In this paper, combustion of a channel charge of a metallized composite solid chunk fuel in the field of mass forces is modeled. We have investigated the influence of the g-force on the total mass influx from the combustion surface of two parallel plates of the metallized solid fuel. The combustion rate of the fuel is calculated based on the nonstationary model of the metallized solid fuel combustion. The conducted computational and theoretical analysis has provided the data on the influence of the mass forces and the composition of the fuel on the total mass influx from the combustion surface. The g-force values are ranged from -650 to 650 m/s2. It is assumed that the g-force is directed along the normal to the combustion surface; otherwise, the projection of the g-force onto the normal to the combustion surface is considered. The obtained results have shown that the effect of the g-force is not symmetric - the g-forces, which are identical in magnitude but different in sign, lead to a different response of the combustion rate. The character of the dependence between the combustion rate and g-force for the particles with the radius greater than 7.5 pm is nonmonotonic. The obtained results demonstrate the importance of taking into account the effect of the g-force on the combustion rate when simulating nonstationary processes in solid propellant engines at the stages of start, maneuvering, and deceleration.
{"title":"Combustion of the metallized composite solid chunk fuel charge with a flat channel in a mass force field","authors":"V. A. Poryazov, D. Krainov, Anna A. Blokhina","doi":"10.17223/19988621/75/10","DOIUrl":"https://doi.org/10.17223/19988621/75/10","url":null,"abstract":"In this paper, combustion of a channel charge of a metallized composite solid chunk fuel in the field of mass forces is modeled. We have investigated the influence of the g-force on the total mass influx from the combustion surface of two parallel plates of the metallized solid fuel. The combustion rate of the fuel is calculated based on the nonstationary model of the metallized solid fuel combustion. The conducted computational and theoretical analysis has provided the data on the influence of the mass forces and the composition of the fuel on the total mass influx from the combustion surface. The g-force values are ranged from -650 to 650 m/s2. It is assumed that the g-force is directed along the normal to the combustion surface; otherwise, the projection of the g-force onto the normal to the combustion surface is considered. The obtained results have shown that the effect of the g-force is not symmetric - the g-forces, which are identical in magnitude but different in sign, lead to a different response of the combustion rate. The character of the dependence between the combustion rate and g-force for the particles with the radius greater than 7.5 pm is nonmonotonic. The obtained results demonstrate the importance of taking into account the effect of the g-force on the combustion rate when simulating nonstationary processes in solid propellant engines at the stages of start, maneuvering, and deceleration.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90795813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The work is devoted to the study of the inverse problem for the Sturm-Liouville operator with a real square-integrable potential. The boundary conditions are non-separated. One of these boundary conditions includes a quadratic function of the spectral parameter. A uniqueness theorem is proved and an algorithm for solving the inverse problem is constructed. As spectral data, we use the spectrum of the considered boundary value problem, the constant term of the quadratic function of the spectral parameter included in the boundary condition, and some special sequence of signs. From these spectral data, the characteristic function of the boundary value problem is first reconstructed in the form of an infinite product and the parameters of the boundary conditions, and then the problem is reduced to the inverse problem of reconstructing the potential of the Sturm-Liouville operator from the spectra of two boundary value problems with separated boundary conditions. The results of the article can be used for solving various versions of inverse problems of spectral analysis for differential operators, as well as for integrating some nonlinear equations of mathematical physics.
