Oscillatory Processes Research Articles

Estimation of influence of smoothness of running of transport-technological machines on driving safety in off-road conditions

BACKGROUND: Safety of movement of transport-technological machines, especially in off-road conditions, to a great extent depends on the elastic and demisting properties of the suspension, which directly affect the smooth running and static transverse stability of the machine on a slope, provide the possibility of long-term movement on rough roads in the range of operating speeds without exceeding the established norms of vibration accelerations, causing unpleasant sensations and rapid fatigue in the driver, uninterrupted movement of the wheel from the road, as well as “no breakdown” Therefore, it is necessary to provide the suspension with the required elastic-damping characteristics by applying in the design of pneumohydraulic shock absorber and assess its impact on the safety of driving in off-road conditions. AIMS: Development of a method for assessing the impact of smooth running of transport and technological machines on the main indicators of traffic safety in off-road conditions in the development of new technical solutions aimed at improving the smooth running. MATERIALS AND METHODS: Modeling of oscillatory processes of the machine masses connected with each other by elastic-damping links at unsteady and steady oscillations, modeling of the influence of the stiffness of the elastic suspension element on the static transverse stability of the machine on a slope, performed in the Mathcad software environment. RESULTS:As a result of mathematical modeling of oscillatory processes of masses of the machine it was established that the application of the proposed shock absorber allows in case of driving over a single bump of 0.08 m height at a speed of 30 km/h to reduce body displacement from 0.070 m to 0.056 m and its acceleration from 3.50 m/s2 to 1.35 m/s2, thereby a complete damping of the oscillatory process of masses is achieved already in the fourth period, and in the case of movement over a sinusoidal bump the oscillatory process is stabilized to a large extent, the wheel copies the profile of the bump, as a result, body displacement decreases from 0.045 m to 0.030 m, and body acceleration after the transition process decreases from 2.2 m/s2 to 0.8 m/s2. The analysis of evaluation of the influence of smooth running on static transverse stability of the machine has shown that as a result of taking into account the elastogemphing characteristics of the shock absorber and the pneumatic tires themselves, it is possible to increase the angle of static stability on lateral overturning from 38° to 43° at the maximum allowable angle of body roll of 8.4°. CONCLUSIONS: The knowledge of methods of estimation of influence of smoothness of running of transport-technological machines on the main indicators of traffic safety in off-road conditions allows to analyze the efficiency of application of the proposed technical solutions aimed at increasing the smoothness of running of the machine in off-road conditions.

Investigation of the spatial distribution of deformations in quartz piezo elements by x-ray topography

Using X-ray topography on laboratory and synchrotron X-ray sources, the distribution of deformations in the volume of two types of AT-cut quartz resonators of different sizes were obtained. From a comparison of X-ray data and the amplitude-frequency characteristics of the resonators, a correlation between the deformation patterns and the features of oscillatory processes for operating modes and their harmonics, as well as for parasitic modes, was established. A connection between oscillations in parasitic modes, which manifest themselves in the amplitude inhomogeneity, and the topology of the resonators is found. The applied significance of the obtained results for the development and optimization of new designs of piezoelectric elements and the development of their manufacturing technology is noted.

The cyanobacterial circadian clock couples to pulsatile processes using pulse amplitude modulation.

Cellular processes are dynamic and often oscillatory, requiring precise coordination for optimal cell function.1,2,3,4,5,6,7 How distinct oscillatory processes can couple within a single cell remains an open question. Here, we use the cyanobacterial circadian clock8,9 as a model system to explore the coupling of oscillatory and pulsatile gene circuits. The cyanobacterial circadian clock generates 24-h oscillations in downstream targets10,11,12,13,14,15 to time processes across the day/night cycle.9,16,17,18,19,20,21,22 This timing is partly mediated by the clock's modulation of the activity of alternative sigma factors,14,23,24,25 which direct RNA polymerase to specific promoters.26 Using single-cell time-lapse microscopy and modeling, we find that the clock modulates the amplitude of expression pulses of the alternative sigma factor RpoD4, which occurs only at cell division. This pulse amplitude modulation (PAM), analogous to AM regulation in radio transmission,27 allows the clock to robustly generate a 24-h rhythm in rpoD4 expression despite rpoD4's pulsing frequency being non-circadian. By modulating cell division rates, we find that, as predicted by our model, PAM regulation generates the same 24-h period in rpoD4 pulse amplitude over a range of rpoD4 pulse frequencies. Furthermore, we identify a functional significance of rpoD4 expression levels: deletion of rpoD4 results in smaller cell sizes, whereas an increase in rpoD4 expression leads to larger cell sizes in a dose-dependent manner. Thus, our work reveals a link between the cell cycle, clock, and RpoD4 in cyanobacteria and suggests that PAM regulation can be a general mechanism for biological clocks to robustly modulate pulsatile downstream processes.

