Methods Of Classical Mechanics Research Articles

A mathematical model of the gravitational potential of the planet taking into account tidal deformations

Objectives. This paper investigates the gravitational potential of a viscoelastic planet moving in the gravitational field of a massive attracting center (star), a satellite and one or more other planets moving in Keplerian elliptical orbits relative to the attracting center. Celestial bodies other than a viscoelastic planet are modeled by material points. Within the framework of the linear model of the theory of viscoelasticity, the problem of finding the vector of elastic displacement has been resolved. Traditionally, a solid body model is used to determine the Earth’s gravitational field, while tidal deformations are taken into account in the form of small corrections to the coefficients of the geopotential model. In this work, the viscoelastic ball model is used to take into account tidal effects. The relevance of the research topic is associated with high-precision forecasting of the movement of artificial satellites of the Earth, high-precision measurement of the Earth’s gravitational field.Methods. In this study the asymptotic and analytical methods developed by V.G. Vilke are used for mechanical systems containing viscoelastic elements of high rigidity, as well as methods of classical mechanics, mathematical analysis. The graphs were plotted using the Octave mathematical package.Results. After resolving the quasi-static problem of elasticity theory by calculating triple integrals over a spherical area, a formula for the gravitational potential of a deformable planet was obtained. In addition, the gravitational potential of the Earth was also calculated taking into account solid-state tidal effects from the Moon, Sun, and Venus at an external point. Graphs were constructed to show the dependence of the Earth’s gravitational potential on time.Conclusions. The theoretical and numerical results established herein show that the main contribution to the gravitational potential of the Earth is made by the Moon and the Sun. The influence of other planets in the solar system is small. The value of the gravitational potential at the outer point of the Earth, taking into account tidal effects, depends both on the position of the point in the moving coordinate system and on the relative position of celestial bodies.

Tracing the classical molecular nature of entropy generation

The second law of thermodynamics and the concept of positive entropy generation are analyzed following classical statistical mechanics methods. Previously, using the generalized Boltzmann–Gibbs entropy and its associated general entropy conservation relation, positive entropy generation expressions were obtained in agreement with phenomenological results and the work of Boltzmann and Gibbs. In this study, using the general approach, we formally and explicitly trace the specific entropy generation expressions to truncations in the full N-body description of the entropy state to a lower s-body description. Using higher-order superposition approximations, it is formally shown that the generalized Boltzmann–Gibbs entropy in the s-order state is always less than the corresponding Boltzmann–Gibbs entropy in the lower (s − 1)-order state. Using the general form of the entropy conservation equation, entropy generation is shown to be a required compensatory effect to ensure that all physical variables and physical processes associated with heat, work, temperature, etc., are independent of the particular entropy definition state.

Determining the Oxidation Stability of Electrolytes for Lithium-Ion Batteries Using Quantum Chemistry and Molecular Dynamics

Determining the Oxidation Stability of Electrolytes for Lithium-Ion Batteries Using Quantum Chemistry and Molecular Dynamics

Investigation of low-cycle fatigue in adhesively-bonded single-lap joints

Adhesively bonded joints are used as an alternative to classical mechanical joining methods, e.g., bolts, rivets, welding, and soldering, due to their advantages such as high strength, uniform stress distribution, and good fatigue resistance. These adhesively bonded joints are becoming more and more important, especially in fields where weight is critical, such as aviation and aerospace. Adhesively bonded joints are preferred because they offer highly reliable connections. In the present study, the low-cycle fatigue of materials joined together as adhesively bonded single-lap joints were investigated experimentally and numerically. Joints of aluminum and steel samples were subjected to variable loads that were lower than the experimentally obtained average breaking loads, and the number of cycles was determined. As a result, the fatigue life of adhesively bonded single-lap stainless steel samples was observed to be higher than that of aluminum samples. In addition, it was also observed that smudging adhesive around the endpoints of the joint significantly increased the fatigue life of steel samples.