{"title":"Uniqueness of recovery of the Sturm-Liouville operator with a spectral parameter quadratically entering the boundary condition","authors":"Leyla I. Mammadova, I. M. Nabiev","doi":"10.17223/19988621/79/2","DOIUrl":"https://doi.org/10.17223/19988621/79/2","url":null,"abstract":"The work is devoted to the study of the inverse problem for the Sturm-Liouville operator with a real square-integrable potential. The boundary conditions are non-separated. One of these boundary conditions includes a quadratic function of the spectral parameter. A uniqueness theorem is proved and an algorithm for solving the inverse problem is constructed. As spectral data, we use the spectrum of the considered boundary value problem, the constant term of the quadratic function of the spectral parameter included in the boundary condition, and some special sequence of signs. From these spectral data, the characteristic function of the boundary value problem is first reconstructed in the form of an infinite product and the parameters of the boundary conditions, and then the problem is reduced to the inverse problem of reconstructing the potential of the Sturm-Liouville operator from the spectra of two boundary value problems with separated boundary conditions. The results of the article can be used for solving various versions of inverse problems of spectral analysis for differential operators, as well as for integrating some nonlinear equations of mathematical physics.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80062110","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Lyaysan Sakhabutdinova, O. Smetannikov, G. V. Il’inykh
The aim of this work is to obtain the evolution of contact pressure on the surface of the forming mandrel during the manufacture of large-scale composite shells by continuous winding. A numerical analogue of a real structure is built in the form of a system of assembly equipment, a forming mandrel and a shell. Effective viscoelastic characteristics for the shell material are obtained on the basis of experimental data and the concept of multilevel modeling. A series of computational experiments has been carried out to verify the model of thermoviscoelastic behavior of a composite material; the model is a combination of anisotropic elastic behavior of a medium with one independent viscoelastic operator. It has been found that, at the stage of winding, the influence of the behavior model of the shell material is not significant because viscoelasticity of the mandrel material makes the greatest contribution to the reduction of the contact pressure on the mandrel surface. Based on the data obtained, a conclusion is made that it is advisable and important to take into account the rheological properties not only of the material of the forming mandrel but also of the multilayer shell. The methods of finite element analysis presented in the work and the computational modules and programs implemented on their basis, as well as the calculation results, are of great practical importance for automating the process of predicting the evolution of the stress-strain state at the technological stages of manufacturing structures of the mandrel-shell type. Contribution of the authors: the authors contributed equally to this article. The authors declare no conflicts of interests.
{"title":"Numerical simulation of the process manufacture of large-scale composite shell taking into account thermo viscoelastic","authors":"Lyaysan Sakhabutdinova, O. Smetannikov, G. V. Il’inykh","doi":"10.17223/19988621/76/12","DOIUrl":"https://doi.org/10.17223/19988621/76/12","url":null,"abstract":"The aim of this work is to obtain the evolution of contact pressure on the surface of the forming mandrel during the manufacture of large-scale composite shells by continuous winding. A numerical analogue of a real structure is built in the form of a system of assembly equipment, a forming mandrel and a shell. Effective viscoelastic characteristics for the shell material are obtained on the basis of experimental data and the concept of multilevel modeling. A series of computational experiments has been carried out to verify the model of thermoviscoelastic behavior of a composite material; the model is a combination of anisotropic elastic behavior of a medium with one independent viscoelastic operator. It has been found that, at the stage of winding, the influence of the behavior model of the shell material is not significant because viscoelasticity of the mandrel material makes the greatest contribution to the reduction of the contact pressure on the mandrel surface. Based on the data obtained, a conclusion is made that it is advisable and important to take into account the rheological properties not only of the material of the forming mandrel but also of the multilayer shell. The methods of finite element analysis presented in the work and the computational modules and programs implemented on their basis, as well as the calculation results, are of great practical importance for automating the process of predicting the evolution of the stress-strain state at the technological stages of manufacturing structures of the mandrel-shell type. Contribution of the authors: the authors contributed equally to this article. The authors declare no conflicts of interests.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84441821","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
N. Kopylov, S. Kopylov, A. Karpov, Dmitry V. Fedotkin, E. Sushkina
Fundamental inefficiency of existing foam fire systems extinguishing tanks with oil and petroleum products having a volume of 5000 m3 or more is shown by methods of mathematical modeling. The required foam supply intensity and foam supply rate allowing effective fire suppression in large tanks with a volume of up to 20000 m3 are theoretically predicted. On this basis of theoretical conclusions, a new method of foam fire extinguishing in large fuel tanks has been developed. To obtain the required intensities and supply rates, fire extinguishing foam is formed in a special container with the use of solid-fuel gas generators. The theoretical predictions were confirmed in 21 full-scale successful experiments, in which fire suppresion system based on the new method was able to extinguish a fully developed gasoline fire in tanks with a volume of 5000 m3 and 20 000 m3 just for 30-90 seconds. The required amount of the foaming agent to extinguish a fire in a 20 000 m3 tank is only 450 liters, which is at least 100 times less than for traditional foam fire fighting Contribution of the authors: the authors contributed equally to this article. The authors declare no conflicts of interests.
