Analytical Mechanics Research Articles

An Approach to Growth Mechanics Based on the Analytical Mechanics of Nonholonomic Systems

An Approach to Growth Mechanics Based on the Analytical Mechanics of Nonholonomic Systems

Methodology for calculating the support reactions of a statically indeterminate tractor drive axle final drive shaft

BACKGROUND: Currently, in the design of vehicle drive axles, bevel final drives are used, forming both statically determinate structures and statically indeterminate ones. In the first case, the bearings on which the bevel final drive shafts rest form two races of rolling elements, in the second case - three or more. Despite the prevalence of bevel final drive designs that form statically indeterminate structures, in the process of teaching the design and calculation of machine elements, statically determinate structures are considered. The relevance of the work lies in the formalization of the analytical calculation of the reactions of the supports of the bevel final drive, forming a statically indeterminate system, with the derivation of formulas for determining the reactions in the extra support. AIMS: The article aim is the formalization the methodology for calculating the support reactions of the drive axle bevel final drive, forming a statically indeterminate system, for calculating bearings. METHODS: The article uses mathematical dependencies of Analytical Mechanics to calculate reactions in the main supports, a corollary of Castigliano theorem and the Force method to calculate reactions in extra supports. "Mathcad" was used for mathematical calculations. RESULTS: A formalized method for the analytical calculation of support reactions in statically indeterminate systems has been developed and presented, using Castigliano theorem to solve static indetermination. The methodology application for calculating the support reactions of the statically indeterminate the Kirovets K-7 series tractors drive axle bevel final drive is considered. CONCLUSIONS: The dependencies obtained during the calculations make it possible to calculate the bevel final drive support reactions, the design of which forms a statically indeterminate system. The bevel final drive mathematical model obtained during the calculations can be used as a basis for developing software that automates this calculation.

Grundlagen einer 'integralen' Grammatik

Within the framework of an integral grammar, syntax, morphology and lexicology represent three types of consideration of the same reality, which is the linguistic construction of meaning. The distinction between these three linguistic disciplines may be useful in some cases, but in other cases it may hinder the explanation of linguistic phenomena. Integral linguistics is capable of unifying the disciplines - integrating them. It can, however, use modular methods where appropriate. It could therefore be seen as a kind of construction grammar with the option of modularising its descriptions and explanations. This is not to say that this approach advocates methodical indifference; on the contrary, it presupposes a particularly rigorous deduction of its concepts and descriptive methods. The foundations for such a grammar have already been laid in Saussure's Cours de linguistique générale, which – with striking foresight – anticipates the ideas of nowadays' construction grammars and provides them with a hitherto unprecedented theoretical foundation. This is the starting point for the present article, which places Saussure's reflections within the framework of a theory of language centred on the speech event. It defines the functional levels of the sentence on the ground of the dimensions of utterance meaning, deduces the notions of syntactic function and syntactic constituency from the synthetic and analytical mechanisms of the syntagmatic dimension of language, and those of form and category from the abstraction principles of the paradigmatic dimension of language. Finally, it will be shown how the basic ideas of constructional grammars, in particular that of the syntax lexicon continuum, can be convincingly and exhaustively explained by the universal principles of grammar postulated by Saussure: the syntagmatic and paradigmatic structuration of language.

Development of a Lagrange Mechanics E-Module Based on a Flipbook Pendulum Spring System

This research is a type of Research and Development (R D) research that uses the 4D development model, namely Define, Design, Develop, Disseminate. This research produces a Lagrange Mechanics E-Module based on a flipbook pendulum spring system. The aim of this research is to produce a Lagrange Mechanics E-Module that is suitable for use as a learning medium for Analytical Mechanics. The data collection instrument used in this research is a questionnaire as a validation assessment for material experts and students, data analysis uses percentages with predetermined categories. The research sample was 14 Physics Education students. The validation results by material experts were 73% in the feasible category. The student response results were 85% in the very appropriate category. From these results, the Lagrange Mechanics E-Module is suitable for use with revisions as an alternative source of learning.