Justification of the effect of the regularities of the flow of nanotribological processes in the materials of joint parts on the increase of wear resistance, reliability and efficiency of the functioning of machines and mechanisms

The article elucidates the essence of nanotribological processes in the materials of conjugation of samples of parts by the methods of the surface force apparatus, scanning tunneling and atomic force microscopy. The substantiation of the mechanisms of their occurrence is given by the methods of molecular dynamics and classical contact mechanics. Attention is paid to dry adhesive and contactless dynamic friction of conjugated samples, physical processes in "sticking-sliding" tribocontacts, adhesive effects, etc. The values of the lateral and normal forces acting on the probe were analyzed. The probe was considered as a collection of point particles of concentrated mass with a multiatomic structure of the material. The contact and movement of the probe with the surface of the sample was considered in the "probe-surface" system with minimal potential energy and lateral load and taking into account conservative and dissipative forces.
 The effect of "sticking-sliding" is substantiated with the help of the apparatus of surface forces. The atomic periodicity of the effect is explained on the basis of the model of the formation and breaking of adhesive bonds and the "atom-magnet" model. It is shown that the patterns of "sticking-sliding" processes can be determined by using the parameters of shear stress and specific work of adhesion.
 It is advisable to use the Johnson-Kendall-Roberts theory to explain the elastic adhesive contacts, and the Deryagin-Mullier-Toporov theory for the residual friction force and probe separation force.
 It is shown that there is a significant connection between friction and adhesion processes. The correlation between the macroscopic value of the surface energy of materials and their shear modulus for homogeneous contacts was determined.
 On the basis of adhesive effects and the effect of "sticking-sliding", it is possible to control frictional forces and create favorable conditions for their absence, which gives grounds for obtaining high wear resistance of tribo-joints of parts, their reliability and maximum efficiency of the functioning of machines and mechanisms

Flexural Buckling Resistance of Stiffeners Reinforcing Wall of a Steel Silo

Stiffeners reinforcing silo’s wall made from corrugated sheets are main structural elements sustaining meridional forces evoked by shear forces, source of which is friction of the material stored inside silo. Buckling resistance of stiffeners can be assessed by the method recommended in PN-EN 1993-4-1:2009/A1-2017-08E and in the draft of the Eurocode prEN 1993-4-1:2022. This method consists in determination of stiffener’s resistance treated as a column resting on elastic substrate which is the susceptible wall of the silo. It means that it was assumed that the stiffness of the sheeting resists buckling displacements normal to the silo wall. The procedure recommended in mentioned Eurocodes requires determination of stiffness coefficient K on the basis of the flexibility of an equivalent arch of the span equal to the double circumferential separation between adjacent stiffeners. The stiffness coefficient K was derived in the paper using classical mechanics methods and its value was compared to the one given in mentioned Eurocodes. Careful comparative analyses resulted in the identification of errors in one of the Eurocode formulae, which could result in a significant misestimation of the buckling resistance of the stiffeners. The proposed amendment led to a full correspondence between the final formula for K derived in the paper and that proposed in the referenced Eurocodes. The errors found were reported to the coordinator of the CEN working group updating EN 1993-4-1.

Parameters of the disc angle of a stepped plow for tillage

The development and creation of energy-saving machines and technologies for high-quality basic processing is one of main tasks today. The existing step plows for smooth, row less plowing have a number of disadvantages. With these plows, the technology of smooth plowing is carried out in conditions of a closed furrow, as a result, they do not ensure the turnover of layers the required degree and the sealing of plant residues, and also have a high energy intensity. The purpose study is to substantiate the parameters the disk angle stepped plow. Theoretical studies were carried out using the methods of classical mechanics. Analytical expressions have been obtained to determine the permissible distance of transverse discarding of soil particles by a disk angle and the range of flight of soil particles under the action disk, depending on its parameters. Theoretical studies have established that the permissible distance of transverse discarding of soil particles by a disk angle should be no more than 29 cm. The analysis of the expressions obtained showed that with an increase in the diameter disk angle-lift, its angle of installation to the pressure of movement, the angle of inclination to the vertical of depth of processing the angle-lift, the range of transverse rejection of soil particles increases. To ensure the established distance of soil discarding, the diameter of the disk angle-lift should be no more than 480 mm, its installation angle to the direction the hole should not exceed 35°, the installation angle to the vertical should not exceed 10° and the processing depth should not exceed 11 cm.

