DETERMINING THE FEATURES OF LOADING THE BEARING STRUCTURE OF A MULTIFUNCTIONAL CAR UNDER OPERATING MODES (p. 6–13)

This paper substantiates the modernization and commissioning of a railroad car for high-temperature, bulk/loose cargoes in order to improve the efficiency of railroad transportation. A feature of the car is the presence of an open-type boiler, which is made of heat-resistant material. To prevent splashing of transported cargo, it is possible to use a removable cover, which is attached to the top of the boiler. The boiler of the car was calculated for strength under the main operating modes. The vertical load on the boiler was taken into consideration while accounting for the transportation of bulk cargo, as well as longitudinal, and the effect of temperature load. The strength was calculated by the method of finite elements. It is taken into consideration that the boiler is made of composite heat-resistant material. The calculation results showed that with the considered load modes, the strength of the boiler is ensured. The dynamic load of the boiler was mathematically modeled at car shunting. The calculation was performed in a flat coordinate system. Solving the mathematical model of the car dynamic load has established that the maximum acceleration that acts on the boiler is 36.5 m/s 2 . The dynamic load of the boiler was simulated. The dislocation fields and numerical values of accelerations that act on it were determined. The maximum acceleration, in this case, is concentrated in the bottom of the boiler; it is 37.4 m/s 2 . To verify the dynamic load model, the F-criterion was used for calculation. It has been established that the hypothesis about the adequacy of the model is confirmed. The study reported here could contribute to improving the efficiency of railroad transport operation and advancing the design of multifunctional car structures. state of the wall of a cylindrical tank with variable thickness, it is possible to use the ratios for a cylindrical shell with a constant wall thickness. The spread of values is no more than 1 %, which indicates the proper selection of the mathematical model. A numerical assessment of the stressed-strained state in the zone of the mounting joint proved the assumption of significant stress concentrations in the zone and indicated the determining effect exerted on the concentration of stresses by its geometric dimensions. The concentration of stresses in the joint zone of the tank wall was investigated at various sizes in the ANSYS programming environment. The result of calculating the stressed-strained state of the reservoir for various values of the dent parameters f / t and a Rt is the constructed polynomials that approximate the stress concentration coefficient K σ . As a result of the calculations, an interpolation polynomial and an approximating stress concentration coefficient were derived, which could be used to assess the strength, durability, residual life of the tank and to normalize the limiting dimensions of the imperfection of the joint. This paper reports comparative results of the calculations of the stress concentration coefficient depending on the geometric dimensions of the imperfection of the mounting joint in the ANSYS software package, as well as using an interpolation polynomial. The results could be used to assess the strength and residual life of such structures. (the least attainable value), it represents the largest total deformation. The equivalent stress (von Mises) responded to the load with a response of 0.045 MPa, which is quite small. Furthermore, the equivalent elastic strain has also been undertaken and it resulted in a value of elastic strain of 3.4*10^7. This paper analyzes the influence of kinetic and physical-mechan-ical parameters of systems on the characteristics of dynamic processes in moving one-dimensional nonlinear-elastic systems. Improved convenient calculation formulas have been derived that describe the laws of changing the amplitude-frequency characteristics of systems for both a non-resonant case and a resonant one. An important issue of studying the influence of the speed of movement of elements of mechanisms on the oscillations of one-dimensional nonlinear-elastic systems has not been considered in detail until now in the scientific literature. This issue relates to the vibrations of shafts in gears, pipe strings when drilling oil and gas wells, the oscillations of turbine blades and rotating turbine discs, the longitudinal vibrations of the beam as an element of structures. The main reason for this in the analytical study of dynamic processes were the shortcomings of the mathematical apparatus for solving the corresponding nonlinear differential equations that describe the laws of motion of those systems. It was found that in the case of longitudinal oscillations in the moving beam with an increase in the longitudinal speed of the me-dium to 10 m/s, the amplitude of the oscillation also increases by 13.5 %. However, when the longitudinal velocity of the beam is 5 m/s, the amplitude will increase by only 3 %. It is established that with the growth of the amplitude, the frequency of longitudinal oscillations decreases sharply, and if the system moves at a higher speed, for example, 20 m/s, it reduces the frequency of oscillation by about 13 %. The results reported here make it possible to assess the effect of kinetic and physical-mechanical parameters on the frequency and amplitude of oscillations. The research that involved the asymptotic method makes it possible to predict resonant phenomena and obtain engineering solutions to improve the efficiency of technological equipment. This paper investigates the process