Mechanism of microwave-assisted coal desulfurization with urea peroxide

To effectively remove organic sulfur from coal for higher resource efficiency, an innovative microwave-assisted urea peroxide for desulfurization system was designed. The experimental group with different microwave frequencies and the conventional pyrolysis control group were set up to prove the desulfurization effect of microwave in coordination with urea peroxide. The experimental results showed that under 1000 W microwave irradiation and the promotion of urea peroxide, the desulfurization efficiency can reach 67.29 %, with an increase of 38.32 % while the conventional pyrolysis is only 28.97 %. According to the Fourier transform infrared (FTIR) analysis, the effectiveness of microwave coordination with urea peroxide for desulfurization is explained from macroscopic point of view. Benzylidene thiol, dibenzyl sulfide, and dibenzyl disulfide were selected as model compounds for the quantum chemical calculation. The simulation results demonstrated that the changes in the pathway energy barriers for desulfurization align with the experimental material transformations, confirming the accuracy of the simulation. The sulfur-containing bonds of mercaptans will be destroyed to form hydrogen sulfide, and the undestroyed bonds will remain in the organic matter. After being oxidized, the sulfur-containing bond will break to form a water-soluble sulfonic acid free radical. The unoxidized sulfur bonds of thioethers will be destroyed to generate unstable phenyl free radicals and free sulfur radicals. To achieve stability, phenyl free radicals can pair to form diphenylethane or combine with other radicals (such as •H). In contrast, sulfur free radicals can only react with hydrogen radicals to form hydrogen sulfide. However, the limited availability of hydrogen radicals in the system restricts the desulfurization efficiency. After oxidation by urea peroxide, the thioethers will form sulfones. The sulfur-containing bonds will be fractured and directly generate phenyl and sulfur dioxide, which reduces the dependence on hydrogen free radicals. The three-dimensional desulfurization path of microwave collaboration with urea peroxide experiment was simulated and converted to the analytical bond breaking and formation mechanism. This study proved that microwave synergizes with urea peroxide can intensify the desulfurization process. It provides a high-efficiency method for the clean and green utilization of coal, which is conducive to supporting environmentally sustainable development.

Mechanical Foundations of the Generalized Second Law and the Irreversibility Principle

We follow the Boltzmann-Clausius-Maxwell (BCM) proposal to establish the generalized second law (GSL) that is applicable to a system of any size, including a single particle system as our example establishes, and that supercedes the celebrated second law (SL) of increase of entropy of an isolated system. It is merely a consequence of the mechanical equilibrium (stable or unstable) principle (Mec-EQ-P) of analytical mechanics and the first law. We justify an irreversibility priciple that covers all processes, spontaneous or not, and having both positive and negative nonequilibrium temperatures temperatures T defined by (dQ/dS)E. Our novel approach to establish GSL/SL is the inverse of the one used in classical thermodynamics and clarifies the concept of spontaneous processes so that dS≥0 for T>0 and dS<0 for T<0. Nonspontaneous processes such as creation of internal constraints are not covered by GSL/SL. Our demonstration establishes that Mec-EQ-P controls spontaneous processes, and that temperature (positive and negative) must be considered an integral part of dissipation.

Black powder and mineral deposits in the LPG production and processing line: Analytical study and formation mechanisms

The accumulation of mineral deposits such as black powder causes severe impacts throughout the gas production and transport process. The phenomenon takes place from gas wells to LNG/LPG treatment plants and terminals. The complexity lies in understanding the mechanisms by which these materials are formed in random quantities, as well as their varied nature. The aim of this study is to monitor black powder and other mineral deposits formation in a chain of gas production and processing situated in the south of Algeria and unravel their root causes. To that extent, an analytical study was carried out on four samples of both mineral deposits and black powder taken from an LPG processing and production unit. The adopted analytical approach included an exploration of the textural and structural properties. It also involves a composition characterizations related to the content of metallic elements, moisture, organic and mineral matter. The particle distribution is also determined. The analytical study was conducted using gravimetric determination, XRD, XRF, SEM/EDX and Raman spectroscopy. Particle distribution was given by Laser granulometry technique. The results of the DRX/FRX and EDX characterization primarily revealed that the samples contain a variety of mineral components such as iron oxides; magnetite Fe3O4 and hematite Fe2O3, iron oxy-hydroxide FeO(OH), iron sulphide FeS2, calcite CaCO3, SiO2 and halite NaCl. The presence distribution of these components depends on the location of the sample in gas line. Granulometry study shows that black powder contamination can be spread over a wide spectrum of particle sizes ranging from 1.51 µm to 678.50 µm. This study has allowed to elucidate the nature and distribution of particles deposited at different positions in the LPG production chain and to propose probable mechanisms for their formation.