{"title":"Theoretical and experimental investigation of fires in large fuel tanks and creation of an innovative technology of their extinguishment","authors":"N. Kopylov, S. Kopylov, A. Karpov, Dmitry V. Fedotkin, E. Sushkina","doi":"10.17223/19988621/76/10","DOIUrl":"https://doi.org/10.17223/19988621/76/10","url":null,"abstract":"Fundamental inefficiency of existing foam fire systems extinguishing tanks with oil and petroleum products having a volume of 5000 m3 or more is shown by methods of mathematical modeling. The required foam supply intensity and foam supply rate allowing effective fire suppression in large tanks with a volume of up to 20000 m3 are theoretically predicted. On this basis of theoretical conclusions, a new method of foam fire extinguishing in large fuel tanks has been developed. To obtain the required intensities and supply rates, fire extinguishing foam is formed in a special container with the use of solid-fuel gas generators. The theoretical predictions were confirmed in 21 full-scale successful experiments, in which fire suppresion system based on the new method was able to extinguish a fully developed gasoline fire in tanks with a volume of 5000 m3 and 20 000 m3 just for 30-90 seconds. The required amount of the foaming agent to extinguish a fire in a 20 000 m3 tank is only 450 liters, which is at least 100 times less than for traditional foam fire fighting Contribution of the authors: the authors contributed equally to this article. The authors declare no conflicts of interests.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82469732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper describes an approximate analytical solution for the geometrically nonlinear bending of a thin elastic cantilever beam under a uniformly distributed gravity load. The solution is based on the linearized Euler-Bernoulli equation of mechanics of materials. Traditionally, such a linear approach is used for small (geometrically linear) deflections. The authors have modified the original equation with an arc-length preservation condition. The modified solution allows one to obtain bending shapes, deflection, and axial displacement in the range of loads corresponding to geometrically nonlinear bending of a beam (large deflections). An experimental study is conducted to verify the proposed solution. A thin steel band bent by gravity is used as a sample. Changes in the length of the bent sample part allow one to obtain various dimensionless load parameters. The deflections and axial displacements averaged on experimental statistics are determined. Bending shapes are obtained by the least square method of 5th order. Experimental and theoretical data are shown to be in good agreement. This fact confirms that the approximate analytical solution can be applied to solve large deflection problems in a wider range of loads than normally considered in the original linear theory.
