Максим Слипченко | ХНТУСГ / Kharkiv Petro Vasylenko National Technical University of Agriculture (KhNTUA) (original) (raw)
Papers by Максим Слипченко
Eastern-European Journal of Enterprise Technologies, Oct 30, 2023
Agricultural Engineering
The paper analyzes the existing theoretical research of corn seed separation and calibration proc... more The paper analyzes the existing theoretical research of corn seed separation and calibration processes. The machines, tools and equipment that implement the process were studied. An innovative sieve with openings in the Cassini oval shape was proposed for the economical separation and calibration of corn seeds. The results of operation of the proposed sieve in the operating conditions of Kharkiv Feed Mill on BSH-100 serial separators were considered. The study of the effectiveness of sifting corn seeds through the holes of the sieves was carried out in partnership with the State University “Ukrainian Research Institute of Forecasting and Testing of Agricultural Production Techniques and Technologies named after Leonid Pohorily” (Kharkiv Branch). The use of sieves with openings in the Cassini oval shape, instead of classic circular base openings, was found to result in an increase in throughput capacity of the sieve and open area of up to 20%.
Zenodo (CERN European Organization for Nuclear Research), Mar 22, 2021
The integral equation of the impact of the elastic cone on obstacle and its approximate solution ... more The integral equation of the impact of the elastic cone on obstacle and its approximate solution © В.
Pelecus cultratus feeding at the top of the reservoir, then at the bottom-chironomid larvae. This... more Pelecus cultratus feeding at the top of the reservoir, then at the bottom-chironomid larvae. This difference is easily explained if we take into account that the heating of water in the upper part is much faster, and accordingly, the departure of chironomids occurs much earlier than in the deeper deep part of it. Other insects include day-old larvae and larvae of beetles and bedbugs, which were found in the food of fish caught in bays or in the branches of rivers, where the thickets of higher plants have been preserved. In the bays of the lower part (Tsibulnytska) of the reservoir, the food of the small Pelecus cultratus (l-16-20 cm) consisted almost entirely of Acanthocyclops vernalis, Cyclops sp. Chironomid larvae were also of secondary importance. In 2018 and in 2019, beetles of the genus Gossinella (Cossinella 7-punctata), whose mass development was observed in these years, played a significant role in Pelecus cultratus feeding. In 2019, as part of the food of Pelecus cultratus caught in the bays of the upper part of the reservoir, carp juveniles were found, the high yield of which was observed in the previous year. Among the Pelecus cultratus caught at the same time in the channel part of the reservoir, the majority (90%) had empty intestines and only in some fish the food consisted of residues of chironomids. Pelecus cultratus feeding ranged from 5 to 78% 00. Higher filling indices were observed more frequently in Pelecus cultratus caught in the bays and, in particular, in those whose food consisted of young fish. Compared to the previous season, in summer the crustacean value in the diet increases, and the larvae of chironomids and other insects decrease accordingly. By 2018, the zooplankton of the reservoir was relatively poor, the value of blue and green algae in the middle and lower parts of the reservoir, which in some cases ranged from 40 to 90% of its weight, increased as part of the Pelecus cultratus food. Larvae and fry of fish were found in the food of fish caught at the top of the reservoir, namely in the arms and bays. The narrowest spectrum of nutrition was observed in the Pelecus cultratus in 2019 crustaceans, mainly daphnia and leptodors, and in smaller fish (l-16-19 cm)bosmines and hydros, as well as the remains of chironomids and beetles. Fish were absent from the Pelecus cultratus food, which could be due to the low yield of carp fry in the previous year. Pelecus cultratus feeding during the study period was on average low and ranged from 13.5 to 19.5%. The highest filling index (195%) was observed in fish 23-25 cm long caught in Vasylkivska bay (upper part of the reservoir), the food of which consisted exclusively of one-day Polymitarcys virgo. In autumn, the Pelecus cultratus diet was very weak, the filling indices ranged from 2.1 to 7.8%. The food of the fish in the middle and lower parts of the reservoir consisted mainly of blue and green algae, which were joined by daphnia, and later the larvae of bedbugs. In the composition of food decreased the importance of insects, except chironomids, and fish, but increased the role of crustaceans and algae, including blue and green.
Zenodo (CERN European Organization for Nuclear Research), Jun 24, 2021
Vìbracìï v tehnìcì ta tehnologìâh, Nov 20, 2019
Вібрації в техніці та технологіях Ольшанський В.П. д.ф.-м.н., професор Бурлака В.В. к.т.н.,доцент... more Вібрації в техніці та технологіях Ольшанський В.П. д.ф.-м.н., професор Бурлака В.В. к.т.н.,доцент Сліпченко М.В. к.т.н., доцент Харківський національний технічний університет сільського господарства імені Петра Василенка
International Applied Mechanics, 2019
The pulsed deformation of a beam with hinged ends and discretely elastically supported span is co... more The pulsed deformation of a beam with hinged ends and discretely elastically supported span is considered. It is assumed that due to separation of the beam from the support, a one-sided constraint (contact) of the beam with the support arises, when the support is compressed but not stretched. The determination of the force of contact interaction between the beam and the compressed support is reduced to numerical solution of the Volterra integral equation using the time-stepping method. Two options of the generalized distribution of the external load along the length of the beam are considered. The conditions are established in which the maximum displacement of the beam over the support in the direction of action of the external force pulse is less than the amplitude of the displacement in the opposite direction after the separation from the support. It is shown that this inequality is observed only for short-time impulsive loads and is inherent in systems with nonsymmetrical elasticity characteristics.