Comprehensive scrutiny of surface mechanical parameters of graphyne-based materials for metal-ions and metal-air batteries applications: A perspective and a hybrid atomistic-continuum model

Graphyne family, as a low-dimensional carbon allotrope, is utilized for metal-ion and –air batteries as the anode and cathode materials due to their unique characteristics. These novel carbon nanomaterials can provide more theoretical storage capacity than graphene, while their specific surface mechanical parameters and vibrational frequencies can influence battery performance. However, there needs to be clear information that can explain the effects of these parameters on battery efficiency. In this respect, the influences of the surface elasticity, residual stress, density, vibrational modes, and frequencies of α, β, and γ-graphyne circular monolayers on anode and cathode materials have been investigated in current research using the hybrid molecular dynamics simulation and modified classical continuum mechanics methods. Concerning metal-ion batteries, the results disclose that the suitability sequence for anode materials can be expressed as γ-graphyne > graphene > β-graphyne > α-graphyne monolayers. In the case of metal-air batteries, the competence sequence for cathode materials is in the order of γ-graphyne > β-graphyne ∼ graphene > α-graphyne monolayers. Therefore, γ-graphyne with suitable storage capacity, low volume expansion, good surface elasticity, low surface residual stress, and appropriate specific surface area is the promising anode and cathode material for metal-ion and -air batteries, respectively.

Semiclassical theory and the Koopman-van Hove equation * *Contribution to the Special Collection ‘Koopman Methods in Classical and Quantum-Classical Mechanics’.

The phase space Koopman-van Hove (KvH) equation can be derived from the asymptotic semiclassical analysis of partial differential equations. Semiclassical theory yields the Hamilton–Jacobi equation for the complex phase factor and the transport equation for the amplitude. These two equations can be combined to form a nonlinear semiclassical version of the KvH equation in configuration space. There is a natural injection of configuration space solutions into phase space and a natural projection of phase space solutions onto configuration space. Hence, every solution of the configuration space KvH equation satisfies both the semiclassical phase space KvH equation and the Hamilton–Jacobi constraint. For configuration space solutions, this constraint resolves the paradox that there are two different conserved densities in phase space. For integrable systems, the KvH spectrum is the Cartesian product of a classical and a semiclassical spectrum. If the classical spectrum is eliminated, then, with the correct choice of Jeffreys–Wentzel–Kramers–Brillouin (JWKB) matching conditions, the semiclassical spectrum satisfies the Einstein–Brillouin–Keller quantization conditions which include the correction due to the Maslov index. However, semiclassical analysis uses different choices for boundary conditions, continuity requirements, and the domain of definition. For example, use of the complex JWKB method allows for the treatment of tunneling through the complexification of phase space. Finally, although KvH wavefunctions include the possibility of interference effects, interference is not observable when all observables are approximated as local operators on phase space. Observing interference effects requires consideration of nonlocal operations, e.g. through higher orders in the asymptotic theory.

Theoretical foundations for intensifying onion set harvesting

The paper shows that upgrading the design of onion harvesting machines through the integration of diverse separation intensifiers demonstrates limited efficacy in improving the quality of cleaning commercial produce. They noted the need to comply with strict technological parameters for setting up separating systems (feeding bulbs to a straight section of the pin web surface in the absence of losses, reducing the maximum speed of collision of the bulbs with the working elements of the cleaning unit to reduce damage, as well as improving the completeness of cleaning). The study reveals that one of the options for intensifying the process of onion set cleaning from soil and soil clods can be ultrasonic-assisted heap moistening during separation. (Research purpose) The research aims to determine theoretical principles driving the intensification of onion set cleaning from mechanical impurities. (Materials and methods) The research employed system analysis and synthesis methods, physical modeling based on probability theory and mathematical statistics, numerical techniques for solving analytical dependencies, classical mechanics methods - fundamental principles of fracture theory, soil mechanics. (Results and discussion) The paper justifies the necessary optimum regime for intensifying onion set harvesting and cleansing them from mechanical impurities. It substantiates the functional diagram of a digging-type onion harvester featuring an ultrasonic cleaning module, taking into account the functions of the state, external and control actions, as well as performance indicators. (Conclusions) The research resulted in developing a design concept for an ultrasonic-equipped separating module of a harvester to improve the onion set cleaning process. This design conforms to the agrotechnical requirements, ensuring maximum soil and impurity sieving (at least 98 percent), minimizing losses (not exceeding 2 percent) and bulb damage (not exceeding 2 percent).