{"title":"The experimental and analytical study of geometrically nonlinear bending of a cantilever beam under a distributed gravity load","authors":"Dmitriy M. Zuev, D. D. Makarov, K. G. Okhotkin","doi":"10.17223/19988621/78/8","DOIUrl":"https://doi.org/10.17223/19988621/78/8","url":null,"abstract":"This paper describes an approximate analytical solution for the geometrically nonlinear bending of a thin elastic cantilever beam under a uniformly distributed gravity load. The solution is based on the linearized Euler-Bernoulli equation of mechanics of materials. Traditionally, such a linear approach is used for small (geometrically linear) deflections. The authors have modified the original equation with an arc-length preservation condition. The modified solution allows one to obtain bending shapes, deflection, and axial displacement in the range of loads corresponding to geometrically nonlinear bending of a beam (large deflections). An experimental study is conducted to verify the proposed solution. A thin steel band bent by gravity is used as a sample. Changes in the length of the bent sample part allow one to obtain various dimensionless load parameters. The deflections and axial displacements averaged on experimental statistics are determined. Bending shapes are obtained by the least square method of 5th order. Experimental and theoretical data are shown to be in good agreement. This fact confirms that the approximate analytical solution can be applied to solve large deflection problems in a wider range of loads than normally considered in the original linear theory.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89881653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mine ventilation network models are widely used in underground coal mining in Russia. The models cover a variety of practical problems ranging from simple air distribution in active mine workings to changes in the static air pressure gradient associated with complex technological or hazardous processes occurring in mines. Isolated gob areas are integral parts of ventilation networks in coal mines. The most commonly used underground coal extraction technology in Russia is the longwall mining. A gob forms when a coal seam is extracted, and the upper layers of the rock cave in. Gobs are isolated from active mine entries with seals, but there is always air leakages from active faces inducing the air circulation in isolated areas. Gobs join different coal seams and often become the sources of underground fires. Therefore, the inclusion of gobs in mine ventilation network models would help contain accidents and eliminate the caused damage. The study uses the method of representative elementary volumes to incorporate a porous medium into mine ventilation network models. Quadratic resistances are assigned to the edges of the model, where Kirchhoffs laws are valid. The aerodynamic resistances of the gob edges are calculated using the Ergun equation. The proposed method has been used to evaluate pressure gradients in the gob area of the Raspadskaya mine. Several scenarios of the aerodynamic resistance variation in the active mine workings surrounding the gob area, such as partial flooding and drilling of boreholes from the surface, have been simulated, and the corresponding changes in pressure gradients have been analyzed.
{"title":"Simulation of the coal mine ventilation with account for gob areas","authors":"G. A. Kolegov, A. Krainov","doi":"10.17223/19988621/79/7","DOIUrl":"https://doi.org/10.17223/19988621/79/7","url":null,"abstract":"Mine ventilation network models are widely used in underground coal mining in Russia. The models cover a variety of practical problems ranging from simple air distribution in active mine workings to changes in the static air pressure gradient associated with complex technological or hazardous processes occurring in mines. Isolated gob areas are integral parts of ventilation networks in coal mines. The most commonly used underground coal extraction technology in Russia is the longwall mining. A gob forms when a coal seam is extracted, and the upper layers of the rock cave in. Gobs are isolated from active mine entries with seals, but there is always air leakages from active faces inducing the air circulation in isolated areas. Gobs join different coal seams and often become the sources of underground fires. Therefore, the inclusion of gobs in mine ventilation network models would help contain accidents and eliminate the caused damage. The study uses the method of representative elementary volumes to incorporate a porous medium into mine ventilation network models. Quadratic resistances are assigned to the edges of the model, where Kirchhoffs laws are valid. The aerodynamic resistances of the gob edges are calculated using the Ergun equation. The proposed method has been used to evaluate pressure gradients in the gob area of the Raspadskaya mine. Several scenarios of the aerodynamic resistance variation in the active mine workings surrounding the gob area, such as partial flooding and drilling of boreholes from the surface, have been simulated, and the corresponding changes in pressure gradients have been analyzed.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76162062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper aims at obtaining formulas for bending moments and shear forces in a rectilinear elastic stepped rod under plane longitudinal-transverse bending. Each step of the rod (segment) can consist of different materials and have its own shape and cross- sectional dimensions. The rod can be loaded by an axial longitudinal force at the beginning of each step. The eccentricity of longitudinal forces at the beginning of each step (segment) is taken into account, which occurs due to the mismatch of longitudinal axes at the current and previous steps. Each segment of the rod can be exposed to a transverse action represented as concentrated bending moments, concentrated forces, and uniformly distributed loading. The resulting algebraic equations of the bending moments and shear forces are obtained for the stepped rod under longitudinal-transverse bending. The numerical model has been considered. The study results show that allowance for longitudinal action on the stepped rod bending with discrete axial loading leads to an increase in the ordinates of epures and bending moments, as well as in shear forces as compared to transverse bending caused by transverse loading only. Moreover, the internal transverse forces do not remain constant on the rod segments which are free from uniformly-distributed transverse loading. The obtained formulas for bending moments and transverse forces can be applied in calculations of elastic stepped rods under longitudinal-transverse bending.