Zenodo (CERN European Organization for Nuclear Research), Aug 28, 2021
До розрахунку і прогнозу температури пластового самонагрівання рослинної сировини To calculation ... more До розрахунку і прогнозу температури пластового самонагрівання рослинної сировини To calculation and forecast of the temperature of formation self-heating of plant raw materials
We have considered the elastic straight impact along a flat border of the stationary half-space o... more We have considered the elastic straight impact along a flat border of the stationary half-space of the body bounded in a zone of contact interaction by the surface of rotation, whose order is smaller than two. The feature of the problem is that for the selected case an infinite curvature of the boundary surface at a point of initial contact, from which the process of dynamic compression of bodies in time starts. In addition to basic assumptions from the quasi-static theory of elastic impact between solid bodies, we have used a known solution to the static axisymmetric contact problem from the theory of elasticity. The process of an impact at a small initial velocity is divided into two stages: the dynamic compression and the dynamic decompression. For each of them, we have built an analytic solution to the nonlinear differential equation of relative convergence of the centers of bodies' masses in time. A solution to the non-linear problem with initial conditions for the differen...
Vibrations in engineering and technology, 2021
A modified hydrodynamic model of a stable grain flow of an inhomogeneous mixture over the surface... more A modified hydrodynamic model of a stable grain flow of an inhomogeneous mixture over the surface of a vertical cylindrical vibrating sieve is proposed under the assumption that the porosity of the mixture in the moving annular layer depends on the velocity of movement. A linear dependence of the porosity of the mixture on the velocity of movement are accepted, where higher speed corresponds to higher porosity.. The calculation of the velocity is reduced to solving an inhomogeneous differential equation of the Bessel type. Further, by "freezing" the variable coefficient of this equation, the problem has been simplified. This simplification is permissible due to the fact that the thickness of the moving layer of the mixture is much less than the radius of the vibrating sieve. As a result, the dependence of the velocity on the radial coordinate is expressed through the elementary functions. A compact formula for determining the maximum grain flow velocity is obtained. By int...
Mechanics And Mathematical Methods, 2021
Nonstationary oscillations of the oscillator with nonlinear positional friction caused by an inst... more Nonstationary oscillations of the oscillator with nonlinear positional friction caused by an instantaneous force pulse are described. The power dependence of the positional friction force on the displacement of the system, which generalizes the known models, is accepted. The corresponding dynamics problems were solved precisely by the method of adding and approximated by the method of energy balance. In the study, using periodic Ateb-functions, an exact analytical solution of the nonlinear differential equation of motion was constructed. Compact formulas for calculating oscillation ranges and half-cycle durations are derived. It is shown that the decrease in the amplitude of oscillations, as well as under the action of the force of linear viscous resistance, follows the law of geometric progression. The denominator of the progression is less than one and depends on the positional friction constants, in particular on the nonlinearity index. Thus, we have not only a decrease in the am...
Науковий журнал «Інженерія природокористування», 2020
Методом енергетичного балансу виведено рекурентні співвідношення для розрахунку послідовності спа... more Методом енергетичного балансу виведено рекурентні співвідношення для розрахунку послідовності спадаючих амплітуд розмахів дисипативного осцилятора з сухим тертям Кулона. Розглянуто різні варіанти нелінійної пружності коливальної системи. У статті розглянуті випадки коливань осцилятора з наступними показниками нелінійності коефіцієнту пружності: степенево-нелінійної пружності з варіантами лінійного пружного осцилятора, осцилятора з м’якою характеристиками пружності при різних її значеннях, квадратичною та кубічною нелінійністю; коливання осцилятора за наявності в виразі сили пружності лінійної складової з різними показниками нелінійності. Виділено випадки, коли виведені рекурентні співвідношення мають замкнені аналітичні розв’язки і побудовано їх. Складені рекурентні співвідношення між амплітудами розмахів та запропоновано їх числове розв’язання методом ітерацій Ньютона. Проведено порівняння числових результатів, до яких призводять такі розв’язки та комп’ютерне інтегрування диференці...