Lagrangian and Hamiltonian formulations of asymmetric rigid body, considered as a constrained system

This work is devoted to a systematic exposition of the dynamics of a rigid body, considered as a system with kinematic constraints. Having accepted the variational problem in accordance with this, we no longer need any additional postulates or assumptions about the behavior of the rigid body. All the basic quantities and characteristics of a rigid body, as well as the equations of motion and integrals of motion, are obtained from the variational problem by direct and unequivocal calculations within the framework of standard methods of classical mechanics. Several equivalent forms for the equations of motion of rotational degrees of freedom are deduced and discussed on this basis. Using the resulting formulation, we revise some cases of integrability, and discuss a number of peculiar properties, that are not always taken into account when formulating the laws of motion of a rigid body.

ETHOSOMES: A NOVEL APPROACH FOR THE DELIVERY OF DRUG

Background: In the past m8any years, there have been many studies that are considering the nanoparticles as the carriers of the drugs for improving the patient compliance. One such approach of delivery of the drug is through the ethosomes. Objectives: This review aims to describe the vesicular approach of ethosomes that had been used to overcome the barrier for the transdermal delivery of drug and also describes brief composition, method of preparation, characterization tests, mechanism of penetration of ethosomes, as well as highlighted various studies of ethosomes in medicine. Methodology: Relevant data was searched using various databases like Google Scholar, PubMed, SpringerLink and Scopus. Results: Ethosomes are the vesicular shaped structures comprising majorly of phospholipids and ethanol. Due to their size in nanometers and presence of increased amount of the ethanol in its structure, it had shown very high permeation of the drug when given through the transdermal route or topically. There are basically two methods for the formulation of the ethosomes that includes the hot method and cold method. Furthermore, recently more two methods have also been developed for formulating ethosomes including classical mechanical dispersion method and transmembrane pH gradient method. After formulation of ethosomes, many characterization tests can be performed on ethosomes such as pH, particle size, zeta potential, in vitro permeation studies, microscopic evaluation and stability studies. Conclusion: Many more studies are needed to enhance these novel drug delivery systems and other vesicular systems such as transferosomes and invasomes for better therapeutic output and ultimately increasing the patient compliance.

METHOD OF ANALYSIS OF THE STRESS-STRAIN STATE OF A BASE-CENTERING DEVICE AND A PIPELINE WHEN CARRYING OUT THE COMPLEX OF EMERGENCY AND RECOVERY REPAIRS

Link for citation: Rakhmatullina Yu.A., Alekseev V.A., Sultanmagomedov T.S., Khasanov R.R. Method of analysis of the stress-strain state of a base-centering device and a pipeline when carrying out the complex of emergency and recovery repairs. Bulletin of the Tomsk Polytechnic University. Geo Аssets Engineering, 2023, vol. 334, no. 7, рр.7-16. In Rus. The relevance of the research is caused by the need to carry out calculations of the stress-strain state of the support-centering device and the pipeline, when the device under consideration is exposed to it, when the axes are displaced due to the presence of residual stresses when carrying out a complex of emergency repair by cutting out a defective section of the pipeline. The purpose of the study is to assess the possibility of using the design of the device and to calculate the stress-strain state of the device when the axes of the boundary sections of the pipeline are displaced due to the release of prestresses during the emergency repair complex for cutting out the defective section of the pipeline. Methods: methods of classical theoretical mechanics, soil mechanics, finite element method. Results. Based on the patent, a preliminary 3D model of the support-centering device and a method for analyzing the boundary conditions and loads affecting the device and the pipeline during the emergency repair complex were developed. The calculation of SSS (stress-strain state) was carried out, where the following results were obtained: when the frame is displaced down/up by 100 mm in the device, respectively, along the length and displacement, stresses arise at the junctions of the enclosing ring and the frame, as well as on the «lugs», exceeding the yield strength of steel; the coefficient of friction μ for the considered diameter of 1020 mm should not exceed 0,15 to prevent the occurrence of areas of plastic deformation of the pipeline during the emergency repair complex for cutting out a defective area in swamp conditions.