{"title":"Calculation of a stepped rod under longitudinal-transverse bending with discrete axis loading","authors":"S. V. Bakushev","doi":"10.17223/19988621/77/4","DOIUrl":"https://doi.org/10.17223/19988621/77/4","url":null,"abstract":"This paper aims at obtaining formulas for bending moments and shear forces in a rectilinear elastic stepped rod under plane longitudinal-transverse bending. Each step of the rod (segment) can consist of different materials and have its own shape and cross- sectional dimensions. The rod can be loaded by an axial longitudinal force at the beginning of each step. The eccentricity of longitudinal forces at the beginning of each step (segment) is taken into account, which occurs due to the mismatch of longitudinal axes at the current and previous steps. Each segment of the rod can be exposed to a transverse action represented as concentrated bending moments, concentrated forces, and uniformly distributed loading. The resulting algebraic equations of the bending moments and shear forces are obtained for the stepped rod under longitudinal-transverse bending. The numerical model has been considered. The study results show that allowance for longitudinal action on the stepped rod bending with discrete axial loading leads to an increase in the ordinates of epures and bending moments, as well as in shear forces as compared to transverse bending caused by transverse loading only. Moreover, the internal transverse forces do not remain constant on the rod segments which are free from uniformly-distributed transverse loading. The obtained formulas for bending moments and transverse forces can be applied in calculations of elastic stepped rods under longitudinal-transverse bending.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90391720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider countable polygons - simply connected half-plane-type domains with translation symmetry along the real axis and a boundary consisting of line segments. The method for determining the parameters in the Christoffel-Schwartz integral extends to the case of a conformal mapping of a half-plane onto a counting-gon.
{"title":"Conformal mapping of a half-plane onto a periodic polygon of half-plane type","authors":"I. Kolesnikov","doi":"10.17223/19988621/77/1","DOIUrl":"https://doi.org/10.17223/19988621/77/1","url":null,"abstract":"We consider countable polygons - simply connected half-plane-type domains with translation symmetry along the real axis and a boundary consisting of line segments. The method for determining the parameters in the Christoffel-Schwartz integral extends to the case of a conformal mapping of a half-plane onto a counting-gon.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78292237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Valeriy M. Pestrenin, I. Pestrenina, O. M. Perelman, Aleksandr S. Fadeykin, Nikolay D. Derkach
Drilling of wells, especially inclined and horizontal ones, is accompanied by the intense interaction of drilling tools with the borehole walls. Inborehole impacts negatively affect the drill pipe connections, electrical connections, strength characteristics of downhole motor structural elements, etc. The impact interaction of a drilling tool with a well is experimentally studied using a test bench, where the drilling tool sample is fixed in the middle of a heavy composite shaft arranged in cylindrical roller bearings. The rotating shaft is involved in the impact interaction with a cylindrical baffle due to bending vibrations. In this paper, a beam model of the described shaft is used to study the effect of the rotation speed, gravity forces, damping, and unbalance on the shaft motion. The research is carried out numerically using the ANSYS engineering software package. It is shown that the gravity forces shift the line of centers of gravity in shaft sections, relative to which it rotates. Damping, which is proportional to the speed, provides the shaft centering. The imbalance of the shaft causes bending vibrations. The possible modes of the shaft motion and the conditions for unstable motion are revealed. The mode of the shaft motion within a cylindrical baffle that ensures a steady periodic impact interaction is determined. This interaction induces elastic waves of the acceleration, transverse force and moments in the shaft.