of destruction of parts of the connecting rod-piston group of the engine due to hydraulic lock after the ingress of liquid into the cylinders of the engine. Compar-ing expert data on actual engine destruction due to hydrolock with existing estimation models has made it possible to identify a number of significant contradictions affecting the objectivity and accuracy of the destruction assessment. To resolve the existing contradictions, a mathematical model for reconstructing the destruction of the connecting rod-piston group of the engine during a hydraulic lock has been improved. Unlike the existing ones, the model makes it possible to take into consideration not only the static deformation of the connecting rod but also to give a comprehensive assessment of the deformations of the connecting rod, piston pin, and piston at different volumes of hydrolock fluid. the model is the hypothesis assuming that the deformation of the piston pin under excessive load caused by hydraulic lock leads to the emergence of tension and an increase in the friction in the mated pin-piston. The calculation from the condition of differential change in the amount of friction in the mated pin-piston produced a satisfactory result that does not contradict the practical data and has confirmed the working hypothesis. engine parts during hydrolock a 17.3 MPa, at crankshaft 346 ° , the the operating conditions, pin-piston the lateral the skirt 17.2 MPa, the permissible one, calculated to procedures, 2.8 times. devised model applicable to the practice of expert studies into the causes of engine malfunctions when violating the operating conditions of a car. This paper reports the analysis of prospects for the use of prefabricated metal corrugated structures in the body of the embankment of a railroad track in the form of a tunnel overpass in order to pass road vehicles and railroad rolling stock. A technique of inertial dynamic tests of the deformed state of a tunnel overpass from prefabricated metal corrugated structures during the passage of railroad rolling stock is given, by measuring accelerations at the top and on the sides of overpass structures. An algorithm is proposed for processing the acceleration signal for assessing the strained state of metal corrugated structures of a tunnel overpass under the action of dynamic load from railroad transport. Experimental dynamic measurements of accelerations arising at the top and on the sides of a tunnel overpass during the passage of passenger and freight railroad rolling stock were carried out. The maximum value of accelerations arising at the top of a tunnel overpass during the passage of a freight train was 7.99 m/s 2 , and when passing a passenger train – 6.21 m/s 2 ; the maximum accelerations that occur on the sides were 2.63 m/s 2 and 1.77 m/s 2 . It is established that the maximum deformations of metal corrugated structures of the top of a tunnel overpass, when passing freight and passenger trains are, respectively, 1.63 mm and 1.11 mm. The maximum strains of metal corrugated structures on the sides of an overpass are 1.07 mm and 0.48 mm. The value of relative deformations in the vertical and horizontal dimensions of the structures of a tunnel overpass under the action of dynamic loads from the railroad rolling stock has been found. The relative vertical strains of an overpass amounted to 0.020 %; horizontal – 0.012 %. The practical significance of this work is that with the help of the devised procedure for measuring accelerations, it is possible to assess the strained state of metal corrugated structures under the influence of dynamic loads from the railroad rolling stock. This paper considers the issue related to the protection of buildings and structures against seismic influences and the prevention, ex-clusion, or reduction of seismic hazards. The catastrophic destruction of modern «earthquake-resistant» buildings in Turkey and Taiwan has shown that existing methods of strengthening and reinforcing structures are not perfect and require further study. Analysis of existing approaches to ensuring seismic resistance showed that seismic insulation and seismic suppression systems still do not have a scientific and technical justification for the effectiveness of their operation from the point of view of ensuring the stability of structures. The es-timation-dynamic models of the «base-seismic insulation-structure» system developed to date do not always make it possible to simulate the joint work of their interaction during an earthquake and account for the transformation of the seismic impact on the structure. An alternative technique has been devised, a geotechnical seismic insulation screen, as a seismic insulation system that reduces the intensity of seismic loads on the structure and ensures its seismic resistance. In a specific example, the effectiveness of this seismic insulation system is confirmed. This seismic insulation technique in the form of damper screens is characterized by reliability and manufacturability in ensuring the seismic resistance of objects under construction. The results of computational and experimental modeling of the interaction of an earthquake-insulated structure with a ground base found that the values of axial forces and bending moments in a building with a seismic insulating screen are less than in a building without seismic insulation by 30–40 %. The geotechnical seismic insulation screen makes it possible to advance the development of new seismic insulation techniques and determine their effectiveness. This technique will also be effective when strengthening the base and seismic insulation systems of his-torical monuments, protecting them against seismic and