Ukrainian Journal of Mechanical Engineering and Materials Science, 2018
The variations of a system with one degree of freedom in the presence of nonlinear positional fri... more The variations of a system with one degree of freedom in the presence of nonlinear positional friction were considered. The restoring force of the oscillator's elasticity is described by the power function. A nonlinear solution of the Cauchy problem for the case of a power nonlinearity of positional friction were constructed. It is expressed through known periodic Ateb functions, which in recent years have become widespread in the theory of oscillations thanks to the efforts of the Lviv School of Mathematics and Mechanics. Formulas for calculating the displacements of the oscillator in time, as well as the amplitudes and periods of oscillations caused by the initial deviation of the system from the equilibrium position or the initial velocity given to the oscillator in this position were derived. The analytical dependence of the oscillation periods on the amplitude for cases of soft and rigid characteristics of the elastic system was established. It was found that due to the non-linearity of the damping of the system of the amplitudes, it leads to a change in the period of the oscillations of the system during its motion. The period may decrease or increase with oscillation, depending on the value of the indicator of non-linearity in the expression of the restoring force. It is shown, that from the obtained analytical solutions, as separate cases, there were known formulas related to free nonlinear oscillation oscillators without friction or with linear position friction. In order to simplify the using of the obtained solutions, we recommend well-known approximations of the Ateb-functions with the help of elementary functions. Examples of calculations are presented, where comparison of the results obtained with the use of constructed analytical solutions and numerical integration of the equation of oscillation on a computer is carried out. The good consistency of numerical results obtained in different ways is noted.
Vibrations in engineering and technology
The unsteady oscillations of a dissipative oscillator caused by an instantaneous impulse of the f... more The unsteady oscillations of a dissipative oscillator caused by an instantaneous impulse of the force are described. The case is considered when the dissipative force consists of quadratic viscous resistance and dry friction, and the theoretical results are generalized to the case of the sum of three forces. The third is the force of positional friction. Formulas for calculating the ranges of oscillations have been constructed In this case, the Lambert function of negative and positive arguments is used. It is a tabulated special function. Its value can also be calculated using its known approximations in elementary functions. It is shown that, due to the action of the dissipative force, the process of post-pulse oscillations consists of a finite number of cycles and is limited in time. This is due to the presence of dry friction among the resistance components. Examples of calculations that illustrate the possibilities of the stated theory are given. In order to check the reliabili...
Vibrations in engineering and technology
The work investigates non-stationary oscillations of dissipative oscillators. The joint influence... more The work investigates non-stationary oscillations of dissipative oscillators. The joint influence of resistance forces of different nature in the composition of the dissipative force on the oscillations of an elastic linear oscillator caused by its instantaneous loading by a constant external force is investigated. The work was limited to the case of small displacements, when the elastic characteristic of the system can be considered linear. The problem is nonlinear due to the account of the action of the dry friction force, but it allows the construction of exact analytical solutions in elementary functions. In this work, by the method of adding solutions, formulas are derived for calculating the amplitude of oscillations and the duration of half cycles. First, a variant is considered when the resistance force consists of linear viscous and dry friction forces. Then a generalization is made to the case of three resistance forces. The third force is the force of positional friction,...
Vibrations in engineering and technology
A nonlinear differential equation of the force of direct central impact of elastic bodies of revo... more A nonlinear differential equation of the force of direct central impact of elastic bodies of revolution, which have a singular point on the boundary contact surface, where its curvature is infinite, is compiled. To determine the coefficients of the equation and the order of its power nonlinearity, the well-known solution of the axisymmetric contact problem of the theory of elasticity, constructed by I. Ya. Shtaermann, is used. In the formulation of the dynamic problem, the classical assumptions of the theory of quasi-static impact proposed by H. Hertz were also used. The constituted equation of impact force is reduced to the Bernoulli equation and its closed analytical solution is constructed, which is expressed in terms of the Ateb-sine. Analytical time dependences of the impact force and the convergence of the centers of mass of elastic bodies are obtained. Compact formulas have been derived for calculating the maxima of these quantities, as well as the durations of the process of...
Bulletin of the National Technical University «KhPI» Series: Dynamics and Strength of Machines
The unsteady oscillations of an oscillator with a quadratic nonlinearity in the expression of the... more The unsteady oscillations of an oscillator with a quadratic nonlinearity in the expression of the elastic force under the action of an instantaneously applied constant force are described. The analytical solution of a second-order nonlinear differential equation is expressed in terms of periodic Jacobi elliptic functions. It is shown that the dynamic coefficient of a nonlinear system depends on the value of the instantaneously applied force and the direction of its action, since the elasticity characteristic of the system is asymmetric. If the force is directed towards positive displacements, then the characteristic of the system is "rigid" and the dynamic coefficient is in the interval , that is, it is smaller than that of a linear system. In the case when the force is directed towards negative displacements, the elasticity characteristic of the system is «soft» and the dynamic coefficient falls into the gap (2, 3), that is, it is larger than in the linear system. In the ...