{"title":"Bending vibrations of a heavy horizontal composite rotating shaft limited by a cylindrical baffle","authors":"Valeriy M. Pestrenin, I. Pestrenina, O. M. Perelman, Aleksandr S. Fadeykin, Nikolay D. Derkach","doi":"10.17223/19988621/79/12","DOIUrl":"https://doi.org/10.17223/19988621/79/12","url":null,"abstract":"Drilling of wells, especially inclined and horizontal ones, is accompanied by the intense interaction of drilling tools with the borehole walls. Inborehole impacts negatively affect the drill pipe connections, electrical connections, strength characteristics of downhole motor structural elements, etc. The impact interaction of a drilling tool with a well is experimentally studied using a test bench, where the drilling tool sample is fixed in the middle of a heavy composite shaft arranged in cylindrical roller bearings. The rotating shaft is involved in the impact interaction with a cylindrical baffle due to bending vibrations. In this paper, a beam model of the described shaft is used to study the effect of the rotation speed, gravity forces, damping, and unbalance on the shaft motion. The research is carried out numerically using the ANSYS engineering software package. It is shown that the gravity forces shift the line of centers of gravity in shaft sections, relative to which it rotates. Damping, which is proportional to the speed, provides the shaft centering. The imbalance of the shaft causes bending vibrations. The possible modes of the shaft motion and the conditions for unstable motion are revealed. The mode of the shaft motion within a cylindrical baffle that ensures a steady periodic impact interaction is determined. This interaction induces elastic waves of the acceleration, transverse force and moments in the shaft.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85050010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, the influence of integration of unit cells on the mechanical behavior of the sample made of mechanical tetrachiral metamaterial is studied by using mathematical modeling. A chiral structure of the cells provides unusual mechanical behavior of the metamaterial, namely, twisting under uniaxial loading. Two methods of integration of unit cells in the metamaterial are discussed: joining and overlapping. The advantages and disadvantages of each method are described. It has been found that in one of the cases, the rotation of the system of two cells is carried out around the center of mass, which favorably affects the stability of the system, but decreases the rotation angle. In another case, the absence of one of the faces leads to the rotation which is not relative to the center of mass and results in the asymmetric strain figure and instability of the system. Such instability is caused by disproportionate arrangement of the cells in the plane, which has been shown using the examples of the systems with two and nine cells. For the system of nine unit cells, both methods of integration lead to a symmetric rotation about two perpendicular axes. Further research of this topic is supposed to allow one to create metamaterials and structures with programmable mechanical behavior.
{"title":"Analysis of some methods of integration of cells in a mechanical metamaterial","authors":"L. Akhmetshin, I. Smolin","doi":"10.17223/19988621/77/3","DOIUrl":"https://doi.org/10.17223/19988621/77/3","url":null,"abstract":"In this paper, the influence of integration of unit cells on the mechanical behavior of the sample made of mechanical tetrachiral metamaterial is studied by using mathematical modeling. A chiral structure of the cells provides unusual mechanical behavior of the metamaterial, namely, twisting under uniaxial loading. Two methods of integration of unit cells in the metamaterial are discussed: joining and overlapping. The advantages and disadvantages of each method are described. It has been found that in one of the cases, the rotation of the system of two cells is carried out around the center of mass, which favorably affects the stability of the system, but decreases the rotation angle. In another case, the absence of one of the faces leads to the rotation which is not relative to the center of mass and results in the asymmetric strain figure and instability of the system. Such instability is caused by disproportionate arrangement of the cells in the plane, which has been shown using the examples of the systems with two and nine cells. For the system of nine unit cells, both methods of integration lead to a symmetric rotation about two perpendicular axes. Further research of this topic is supposed to allow one to create metamaterials and structures with programmable mechanical behavior.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87772690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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