dynamic influences. This paper has defined and investigated for stability the steady state modes of motion of a single-mass resonant vibratory machine. The vibratory machine has a platform that is supported by viscoelastic supports. The platform moves rectilinearly translationally. A vibration exciter is installed on the platform. The vibration exciter consists of N identical loads – balls, rollers, or pendulums. The center of mass of each load can move in a circle of a certain radius with a center on the longitudinal axis of the rotor. Each load, when moving relative to the body of the vibration exciter, is exposed to a viscous resistance force. It was established theoretically that with small forces of viscous resistance and any number of loads, the vibratory machine has jamming modes under which the loads that are collected form a conditional combined load and lag behind the rotor. In this case, there are two bifurcation speeds of the rotor. At speeds less than the first bifurcation speed, the vibratory machine has one single (first) jamming mode. When the first bifurcation speed is exceeded, the second and third jamming modes appear. When the second bifurcation speed is exceeded, the first and second jamming modes disappear. The first jamming mode is resonant. In the cases of two or more loads, the vibratory machine also has an auto balancing mode (no vibrations), under which the loads rotate synchronously with the body of the vibration exciter and mu-tually balance each other. With small forces of viscous resistance, the computational experiment found that odd jamming modes are stable if they are num-bered in ascending order of the frequency of load jamming. An auto-ba lancing mode is stable at the rotor speeds above the resonance. For the onset of a resonant mode of motion of the vibratory machine, it is enough to slowly accelerate the rotor to a speed lower than the second bifurcation speed. The results reported here are applicable in the design of resonant single-mass vibratory machines with inertial vibration exciters of the ball, roller, or pendulum type.

Determination of the influence of deflections in the thickness of a composite material on its physical and mechanical properties with a local damage to its wholeness. Eastern-European Journal of Enterprise Technologies, 4 (1 (100)), [6][7][8][9][10][11][12][13] state of the wall of a cylindrical tank with variable thickness, it is possible to use the ratios for a cylindrical shell with a constant wall thickness. The spread of values is no more than 1 %, which indicates the proper selection of the mathematical model. A numerical assessment of the stressed-strained state in the zone of the mounting joint proved the assumption of significant stress concentrations in the zone and indicated the determining effect exerted on the concentration of stresses by its geometric dimensions.
The concentration of stresses in the joint zone of the tank wall was investigated at various sizes in the ANSYS programming environment. The result of calculating the stressed-strained state of the reservoir for various values of the dent parameters f/t and a Rt is the constructed polynomials that approximate the stress concentration coefficient K σ .
As a result of the calculations, an interpolation polynomial and an approximating stress concentration coefficient were derived, which could be used to assess the strength, durability, residual life of the tank and to normalize the limiting dimensions of the imperfection of the joint. This paper reports comparative results of the calculations of the stress concentration coefficient depending on the geometric dimensions of the imperfection of the mounting joint in the ANSYS software package, as well as using an interpolation polynomial.
The results could be used to assess the strength and residual life of such structures.
Keywords: steel tank, stress concentration, mounting joint, joint parameters, numerical method. In this paper, the numerical simulation of the mechanical performance of a composite prosthetic keel structure under static load has been explored, and the findings of this inquiry have been included. The prosthetic keel is constructed from an epoxy and glass fiber composite, 3 percent weight (MWCNTs with SiC), and a carbon nanotube, which are utilized in conjunction with other materials to create the structure. The force that is applied in this example is 1,000 N, and it is applied in accordance with the boundary condition that has been previously established in this case. The ANSYS modeling software package was used to create the prosthetic keel model, which was meshed and created. Because of the total deformation, the fundamental simulation results of the prosthetic keel model have been converged in line with the total deformation, which was used as a reference to determine the total deformation. The major outcome of the current numerical analysis has been successfully validated by considering the findings of the earlier experimental study. The mechanical performance of the composite prosthetic keel structure is determined by four primary criteria, the results of which are based on the findings. Aspects to analyze include equivalent elastic strain, three-axis directed deformation, total deformation, and equivalent stress (von Mises). Although only 0.00058 mm total deformation is created by the imposed static load of 1,000 N (the least attainable value), it represents the largest total deformation. The equivalent stress (von Mises) responded to the load with a response of 0.045 MPa, which is quite small. Furthermore, the equivalent elastic strain has also been undertaken and it resulted in a value of elastic strain of 3.4*10^7.