International Conference on Applied Sciences ICAS2022

Banja Luka, Bosnia and Herzegovina, May 25-28, 2022 International Conference on Applied Sciences ICAS2022 took place in Banja Luka, Bosnia and Herzegovina, in the period May 25–28, 2022, at the University of Banja Luka, with the aims to serve as a platform for exchange of information between various areas of applied sciences, and to promote the communication between the scientists of different nations, countries and continents.The conference has been focused on several fields of application, operation and influence of the applied sciences and technologies on industry. Topics of the conference covers a comprehensive spectrum of issues from: 1. Fundamental Sciences: Numerical approximation and analysis, Numerical simulation, Numerical optimization, General statistical methods, Stochastic analysis methods, Analytical and numerical techniques, Finite element methods, Dynamical systems methods, Chemical composition analysis, Energy analysis, Heat transfer, Interdisciplinary applications of physics, Environmental aspects, Effects of pollution, Fuzzy logic, and others… 2. Computers Engineering: Computer modeling and simulation, Algorithms, Software engineering, Artificial intelligence, Neural networks, Image processing, Data acquisition: hardware and software, Data presentation and visualization, Data analysis: algorithms and implementation, Data management, Big Data, Internet and network applications, and others… 3. Electrical Engineering: Electrical and electronic instruments and components, Circuits and circuit components, Signal processing electronics, Power electronics, Electric motors, Electric vehicles, Biomass energy, Wind energy, Solar energy, Solar cells (photovoltaics), Conventional hydropower, Hydroturbines, and others… 4. Mechanical Engineering: General theory of classical mechanics, Computational methods in classical mechanics, Control of mechanical systems, Dynamics and kinematics of rigid bodies, Mechanical properties of solids, Applied mechanics and design, Deformation and plasticity, Mechanical modes of vibration, Mechatronics, Robotic systems engineering, Automotive engineering, Vehicle technology, Aerospace systems and technology, and others… 5. Materials Engineering: Methods of materials synthesis and materials processing, Methods of materials testing and analysis, Metals and metallic alloys, Metallurgy, Nonmetals, Porous materials, Granular materials, Polymers, Biomaterials, Composite materials, Organic compounds, Nanoscale materials and structures, Structural failure of materials, and others…During the four days of the conference, 4 keynote lectures and 121 oral talks were delivered.Based on the works presented at the conference, 45 papers have been selected to be included in this volume of Journal of Physics: Conference Series.List of Organizers, Event sponsored, Honorary Committee, Organizing Committee, Scientific Committee are available in the pdf.

A transfer operator approach to relativistic quantum wavefunction * *Contribution to the Special Collection ‘Koopman Methods in Classical and Quantum-Classical Mechanics’.

The original intent of the Koopman–von Neumann formalism was to put classical and quantum mechanics on the same footing by introducing an operator formalism into classical mechanics. Here we pursue their path the opposite way and examine what transfer operators can say about quantum mechanical evolution. To that end, we introduce a physically motivated scalar wavefunction formalism for a velocity field on a 4-dimensional pseudo-Riemannian manifold, and obtain an evolution equation for the associated wavefunction, a generator for an associated weighted transfer operator. The generator of the scalar evolution is of first order in space and time. The probability interpretation of the formalism leads to recovery of the Schrödinger equation in the non-relativistic limit. In the special relativity limit, we show that the scalar wavefunction of Dirac spinors satisfies the new equation. A connection with string theoretic considerations for mass is provided.

Numerical Simulation and Deformation Behavior of a Ti/Steel Clad Plate during the Rolling Process

The deformation mechanism is complex in the hot rolling process of clad plates, and head bending is a common defect. In this paper, an analytical computational mechanical model of a metal plate was established by the classical elastic mechanics method, and the relationship between uneven thickness extension and warpage was obtained. The hot rolling bonding process of dissimilar bimetallic plates of Ti/Steel was investigated. On this basis, the mechanical origins of the plate bending defects and the influence of various factors on the evolution of the plate bending defects of the metal plates were revealed. The results indicated that the rolling forces increased with the increase in reduction ratio and thickness ratio. As the total reduction ratios of the clad plates increased, the reduction ratio of each layer increased. Furthermore, it was found that the thickness reduction ratios of steel were larger than those of Ti at a certain total reduction ratio, which could reach up to 59.6%. When the reduction ratios were 0.4 and 0.45, the bending degree increased with the thickness ratio of the upper and lower plates increasing gradually. The maximum warpage could reach 0.349 m. The clad plate shape was better when the roll speed ratio was 1.02 and the reduction rate was 0.4. The present numerical results provide a valuable insight into the deformation behaviors and mechanisms involved in the hot rolling of clad plates.