Mechanics-based machine learning for failure classification of load-bearing walls

This paper presents novel methodologies that combine analytical mechanics with artificial intelligence to classify the failure mode of reinforced concrete walls under lateral loading. The adequacy of existing approaches is examined, including design equations and established machine learning algorithms, against experimental datasets consisting of 330 specimens. Findings indicate that the machine learning algorithms outperform the empirical design equations in terms of failure mode classification; however, the former lacks physical interpretability. To address this limitation, a new concept is proposed by integrating analytical and computational platforms for identifying attributes that dominate the failure characteristics of the walls. Non-dimensional features are derived and substituted into the machine learning algorithms. The aspect ratio of the walls and the amount of vertical rebars in boundary elements are found to be salient factors when categorizing failure modes, followed by the amount of horizontal rebars in the web. Through the application of decision boundaries stemming from the mechanics-based machine learning protocol, design recommendations are suggested to effectively classify the failure mode of load-bearing walls.

Research on the Cultivation of Students' Application Ability in Theoretical Mechanics Courses in Applied Undergraduate Colleges and Universities

Research on the Cultivation of Students' Application Ability in Theoretical Mechanics Courses in Applied Undergraduate Colleges and Universities

Application of the Lambert function in the analytical solution of ballistics problems for flat flight trajectories of a material body, taking into account the gaseous (air) medium

Annotation. The paper describes the use of a special Lambert function for solving problems of ballistics of a material body, when the resistance of a gaseous (air) medium is taken into account. A model of quadratic (based on the speed of movement of a body) resistance of the medium within the limits of an approaching flat trajectory is considered. Problem. Problems of ballistics of a material body are considered in courses of theoretical mechanics, as well as in specialized literature. But, in addition to the cited literature, this research, like, for unraveling the simplified level of the material body in the problems of ballistics for flat trajectories of the power of a special function Lambert, which allows us to essentially simplify the algorithm for developing the parameters of the trajectory of a gentle slope (floor) type. Goal. The goal of the work is based on a framed model of a material body for flat trajectories in problems of modern ballistics on this basis, using a special Lambert function, to be controlled by a visible decoupling Didion, the determination of the main parameters of these types of crash trajectories. Methodology. Physic, mechanical and mathematical models are constructed that adequately describe the parameters of the collapse of a material body/particle that collapses along a flat trajectory when the wind is not supported , which are proportional to the square of the fluidity of the particles. For a more manual description of the parameters of the trajectory of the motion, there is a special Lambert function, which is tabulated in [1], or can be expanded with the help of computer in the middle of “Maple 8”. Practical value. The results obtained in the work can be used to improve and clarify engineering methods of calculation in problems of external ballistics of a material body, taking into account the quadratic (in terms of movement speed) resistance of the air environment

Basic Principles of Deformed Objects with Methods of Analytical Mechanics

Analytical mechanics is the most fundamental discipline in this field. The basic principles of analytical mechanics should also be applicable to deformed objects. However, the virtual displacement principle proposed by analytical mechanics is only applicable to particle systems and rigid body systems, and not to general deformed objects. In this study, the basic principle, which includes the virtual displacement principle and d’Alembert–Lagrange principle (also called the virtual displacement principle of dynamics), of general deformed objects (such as, elastic, plastic, elasto-plastic, and flexible objects) is derived using analytical mechanics. First of all, according to the method of analytical mechanics, the external force, internal force, constraint reaction force and elastic recovery force of the deformed object system under the equilibrium state are analyzed, and the concepts of virtual displacement, ideal constraint and virtual work are introduced, and the virtual displacement principle (also called virtual work principle) of deformed objects is proposed; secondly, vector form, coordinate component form and generalized coordinate form of generalized virtual displacement principle of deformed object are given; thirdly, Introduce inertial force and use analytical mechanics to derive the d’Alembert–Lagrange principle of dynamic systems; fourthly, as application of the principle, the virtual displacement principle of deformed objects in plane polar coordinate system, space cylindrical coordinate system and spherical coordinate system are given; fifthly, the constitutive relationship between the gravitational strain of elastic–plastic materials was introduced, and an example of the application of the d'Alembert–Lagrange principle in elastic–plastic objects was given; finally, a brief conclusion is drawn. This study unifies the virtual displacement principle of elastic objects, plastic, elastoplastics, deformed object systems and rigid object systems using the basic analytical mechanics method. This is a basic principle for dealing with the static problems of deformed objects. This work also lays the foundation for further study of the dynamics of deformed object systems.