ADVANCING ASYMPTOTIC APPROACHES TO STUDYING THE LONGITUDINAL AND TORSIONAL OSCILLATIONS OF A MOVING BEAM (р. 31-39)
Andrii Slipchuk Lviv Polytechnic National University, Lviv, Ukraine ORCID: https://orcid.org/0000-0003-0584-6104 Petro Pukach Lviv Polytechnic National University, Lviv, Ukraine ORCID: https://orcid.org/0000-0002-0359-5025 Myroslava Vovk Lviv Polytechnic National University, Lviv, Ukraine ORCID: https://orcid.org/0000-0002-7818-7755 Olha Slyusarchuk Lviv Polytechnic National University, Lviv, Ukraine ORCID: https://orcid.org/0000-0003-3464-0252 This paper analyzes the influence of kinetic and physical-mechanical parameters of systems on the characteristics of dynamic processes in moving one-dimensional nonlinear-elastic systems. Improved convenient calculation formulas have been derived that describe the laws of changing the amplitude-frequency characteristics of systems for both a non-resonant case and a resonant one. An important issue of studying the influence of the speed of movement of elements of mechanisms on the oscillations of one-dimensional nonlinear-elastic systems has not been considered in detail until now in the scientific literature. This issue relates to the vibrations of shafts in gears, pipe strings when drilling oil and gas wells, the oscillations of turbine blades and rotating turbine discs, the longitudinal vibrations of the beam as an element of structures. The main reason for this in the analytical study of dynamic processes were the shortcomings of the mathematical apparatus for solving the corresponding nonlinear differential equations that describe the laws of motion of those systems.
It was found that in the case of longitudinal oscillations in the moving beam with an increase in the longitudinal speed of the medium to 10 m/s, the amplitude of the oscillation also increases by 13.5 %. However, when the longitudinal velocity of the beam is 5 m/s, the amplitude will increase by only 3 %. It is established that with the growth of the amplitude, the frequency of longitudinal oscillations decreases sharply, and if the system moves at a higher speed, for example, 20 m/s, it reduces the frequency of oscillation by about 13 %.
The results reported here make it possible to assess the effect of kinetic and physical-mechanical parameters on the frequency and amplitude of oscillations. The research that involved the asymptotic method makes it possible to predict resonant phenomena and obtain engineering solutions to improve the efficiency of technological equipment.

Oleksii Saraiev
Kharkiv National Automobile and Highway University, Kharkiv, Ukraine ORCID: https://orcid.org/0000-0001-6582-560X This paper investigates the process of destruction of parts of the connecting rod-piston group of the engine due to hydraulic lock after the ingress of liquid into the cylinders of the engine. Comparing expert data on actual engine destruction due to hydrolock with existing estimation models has made it possible to identify a number of significant contradictions affecting the objectivity and accuracy of the destruction assessment.
To resolve the existing contradictions, a mathematical model for reconstructing the destruction of the connecting rod-piston group of the engine during a hydraulic lock has been improved. Unlike the existing ones, the model makes it possible to take into consideration not only the static deformation of the connecting rod but also to give a comprehensive assessment of the deformations of the connecting rod, piston pin, and piston at different volumes of hydrolock fluid.
Underlying the model is the hypothesis assuming that the deformation of the piston pin under excessive load caused by hydraulic lock leads to the emergence of tension and an increase in the friction in the mated pin-piston. The calculation from the condition of differential change in the amount of friction in the mated pin-piston produced a satisfactory result that does not contradict the practical data and has confirmed the working hypothesis.
By calculation, the onset of the destruction of engine parts during hydrolock at a pressure in the cylinder close to 17.3 MPa, at a crankshaft angle of about 346°, was revealed. In addition, it was found that in the case of violating the operating conditions, due to friction, the mated pin-piston is exposed to the lateral force on the skirt that reaches 17.2 MPa, which exceeds the permissible one, calculated according to known procedures, by 2.8 times.
The results reported here are confirmed by known practical data, which makes the devised model applicable to the practice of expert studies into the causes of engine malfunctions when violating the operating conditions of a car.
Keywords: violation of operating conditions, hydrolock in the cylinder, connecting rod-piston group, deformation of parts.
A technique of inertial dynamic tests of the deformed state of a tunnel overpass from prefabricated metal corrugated structures during the passage of railroad rolling stock is given, by measuring accelerations at the top and on the sides of overpass structures.
An algorithm is proposed for processing the acceleration signal for assessing the strained state of metal corrugated structures of a tunnel overpass under the action of dynamic load from railroad transport.
