formation, predicting their development over time, and assessing how these defects affect the functional performance of the roadway and the load-bearing capacity of the pavement structure. This includes evaluating the consequences of cracks on user comfort and safety, determining effective methods for their mitigation, and establishing a comprehensive database of crack characteristics.

This study investigates the deflection of a cantilever plate fixed at one end under the action of soil self-weight and additional surcharge loads. Based on experimental observations and theoretical calculations, an exponential expression is proposed to describe the plate’s deflection profile. Differentiation of this expression yields the corresponding stress distribution, which is compared against the conventional Coulomb-Mohr earth-pressure formulation. The results show that the exponential model provides a more accurate assessment of stresses on slopes and flexible retaining walls, highlighting its practical significance for design and evaluation. The proposed exponential approach can also serve as a foundation for dynamic and seismic extensions in future studies.

Railways in Uzbekistan mainly pass through irrigated, desert, and mountainous areas, and the Bukhara–Misken railway line is located in a desert region. Under sandy desert conditions, it is necessary to study the impact of wind on railway subgrade slopes and track superstructure elements. In railway design, operation, and reconstruction, wind speed, direction, single-event duration, and the annual number of windy days are important factors. As a result of wind–sand effects, the cross section of the railway subgrade may be damaged, and sand deposition on track superstructure elements may disturb the ballast layer structure, reduce the freight and passenger carrying capacity of the line, compromise traffic safety, or lead to line closure. This article analyzes experiments and studies conducted in Uzbekistan and other countries on the effects of wind on railways and develops recommendations for mitigating these impacts.