Physico-mechanical properties of seed pile of fodder crops

The purpose of the study is to study and analyze the physical and mechanical properties of the seed pile of fodder crops. The results of determining the physico-mechanical properties of the seed pile of fodder crops obtained in the combing clover plants with a comb of the combing drum of the harvesting machine are presented. The basic principles and methods of classical mechanics, mathematical analysis, and statistics were used in this study. It was found that the stiffness of the stems of the seed pile at a humidity of 40-60% is in the range of 0.07-0.008 N / m2. At the same time, with a moisture content of 35-65%, its bulk mass is 80-185 kg/ m3, respectively. The minimum value of the angle of the natural slope of the clover seed pile is 48o, and its maximum value reaches up to 90o; the value of the static friction coefficient at a humidity of 40-60% is within 0.98-1.02, and the value of the dynamic friction coefficient is within 0.5-0.7. The pile's temperature is directly proportional to the storage time; during self-heating, the appearance of the pile gradually changes depending on the storage time and temperature duration.

Pulling resistance of the front plow cornercutter

When installed on the frontal plow, the bodies will work in conditions of semi-blocked cutting. The purpose of the study is the theoretical determination of the traction resistance of the frontal plough's cornercutter. The basic principles and methods of classical mechanics, mathematical analysis and statistics were used in this study. Analytical equations for determination of traction resistance of cornercutter beam and plough have been obtained. It is established that traction resistance of frontal plough corners depends on cornersner and plough parameters as well as on physical-mechanical soil properties. At speeds of 1.8-2.3 m/s, traction resistance of the corrugated plough is 0.36-0.39 kN.

Parameters of slitter for embedding manure in soil for melon crops

The purpose of the study is the theoretical justification of the parameters of the slitter for embedding manure in the soil. A slitter has been developed for lifting the formation, forming a gap along the manure strip lying on the field's surface, pushing it into the gap, and leveling the gap with soil. The basic principles and methods of classical mechanics, mathematical analysis, and statistics were used in this study. The slitter includes a rack, large and small cheeks connected to a soil-supporting plate with an increasing slope from the bottom to the top towards the small cheek and adjacent to the soil-supporting plate. A window is made in the big cheek for the passage of manure. The large cheek is somewhat pushed forward relative to the soil-bearing plate, and its front face is pointed. It is established that when planting fertilizers, the following operations must be carried out: lifting the formation, forming a gap along the manure strip lying on the field's surface, pushing the latter into the gap, and leveling the gap with soil. The working bodies of the dump type are the most acceptable for lifting the formation and the formation of a gap. The following optimal values of the parameters of the slitter are established: the removal of the large cheek is 710 mm, the width is 200 mm, the length and height of the window are 550 and 250 mm, respectively, and the angle between the forming and field edge in the horizontal plane is 42°, the height of the small and large cheeks of the slitter is 300 and 250 mm, respectively.

Theoretical and experimental substation of the parameters of hulls that form furrows

In all countries the creation, operation and use of energy- and resource-saving, high-performance machines for turning the soil and preparing crops for planting plays an important role. In particular, in this direction it is important to carry out specific scientific and practical research on the preparation of a universal machine and the technological operation of its main nodes, as well as the achievement of resource savings in the case of interaction with the soil. A semi-screw body was selected as a furrow forming device of the machine that prepares the soil for planting potatoes in the field, and its parameters were theoretically and experimentally justified. Mathematical analysis, the most important principles and methods of classical mechanics were used in the conducted research. According to the results of theoretical and experimental scientific research, the covering width of the housing, which ensures compliance with the requirements of the formation of the nucleus by consuming less energy, should be 200 mm, and the minimum height of its pillar and column should be 330 mm and 560 mm. and the length of the wing should be between 515-545 mm.