Bulletin of the National Technical University «KhPI» Series: Dynamics and Strength of Machines
The motion of an oscillator instantaneously loaded with a constant force under conditions of nonl... more The motion of an oscillator instantaneously loaded with a constant force under conditions of nonlinear external resistance, the components of which are quadratic viscous resistance, dry and positional friction, are considered. Using the first integral of the equation of motion and the Lambert function, compact formulas for calculating the ranges of oscillations are derived. In order to simplify the search for the values of the Lambert function, asymptotic formulas are given that, with an error of less than one percent, express this special function in terms of elementary functions. It is shown that as a result of the action of the resistance force, including dry friction, the oscillation process has a finite number of cycles and is limited in time, since the oscillator enters the stagnation region, which is located in the vicinity of the static deviation of the oscillator caused by the applied external force. The system dynamic factor is less than two. Examples of calculations that ...
Науковий журнал «Інженерія природокористування»
Викладено спрощений спосіб наближеного обчислення розмахів вільних затухаючих коливань осцилятора... more Викладено спрощений спосіб наближеного обчислення розмахів вільних затухаючих коливань осцилятора зі слабкою степеневою нелінійністю у виразі сили пружності. В основу запропонованого способу покладено припущення, що нелінійний доданок у виразі сили пружності мало впливає на рівняння обвідної графіка вільних коливань. Використане тут рівняння обвідної, за прийнятим припущенням, відповідає першому наближенню асимптотичного методу теорії нелінійних коливань і було одержане при дослідженні вільних коливань дисипативного осцилятора Дуффінга в роботах інших авторів. Але тут додатково враховано залежність тривалостей напівциклів від змінної амплітуди коливань, що властиво нелінійним системам. За виведеними формулами проведено розрахунки розмахів коливань в умовах дії різних сил опору, а саме: сухого тертя Кулона, лінійного в’язкого тертя та квадратичного в’язкого опору. Розглянуто різні варіанти степеневих нелінійностей, що доповнюють лінійну складову в виразі сили пружності. З метою з’ясу...
Eastern-European Journal of Enterprise Technologies, Oct 30, 2023
Agricultural Engineering
The paper analyzes the existing theoretical research of corn seed separation and calibration proc... more The paper analyzes the existing theoretical research of corn seed separation and calibration processes. The machines, tools and equipment that implement the process were studied. An innovative sieve with openings in the Cassini oval shape was proposed for the economical separation and calibration of corn seeds. The results of operation of the proposed sieve in the operating conditions of Kharkiv Feed Mill on BSH-100 serial separators were considered. The study of the effectiveness of sifting corn seeds through the holes of the sieves was carried out in partnership with the State University “Ukrainian Research Institute of Forecasting and Testing of Agricultural Production Techniques and Technologies named after Leonid Pohorily” (Kharkiv Branch). The use of sieves with openings in the Cassini oval shape, instead of classic circular base openings, was found to result in an increase in throughput capacity of the sieve and open area of up to 20%.
Zenodo (CERN European Organization for Nuclear Research), Mar 22, 2021
The integral equation of the impact of the elastic cone on obstacle and its approximate solution ... more The integral equation of the impact of the elastic cone on obstacle and its approximate solution © В.
Pelecus cultratus feeding at the top of the reservoir, then at the bottom-chironomid larvae. This... more Pelecus cultratus feeding at the top of the reservoir, then at the bottom-chironomid larvae. This difference is easily explained if we take into account that the heating of water in the upper part is much faster, and accordingly, the departure of chironomids occurs much earlier than in the deeper deep part of it. Other insects include day-old larvae and larvae of beetles and bedbugs, which were found in the food of fish caught in bays or in the branches of rivers, where the thickets of higher plants have been preserved. In the bays of the lower part (Tsibulnytska) of the reservoir, the food of the small Pelecus cultratus (l-16-20 cm) consisted almost entirely of Acanthocyclops vernalis, Cyclops sp. Chironomid larvae were also of secondary importance. In 2018 and in 2019, beetles of the genus Gossinella (Cossinella 7-punctata), whose mass development was observed in these years, played a significant role in Pelecus cultratus feeding. In 2019, as part of the food of Pelecus cultratus caught in the bays of the upper part of the reservoir, carp juveniles were found, the high yield of which was observed in the previous year. Among the Pelecus cultratus caught at the same time in the channel part of the reservoir, the majority (90%) had empty intestines and only in some fish the food consisted of residues of chironomids. Pelecus cultratus feeding ranged from 5 to 78% 00. Higher filling indices were observed more frequently in Pelecus cultratus caught in the bays and, in particular, in those whose food consisted of young fish. Compared to the previous season, in summer the crustacean value in the diet increases, and the larvae of chironomids and other insects decrease accordingly. By 2018, the zooplankton of the reservoir was relatively poor, the value of blue and green algae in the middle and lower parts of the reservoir, which in some cases ranged from 40 to 90% of its weight, increased as part of the Pelecus cultratus food. Larvae and fry of fish were found in the food of fish caught at the top of the reservoir, namely in the arms and bays. The narrowest spectrum of nutrition was observed in the Pelecus cultratus in 2019 crustaceans, mainly daphnia and leptodors, and in smaller fish (l-16-19 cm)bosmines and hydros, as well as the remains of chironomids and beetles. Fish were absent from the Pelecus cultratus food, which could be due to the low yield of carp fry in the previous year. Pelecus cultratus feeding during the study period was on average low and ranged from 13.5 to 19.5%. The highest filling index (195%) was observed in fish 23-25 cm long caught in Vasylkivska bay (upper part of the reservoir), the food of which consisted exclusively of one-day Polymitarcys virgo. In autumn, the Pelecus cultratus diet was very weak, the filling indices ranged from 2.1 to 7.8%. The food of the fish in the middle and lower parts of the reservoir consisted mainly of blue and green algae, which were joined by daphnia, and later the larvae of bedbugs. In the composition of food decreased the importance of insects, except chironomids, and fish, but increased the role of crustaceans and algae, including blue and green.