Experimental dynamic measurements of accelerations arising at the top and on the sides of a tunnel overpass during the passage of passenger and freight railroad rolling stock were carried out. The maximum value of accelerations arising at the top of a tunnel overpass during the passage of a freight train was 7.99 m/s 2 , and when passing a passenger train -6.21 m/s 2 ; the maximum accelerations that occur on the sides were 2.63 m/s 2 and 1.77 m/s 2 .
It is established that the maximum deformations of metal corrugated structures of the top of a tunnel overpass, when passing freight and passenger trains are, respectively, 1.63 mm and 1.11 mm. The maximum strains of metal corrugated structures on the sides of an overpass are 1.07 mm and 0.48 mm.
The value of relative deformations in the vertical and horizontal dimensions of the structures of a tunnel overpass under the action of dynamic loads from the railroad rolling stock has been found. The relative vertical strains of an overpass amounted to 0.020 %; horizontal -0.012 %.
The practical significance of this work is that with the help of the devised procedure for measuring accelerations, it is possible to assess the strained state of metal corrugated structures under the influence of dynamic loads from the railroad rolling stock.
Keywords: tunnel overpass, prefabricated metal corrugated structures, railroad track, acceleration of metal structures, vertical and horizontal strains of structures. This paper considers the issue related to the protection of buildings and structures against seismic influences and the prevention, exclusion, or reduction of seismic hazards. The catastrophic destruction of modern «earthquake-resistant» buildings in Turkey and Taiwan has shown that existing methods of strengthening and reinforcing structures are not perfect and require further study. Analysis of existing approaches to ensuring seismic resistance showed that seismic insulation and seismic suppression systems still do not have a scientific and technical justification for the effectiveness of their operation from the point of view of ensuring the stability of structures. The estimation-dynamic models of the «base-seismic insulation-structure» system developed to date do not always make it possible to simulate the joint work of their interaction during an earthquake and account for the transformation of the seismic impact on the structure. An alternative technique has been devised, a geotechnical seismic insulation screen, as a seismic insulation system that reduces the intensity of seismic loads on the structure and ensures its seismic resistance. In a specific example, the effectiveness of this seismic insulation system is confirmed. This seismic insulation technique in the form of damper screens is characterized by reliability and manufacturability in ensuring the seismic resistance of objects under construction.
The results of computational and experimental modeling of the interaction of an earthquake-insulated structure with a ground base found that the values of axial forces and bending moments in a building with a seismic insulating screen are less than in a building without seismic insulation by 30-40 %.
The geotechnical seismic insulation screen makes it possible to advance the development of new seismic insulation techniques and determine their effectiveness. This technique will also be effective when strengthening the base and seismic insulation systems of historical monuments, protecting them against seismic and dynamic influences.
Keywords: seismic impacts, ground movement, seismic protection and seismic insulation, geotechnical damper of horizontal stresses, geotechnical seismic insulating screen. This paper has defined and investigated for stability the steady state modes of motion of a single-mass resonant vibratory machine. The vibratory machine has a platform that is supported by viscoelastic supports. The platform moves rectilinearly translationally. A vibration exciter is installed on the platform. The vibration exciter consists of N identical loads -balls, rollers, or pendulums. The center of mass of each load can move in a circle of a certain radius with a center on the longitudinal axis of the rotor. Each load, when moving relative to the body of the vibration exciter, is exposed to a viscous resistance force.
It was established theoretically that with small forces of viscous resistance and any number of loads, the vibratory machine has jamming modes under which the loads that are collected form a conditional combined load and lag behind the rotor. In this case, there are two bifurcation speeds of the rotor. At speeds less than the first bifurcation speed, the vibratory machine has one single (first) jamming mode. When the first bifurcation speed is exceeded, the second and third jamming modes appear. When the second bifurcation speed is exceeded, the first and second jamming modes disappear. The first jamming mode is resonant.
In the cases of two or more loads, the vibratory machine also has an auto balancing mode (no vibrations), under which the loads rotate synchronously with the body of the vibration exciter and mutually balance each other.
With small forces of viscous resistance, the computational experiment found that odd jamming modes are stable if they are numbered in ascending order of the frequency of load jamming. An autoba lancing mode is stable at the rotor speeds above the resonance. For the onset of a resonant mode of motion of the vibratory machine, it is enough to slowly accelerate the rotor to a speed lower than the second bifurcation speed.
The results reported here are applicable in the design of resonant single-mass vibratory machines with inertial vibration exciters of the ball, roller, or pendulum type.