A numerical study on MHD Casson fluid flow in a non-uniform rough channel with temperature-dependent properties using OHAM

This study explores the complex dynamics of magnetohydrodynamic (MHD) Casson fluid in a non-uniform rough channel, focusing on the effects of temperature-dependent viscosity and variable thermal conductivity under no-slip boundary conditions. The study employs an innovative approach by utilising a rough surface with irregular textures to analyse flow patterns and assess drag forces on channel objects. A novel mathematical model, governed by continuity, momentum, and heat transfer equations, is developed and transformed into dimensionless, nonlinear Ordinary Differential Equations (ODEs) using non-dimensional quantities and fundamental assumptions. The Optimal Homotopy Analysis Method (OHAM) is applied to solve these equations to enhance convergence speed and accuracy. The research explores the impact of surface roughness on velocity profiles and temperature distributions under various physical constraints. Numerical simulations are conducted to determine skin friction coefficients and Nusselt numbers. Furthermore, the study examines the influence of confined boluses on fluid flow in diverse physiological conditions. A comprehensive analysis is performed to elucidate the combined effects of surface roughness on fluid passage, including flow separation, pattern alterations, pressure distribution and drop, heat transfer characteristics, and flow resistance. The intricate interplay between temperature-dependent viscosity, varying thermal conductivity, and surface roughness is thoroughly investigated to explain the complex dynamics of MHD Casson fluid movement in non-uniform channels. Implementing a magnetic field over the rough, non-uniform channel is found to provide stability and prevent fluid overflow. This research has significant real-world applications, including soil erosion prevention, blood flow regulation in arteries, and optimisation of hydropower channels and penstocks. By enhancing our understanding of flow dynamics through rough and non-uniform channels, this study contributes valuable insights into both theoretical fluid mechanics and practical engineering applications.

D’Alembert–Lagrange Principle in Symmetry of Advanced Dynamics of Systems

The D’Alembert–Lagrange principle is a fundamental concept in analytical mechanics that simplifies the analysis of multi-degree-of-freedom mechanical systems, facilitates the dynamic response prediction of structures under various loads, and enhances the control algorithms in robotics. It is essential for solving complex problems in engineering and robotics. This theoretical study aims to highlight the advantages of using acceleration energy to obtain the differential equations of motion and the generalized driving forces, compared to the classical approach based on the Lagrange equations of the second kind. It was considered a mechanical structure with two degrees of freedom (DOF), namely, a planar robot consisting of two homogeneous rods connected by rotational joints. Both the classical Lagrange approach and the acceleration energy model were applied. It was noticed that while both approaches yielded the same results, using acceleration energy requires only a single differentiation operation, whereas the classical approach involves three such operations to achieve the same results. Thus, applying the acceleration energy method involves fewer mathematical steps and simplifies the calculations. This demonstrates the efficiency and effectiveness of using acceleration energy in dynamic system analysis. By incorporating acceleration energy into the model, enhanced robustness and accuracy in predicting system behavior are achieved.

Stress-deformation analysis of the cracked elastic body

A new analytical plane Elastic Fracture Mechanics (LEFM) model of the effective elastic moduli exhibited by an isotropic elastic cracked solid in tensile and compressive stress fields is presented. The effective Young’s modulus and Poisson’s ratio E¯,v¯, respectively, relate the stresses applied to the cracked solid with its macroscopic deformation. In the case of a compressive stress field the effective elastic moduli depend solely on properly oriented cracks that are either open or closed. This model is then used for the stress and displacement estimations around a circular axisymmetric hole under internal pressure and external hydrostatic stress. The creation of the hole alters the stresses in its neighborhood, and induces a deterioration of the elastic moduli. In this manner, the effective elastic moduli depend on the radial distance from the hole’s boundary. The validation of the algorithm was done against Kirsch’s analytical solution of the axisymmetric hole problem for nearly zero density of cracks as well as for large values of the friction angle. The model predicts a lower tangential stress concentration at the wall of the hole compared to that predicted by the constant linear elasticity solution and a maximum stress concentration that is not necessarily located at the wall of the hole. This apparent enhancement of rock strength adjacent to the wall is more pronounced for larger concentrations of open cracks.