Zenodo (CERN European Organization for Nuclear Research), Jun 24, 2021
Vìbracìï v tehnìcì ta tehnologìâh, Nov 20, 2019
Вібрації в техніці та технологіях Ольшанський В.П. д.ф.-м.н., професор Бурлака В.В. к.т.н.,доцент... more Вібрації в техніці та технологіях Ольшанський В.П. д.ф.-м.н., професор Бурлака В.В. к.т.н.,доцент Сліпченко М.В. к.т.н., доцент Харківський національний технічний університет сільського господарства імені Петра Василенка
International Applied Mechanics, 2019
The pulsed deformation of a beam with hinged ends and discretely elastically supported span is co... more The pulsed deformation of a beam with hinged ends and discretely elastically supported span is considered. It is assumed that due to separation of the beam from the support, a one-sided constraint (contact) of the beam with the support arises, when the support is compressed but not stretched. The determination of the force of contact interaction between the beam and the compressed support is reduced to numerical solution of the Volterra integral equation using the time-stepping method. Two options of the generalized distribution of the external load along the length of the beam are considered. The conditions are established in which the maximum displacement of the beam over the support in the direction of action of the external force pulse is less than the amplitude of the displacement in the opposite direction after the separation from the support. It is shown that this inequality is observed only for short-time impulsive loads and is inherent in systems with nonsymmetrical elasticity characteristics.
Zenodo (CERN European Organization for Nuclear Research), Aug 28, 2021
До розрахунку і прогнозу температури пластового самонагрівання рослинної сировини To calculation ... more До розрахунку і прогнозу температури пластового самонагрівання рослинної сировини To calculation and forecast of the temperature of formation self-heating of plant raw materials
We have considered the elastic straight impact along a flat border of the stationary half-space o... more We have considered the elastic straight impact along a flat border of the stationary half-space of the body bounded in a zone of contact interaction by the surface of rotation, whose order is smaller than two. The feature of the problem is that for the selected case an infinite curvature of the boundary surface at a point of initial contact, from which the process of dynamic compression of bodies in time starts. In addition to basic assumptions from the quasi-static theory of elastic impact between solid bodies, we have used a known solution to the static axisymmetric contact problem from the theory of elasticity. The process of an impact at a small initial velocity is divided into two stages: the dynamic compression and the dynamic decompression. For each of them, we have built an analytic solution to the nonlinear differential equation of relative convergence of the centers of bodies' masses in time. A solution to the non-linear problem with initial conditions for the differen...
Vibrations in engineering and technology, 2021
A modified hydrodynamic model of a stable grain flow of an inhomogeneous mixture over the surface... more A modified hydrodynamic model of a stable grain flow of an inhomogeneous mixture over the surface of a vertical cylindrical vibrating sieve is proposed under the assumption that the porosity of the mixture in the moving annular layer depends on the velocity of movement. A linear dependence of the porosity of the mixture on the velocity of movement are accepted, where higher speed corresponds to higher porosity.. The calculation of the velocity is reduced to solving an inhomogeneous differential equation of the Bessel type. Further, by "freezing" the variable coefficient of this equation, the problem has been simplified. This simplification is permissible due to the fact that the thickness of the moving layer of the mixture is much less than the radius of the vibrating sieve. As a result, the dependence of the velocity on the radial coordinate is expressed through the elementary functions. A compact formula for determining the maximum grain flow velocity is obtained. By int...
Mechanics And Mathematical Methods, 2021
Nonstationary oscillations of the oscillator with nonlinear positional friction caused by an inst... more Nonstationary oscillations of the oscillator with nonlinear positional friction caused by an instantaneous force pulse are described. The power dependence of the positional friction force on the displacement of the system, which generalizes the known models, is accepted. The corresponding dynamics problems were solved precisely by the method of adding and approximated by the method of energy balance. In the study, using periodic Ateb-functions, an exact analytical solution of the nonlinear differential equation of motion was constructed. Compact formulas for calculating oscillation ranges and half-cycle durations are derived. It is shown that the decrease in the amplitude of oscillations, as well as under the action of the force of linear viscous resistance, follows the law of geometric progression. The denominator of the progression is less than one and depends on the positional friction constants, in particular on the nonlinearity index. Thus, we have not only a decrease in the am...