РАЗРАБОТКА МОБИЛЬНОГО КОЛЕСНОГО РОБОТА ДЛЯ ДОСТАВКИ ПОСЫЛОК

The study objective is to develop approaches to the design of a mobile wheeled robot for transporting small-sized goods, operating autonomously without the participation of a human operator. At the same time, the main task is to develop a mathematical model of a wheeled robot that takes into account the moments of rolling friction and sliding of the driving wheels on the support surface, and which allows to study the starting operation modes of the electromechanical drive of a mobile device. The increase in the speed of the mobile robot is achieved by minimizing the acceleration time to the required speed values through the use of a 2-stage algorithm for changing the control voltage. The development of a mathematical model of a robotic system is carried out on the basis of methods of analytical mechanics and the theory of automatic control. Using the Laplace transforms, an analytical solution of differential equations describing the dynamics of a mobile robot is obtained. Numerical solution of the obtained equations is carried out in Mathcad interface. The novelty of the work consists in obtaining time dependencies for the speed and current in the circuit of the electric motor of the mobile robot wheeled drive and finding out the basic patterns of movement at its launch. The results of the conducted research can be used in the development of motion control systems for mobile robots with feedback, ensuring the stabilization of a set value of the movement speed in steady-state modes. Conclusions: a mathematical model of a mobile robotic system is developed, the starting modes of its operation and the method of combined motion control are studied, the speed of a mobile wheeled device is increased when moving along a given trajectory.

Regarding the issue of the influence of factors on the braking parameters of M1 category vehicles with electric or hybrid power unit

Problem. The relevance of this work is explained by the fact that there are no works at all in the reference and normative literature on the theory and practice of forensic auto technical examination, and even more so, methodical recommendations regarding the values ​​of the braking parameters of vehicles of the M1 category with an electric power plant. Goal. The purpose of the work is to establish the factors that affect the braking parameters of M1 category vehicles with an electric or hybrid power unit. Methodology. The approaches adopted in the work to solve the set goals are based on the theory of conducting the experiment, the theory of the interaction of the pneumatic tire with the road surface, the theory of the car and the laws of theoretical mechanics. Results. On the basis of the obtained experimental data regarding the value of permanent deceleration and the time value of the increasing deceleration during emergency braking of the M1 category vehicles with an electric or hybrid power unit, the tasks will be solved necessary for conducting forensic engineering and transport examinations for specific road traffic events with the participation of M1 category vehicles with an electric or hybrid power unit. Originality. The results of the study provided an opportunity to get an idea of the influence of factors on the braking parameters of M1 category vehicles with an electric or hybrid power unit. Practical value. The obtained results can be recommended to forensic experts when writing expert opinions or expert studies.

Failure mode maps for glass fibre-reinforced polymer/polyvinyl chloride foam-cored sandwich structures