Науковий журнал «Інженерія природокористування», 2020
Методом енергетичного балансу виведено рекурентні співвідношення для розрахунку послідовності спа... more Методом енергетичного балансу виведено рекурентні співвідношення для розрахунку послідовності спадаючих амплітуд розмахів дисипативного осцилятора з сухим тертям Кулона. Розглянуто різні варіанти нелінійної пружності коливальної системи. У статті розглянуті випадки коливань осцилятора з наступними показниками нелінійності коефіцієнту пружності: степенево-нелінійної пружності з варіантами лінійного пружного осцилятора, осцилятора з м’якою характеристиками пружності при різних її значеннях, квадратичною та кубічною нелінійністю; коливання осцилятора за наявності в виразі сили пружності лінійної складової з різними показниками нелінійності. Виділено випадки, коли виведені рекурентні співвідношення мають замкнені аналітичні розв’язки і побудовано їх. Складені рекурентні співвідношення між амплітудами розмахів та запропоновано їх числове розв’язання методом ітерацій Ньютона. Проведено порівняння числових результатів, до яких призводять такі розв’язки та комп’ютерне інтегрування диференці...
Ukrainian Journal of Mechanical Engineering and Materials Science, 2018
The variations of a system with one degree of freedom in the presence of nonlinear positional fri... more The variations of a system with one degree of freedom in the presence of nonlinear positional friction were considered. The restoring force of the oscillator's elasticity is described by the power function. A nonlinear solution of the Cauchy problem for the case of a power nonlinearity of positional friction were constructed. It is expressed through known periodic Ateb functions, which in recent years have become widespread in the theory of oscillations thanks to the efforts of the Lviv School of Mathematics and Mechanics. Formulas for calculating the displacements of the oscillator in time, as well as the amplitudes and periods of oscillations caused by the initial deviation of the system from the equilibrium position or the initial velocity given to the oscillator in this position were derived. The analytical dependence of the oscillation periods on the amplitude for cases of soft and rigid characteristics of the elastic system was established. It was found that due to the non-linearity of the damping of the system of the amplitudes, it leads to a change in the period of the oscillations of the system during its motion. The period may decrease or increase with oscillation, depending on the value of the indicator of non-linearity in the expression of the restoring force. It is shown, that from the obtained analytical solutions, as separate cases, there were known formulas related to free nonlinear oscillation oscillators without friction or with linear position friction. In order to simplify the using of the obtained solutions, we recommend well-known approximations of the Ateb-functions with the help of elementary functions. Examples of calculations are presented, where comparison of the results obtained with the use of constructed analytical solutions and numerical integration of the equation of oscillation on a computer is carried out. The good consistency of numerical results obtained in different ways is noted.
Vibrations in engineering and technology
The unsteady oscillations of a dissipative oscillator caused by an instantaneous impulse of the f... more The unsteady oscillations of a dissipative oscillator caused by an instantaneous impulse of the force are described. The case is considered when the dissipative force consists of quadratic viscous resistance and dry friction, and the theoretical results are generalized to the case of the sum of three forces. The third is the force of positional friction. Formulas for calculating the ranges of oscillations have been constructed In this case, the Lambert function of negative and positive arguments is used. It is a tabulated special function. Its value can also be calculated using its known approximations in elementary functions. It is shown that, due to the action of the dissipative force, the process of post-pulse oscillations consists of a finite number of cycles and is limited in time. This is due to the presence of dry friction among the resistance components. Examples of calculations that illustrate the possibilities of the stated theory are given. In order to check the reliabili...
Vibrations in engineering and technology
The work investigates non-stationary oscillations of dissipative oscillators. The joint influence... more The work investigates non-stationary oscillations of dissipative oscillators. The joint influence of resistance forces of different nature in the composition of the dissipative force on the oscillations of an elastic linear oscillator caused by its instantaneous loading by a constant external force is investigated. The work was limited to the case of small displacements, when the elastic characteristic of the system can be considered linear. The problem is nonlinear due to the account of the action of the dry friction force, but it allows the construction of exact analytical solutions in elementary functions. In this work, by the method of adding solutions, formulas are derived for calculating the amplitude of oscillations and the duration of half cycles. First, a variant is considered when the resistance force consists of linear viscous and dry friction forces. Then a generalization is made to the case of three resistance forces. The third force is the force of positional friction,...