Purpose This study aims to understand how the facesheet size, orientation and core size influence the analytical failure mechanism mode of glass fibre reinforced polymer (GFRP)/polyvinyl chloride (PVC) sandwich structures subjected to three-point bending. The purpose of this study was to develop failure-mode map of GFRP/PVC sandwich structures. Sandwich structures with different facesheet and core thicknesses were used to develop the failure map. Design/methodology/approach The sandwich structure and facesheet were fabricated using a vacuum-assisted resin infusion method with core sizes of 10, 15 and 20 mm and facesheet thicknesses of 1.5 and 3 mm and were arranged in three different orientations: angle-ply, cross-ply and quasi-isotropic. The key failure modes that occur in sandwich structures were used to predict possible failures in the developed material. Analytical equations were used in MATLAB for each observed failure mode. The probable failure modes, namely, face yielding, core shear and indentation equations, were used to construct the failure maps and were compared with the experimental data. Findings The boundary of the two failure modes shifts with changes in the facesheet and core thicknesses. The theoretical stiffness of sandwich panels was higher than the experimental stiffness. Based on strength-to-weight ratio, specimens E10-4, A15-8 and E20-8 exhibited the best optimum values owing to their shorter distance to the boundary lines. Originality/value In this study, a failure map was used to predict the possible failure modes for different GFRP facesheet orientations and thicknesses and PVC core thickness sandwich structures. Little is known about the prediction of the failure modes of unidirectional GFRP arranged in different orientations and thicknesses and PVC core thicknesses for sandwich structures. Few studies have used failure mode maps with unidirectional GFRP oriented in angle-ply, cross-ply and quasi-isotropic directions as a facesheet for sandwich structures compared to bidirectional mats. This study can serve as a guide for the correct selection of materials during the design process of sandwich structures.

Analytical mechanisms for heat flux reduction on a V-shaped blunt leading edge

Analytical mechanisms for heat flux reduction on a V-shaped blunt leading edge

The asymptotic solutions for the motion of a charged symmetric gyrostat in the irrational frequency case

The primary objective of this study is to explore the spatial rotary movements of a symmetrically charged rigid body (RB) that is rotating around a fixed point, akin to Lagrange’s scenario as a novel scenario where its center of mass experiences a slight displacement from the symmetry dynamic axis. The body’s movement is presumed to be affected by a gyrostatic moment and a force from an electromagnetic field, attributed to the presence of a located point charge on this axis. The regulating equations of motion that are pertaining to the equations Euler–Poisson are solved through the utilization of Poincaré’s small parameter method along with its adaptations when the scenario of irrational frequencies is considered. The three angles of Euler are derived and graphed to ascertain the body’s position at any point throughout the motion. The temporal evolutions of the achieved outcomes are drawn to showcase the significant impact of the selected parameters on the motion. The phase plane diagrams have been generated to illustrate the stability of the body during the motion. The novelty of studying the rotatory motion of a charged RB under these specific conditions lies in the intricate interplay of gyrostatic effects, magnetic interactions, and nonlinear dynamics. This research can push the boundaries of theoretical mechanics and provide valuable insights and tools for both theoretical advancements and practical applications. Moreover, the achieved results from this analysis can be utilized to improve the dynamic performance of diverse engineering applications, particularly those dependent on gyroscopic theory. This includes enhancing the functionality of satellites, compasses, submarines, and automatic pilots used in aircraft. Essentially, the findings have practical implications for optimizing the performance and stability of these systems.

Design and Research of Intelligent Fixture for Drawing Machine

Tensile machine is a very sophisticated test equipment, which can test the mechanical properties of some materials. In the drawing machine, the clamping device is to prevent the relative displacement and vibration phenomenon in the process of tensile test. The clamping device is the most important part of the structure of the test machine, and the main task of the clamping device is to control the degree of freedom of the specimen needs to be clamped, so as to further add loads to the various specimens to be held, and finally complete the mechanical property test of the material. But at present, the existing fixture mechanism is mainly hydraulic, pneumatic, mechanical fixture. At present, the existing mechanical fixture still has bending stress during the clamping process, which will affect the accuracy of the experiment. Therefore, a clamping mechanism with adjustable clamping force and flat pushing is designed. An electric control type fixture mechanism is very rare, so in this paper, an electrically controlled fixture is designed on this basis. The main contents are as follows: (1) On the basis of the existing fixture types, the working mode of the fixture is studied, and the working principle related to the fixture is mastered. (2) The main components of the fixture mechanism are analysed, the design scheme is determined, and the selection of the components of the drive part and the selection of the related components within the fixture mechanism is completed. ( 3) The force analysis of the main body of the fixture is carried out by using theoretical mechanics knowledge, and the relevant calculations are completed. The solid modeling of the whole mechanism is completed by using SolidWorks. The force analysis of key parts is carried out by using ANSYS software, and the correctness and safety of material selection and design are verified. The main parts of the fixture mechanism to complete the corresponding force analysis, and the theoretical calculation results are compared and verified, and finally realize the electric control of the fixture mechanism and complete the design of the fixture mechanism.