Vibrations in engineering and technology
A nonlinear differential equation of the force of direct central impact of elastic bodies of revo... more A nonlinear differential equation of the force of direct central impact of elastic bodies of revolution, which have a singular point on the boundary contact surface, where its curvature is infinite, is compiled. To determine the coefficients of the equation and the order of its power nonlinearity, the well-known solution of the axisymmetric contact problem of the theory of elasticity, constructed by I. Ya. Shtaermann, is used. In the formulation of the dynamic problem, the classical assumptions of the theory of quasi-static impact proposed by H. Hertz were also used. The constituted equation of impact force is reduced to the Bernoulli equation and its closed analytical solution is constructed, which is expressed in terms of the Ateb-sine. Analytical time dependences of the impact force and the convergence of the centers of mass of elastic bodies are obtained. Compact formulas have been derived for calculating the maxima of these quantities, as well as the durations of the process of...
Bulletin of the National Technical University «KhPI» Series: Dynamics and Strength of Machines
The unsteady oscillations of an oscillator with a quadratic nonlinearity in the expression of the... more The unsteady oscillations of an oscillator with a quadratic nonlinearity in the expression of the elastic force under the action of an instantaneously applied constant force are described. The analytical solution of a second-order nonlinear differential equation is expressed in terms of periodic Jacobi elliptic functions. It is shown that the dynamic coefficient of a nonlinear system depends on the value of the instantaneously applied force and the direction of its action, since the elasticity characteristic of the system is asymmetric. If the force is directed towards positive displacements, then the characteristic of the system is "rigid" and the dynamic coefficient is in the interval , that is, it is smaller than that of a linear system. In the case when the force is directed towards negative displacements, the elasticity characteristic of the system is «soft» and the dynamic coefficient falls into the gap (2, 3), that is, it is larger than in the linear system. In the ...
Bulletin of the National Technical University «KhPI» Series: Dynamics and Strength of Machines
The motion of an oscillator instantaneously loaded with a constant force under conditions of nonl... more The motion of an oscillator instantaneously loaded with a constant force under conditions of nonlinear external resistance, the components of which are quadratic viscous resistance, dry and positional friction, are considered. Using the first integral of the equation of motion and the Lambert function, compact formulas for calculating the ranges of oscillations are derived. In order to simplify the search for the values of the Lambert function, asymptotic formulas are given that, with an error of less than one percent, express this special function in terms of elementary functions. It is shown that as a result of the action of the resistance force, including dry friction, the oscillation process has a finite number of cycles and is limited in time, since the oscillator enters the stagnation region, which is located in the vicinity of the static deviation of the oscillator caused by the applied external force. The system dynamic factor is less than two. Examples of calculations that ...
Науковий журнал «Інженерія природокористування»
Викладено спрощений спосіб наближеного обчислення розмахів вільних затухаючих коливань осцилятора... more Викладено спрощений спосіб наближеного обчислення розмахів вільних затухаючих коливань осцилятора зі слабкою степеневою нелінійністю у виразі сили пружності. В основу запропонованого способу покладено припущення, що нелінійний доданок у виразі сили пружності мало впливає на рівняння обвідної графіка вільних коливань. Використане тут рівняння обвідної, за прийнятим припущенням, відповідає першому наближенню асимптотичного методу теорії нелінійних коливань і було одержане при дослідженні вільних коливань дисипативного осцилятора Дуффінга в роботах інших авторів. Але тут додатково враховано залежність тривалостей напівциклів від змінної амплітуди коливань, що властиво нелінійним системам. За виведеними формулами проведено розрахунки розмахів коливань в умовах дії різних сил опору, а саме: сухого тертя Кулона, лінійного в’язкого тертя та квадратичного в’язкого опору. Розглянуто різні варіанти степеневих нелінійностей, що доповнюють лінійну складову в виразі сили пружності. З метою з’ясу...
Динаміка імпульсно навантажених нелінійних осциляторів, 2021
Робота складається з трьох розділів і присвячена теоретичному дослідженню руху нелінійних осцилят... more Робота складається з трьох розділів і присвячена теоретичному дослідженню руху
нелінійних осциляторів при дії нестаціонарних навантажень. Розглянуто варіанти степеневих нелінійностей пружності та сил опору. Незважаючи на нелінійність моделей, для
проведення дослідження використано аналітичні методи. Задіяні метод припасування
розв’язків та спеціальні функції, зокрема еліптичні функції Якобі, періодичні Ateb-функції
та функція Ламберта. З метою спрощення числової реалізації одержаних аналітичних
розв’язків запропоновано апроксимації використаних спеціальних функцій елементарними функціями. З метою підтвердження адекватності одержаних залежностей числові
результати систематично порівнюються з результатами чисельного комп’ютерного інтегрування диференціальних рівнянь руху.
Видання розраховано на широке коло читачів та буде корисним для поглибленого
вивчення теорії нелінійних механічних коливань.
Работа состоит из трех разделов и посвящена теоретическому исследованию движения нелинейных осцилляторов при воздействии нестационарных нагрузок. Рассмотрены варианты степенных нелинейностей упругости и сил сопротивления. Несмотря
на нелинейность моделей, для проведения исследования использованы аналитические
методы. Задействованы метод припасовывания решений и специальные функции, в частности эллиптические функции Якоби, периодические Ateb и функция Ламберта. С целью
упрощения числовой реализации полученных аналитических решений предложено аппроксимации использованных специальных функций элементарными функциями. С целью подтверждения адекватности полученных зависимостей числовые результаты систематически сравниваются с результатами численного компьютерного интегрирования
дифференциальных уравнений движения.
Издание рассчитано на широкий круг читателей и будет полезным для углубленного изучения теории нелинейных механических колебаний.
ДИНАМИКА ВИБРОЦЕНТРОБЕЖНОЙ ЗЕРНООЧИСТКИ. МОНОГРАФИЯ, 2013
Л.Н. Тищенко, В.П. Ольшанский, С.В. Ольшанский, Ф.М. Харченко, М.В. Слипченко Динамика виброцентр... more Л.Н. Тищенко, В.П. Ольшанский, С.В. Ольшанский,
Ф.М. Харченко, М.В. Слипченко
Динамика виброцентробежной зерноочистки. – Харьков: “Міськдрук”,
2013 – 439 с. Ил. – 166. Табл. – 38. Библ. – 251 назв. – На рус. яз.
В монографии на основе гидродинамической аналогии
разработаны математические модели осесимметричного движения
кольцевого слоя зерновых смесей по внутренним поверхностям
вертикальных цилиндрических решет вибросепараторов. Рассмотрены
варианты движения без и с учётом разделения смесей на фракции.
Описаны поля вибраций в смесях, вызванные осевыми колебаниями
решет или неравномерностью их вращения. Рассмотрена очистка
зерновых смесей от легких примесей с использованием положений
теории сплошных сред.
У монографії на підставі гідродинамічної аналогії розроблено
математичні моделі вісісиметричного руху кільцевого шару зернових
сумішей по внутрішнім поверхням вертикальних циліндричних решіт
вібросепараторів. Розглянуто варіанти руху без та з урахуванням
поділу сумішей на фракції. Описано поля вібрацій в сумішах,
спричинені осьовими коливаннями решіт або нерівномірністю їх
обертання. Розглянуто очистку зернових сумішей від легких домішок з
використанням положень теорії суцільних середовищ.
L.N. Tishchenko, V.P. Olshanskii,
S.V. Olshanskii, F.M. Kharchenko, M.V. Slipchenko
Dynamics of vibrocentrifugal grain cleaning
The monograph consist of the following parts:
Foreword
Introduction
Chapter 1 – Simplified model charter curled motion homogeneous and piecewise inhomogeneous grain mix
Chapter 2 – Simplified model of the steady motion of inhomogeneous circular layer.
Chapter 3 – Speed vibrations of the homogeneous circular layer of grain (solutions in Kelvin functions).
Chapter 4 – Approximate calculation of the velocity vibrations homogeneous circular layer (solution in elementary functions).
Chapter 5 – Vibrations of inhomogeneous grain stream.
Chapter 6 – Nonlinear dynamics of the process of grain mixtures clearning.
Chapter 7 – Grain clearning processes.
Теорія сепарування зерна, 2017
У монографії представлено теоретичне обґрунтування процесів зернових сепараторів. Розроблені мате... more У монографії представлено теоретичне обґрунтування процесів зернових сепараторів.
Розроблені математичні моделі та досліджена нелінійна динаміка очищення зернових сумішей від
легких домішок віяло-кільцевим конусно-каскадним пневмосепаруючим пристроєм, завантаження
робочої поверхні віброрешета, руху сипких матеріалів по поверхнях вібраційних та
вібровідцентрових решіт, сегрегації зернових сумішей на решетах з розпушувачами, просіювання
зерна на віброрешетах з активаторами просіювання, віброфрикційного сепарування зернових
сумішей неперфорованими поверхнями, вібропневмовідцентрового розділення насіння за
густиною на рифлених повітропроникних поверхнях з анізотропним тертям, забивання отворів
решіт та їх очищення роторно-кільцевими очисниками, очищення повітряного потоку від домішок
пилоосаджувальними камерами з керованим відбором та відведенням домішок.
Для науковців та фахівців, які займаються розрахунками, проектуванням, виготовленням та
експлуатацією вібраційних сепараторів для зернопереробної промисловості.
Динаміка, міцність та моделювання в машинобудуванні: Тези доповідей IІ Міжнародної науково-технічної конференції. – Харків: Інститут проблем машинобудування ім. А.М. Підгорного НАН України, 2020. – 399 с, 2020
Динаміка, міцність та моделювання в машинобудуванні: Тези доповідей IІ Міжнародної науково-техніч... more Динаміка, міцність та моделювання в машинобудуванні: Тези доповідей
IІ Міжнародної науково-технічної конференції. – Харків: Інститут проблем
машинобудування ім. А.М. Підгорного НАН України, 2020. – 399 с
EFFECT OF ASYMMETRY OF ELASTIC CHARACTERISTICS. P. 323-324