Consideration of ways to improve the efficiency of deep well drilling

The object of the research is the composition of the bottom of the drill string when installing screw amplifiers. One of the biggest problems is the place of installation of the screw amplifier in the arrangement of the bottom of the drill string and its influence on the dynamic properties of the rock-crushing tool. The results of the study of the influence of the use of a screw amplifier on the efficiency of drilling deep wells were obtained. According to the results of research, it was determined in particular that the imposition of vibrations often causes a change in the nature of the interaction of the bit with the hole rock, therefore, the installation of the amplifier at different points of the layout will have different effects on the drilling performance. It is shown that the kinetic energy accumulated by the weighted drill pipes, when the amplifier is installed above the bit, is transmitted through the screw mechanism to the rock-destroying tool (bit) and is an operation that leads to an increase in drilling performance. Thanks to the conducted research, it has been proven that the property of the drill string elements and the disturbances of the oscillatory processes of various nature acting on them are related to the dynamic loading of its elements due to the installation of the amplifier in different places of the layout of the bottom of the string. This is due to the fact that the proposed screw amplifier is used with a friction fuse, which causes the rotary movement of the screw under the action of the torque and the translational movement of the nut together with the overbit mass attached to the bit. In most practical cases, especially during deep drilling, bits fail due to the destruction of the rolling bearings of the roller bit, which leads to jamming of the roller bit and leaving them in the holes. For practical use, the proposed design uses a friction fuse, which connects the bit to the drill pipe column through an elastic element. Analytical studies and performed calculations show that this screw amplifier will effectively ensure the destruction of any rocks, especially during overloads without slippage of reaches and be used for the construction of wells in native mining and geological conditions.

Математическое моделирование бипланетарного механизма для привода смесительных машин

A study on the development of a kinematic scheme of a planetary mechanism with an opening kinematic circuit for driving the working body of mixing machines is presented. The main purpose of the study is to create two kinematic cycles in the planetary mechanism, in which, during one revolution, the satellite drivers consistently perform movements of the epicyclic trajectory of hypocyclic motion. To achieve this goal, braking devices for damping the kinematic energy of satellites and synchronizer devices were used in the transition zones between two segments of different names, for smooth entry of the satellite gear into the gear engagement of these gears. The oscillatory process of the synchronizer at the entrance of the tooth of the satellite gear with the front teeth of the synchronizer is considered. Practical significance includes ensuring the possibility of assembling a planetary mechanism, taking into account the choice of the angle of rotation of the synchronizer around the axis of the support. The discussion makes recommendations for further improvement of the developed biplanetary mechanism for driving mixing machines.

Numerical Simulation of “Submachinegun - Grenade Launcher” Dynamic System

In modern small arms, one of the most important technical characteristics is the survivability of barrel, which greatly affects the competitiveness of the product on the market. The task of increasing the survivability of the barrel of automatic small arms has not yet lost its relevance. Based on the modern nature of combat and the multitasking of combat operations, complexes of manual automatic weapons with the use of various external devices, such as sighting devices of various designs, under-barrel grenade launchers, low-noise shooting devices, etc., are currently being developed on the basis of a single reference sample. When designing new samples, several approximated mathematical models are currently used, that do not take into account the impact of external devices on the dynamic and oscillatory processes occurring during firing from modern hand-held automatic weapons. This article describes a physical and mathematical model of the dynamic interaction of an under-barrel grenade launcher and small arms (submachine gun), demonstrates a computational mathematical model for different types and methods of securing a device such as an under-barrel grenade launcher. The optimal computational model is revealed, allowing to describe the dynamic process of interaction of the system elements in the numerical simulation of the shot. Advantages and disadvantages have been identified, on the basis of which the goals and objectives of further work have been determined, consisting in studying the influence of external devices on the parameters of the barrel of automatic small arms, in order to improve the operational, tactical and technical characteristics of automatic small arms systems based on the development of a numerical and analytical approach, and a modular mathematical model of automatic small arms weapons.

PERIODIC ATEB-FUNCTIONS AND THE VAN DER POL METHOD FOR CONSTRUCTING SOLUTIONS OF TWO-DIMENSIONAL NONLINEAR OSCILLATIONS MODELS OF ELASTIC BODIES

In the process of operation, the simplest elements (hereinafter elastic bodies) of machines and mechanisms under the influence of external and internal factors carry out complex oscillations ‒ a combination of longitudinal, bending and torsion combinations in various combinations. In general, mathematical models of the process of such complex phenomena in elastic bodies, even for one-dimensional calculation models, are boundary value problems for systems of partial differential equations. A two-dimensional mathematical model of oscillatory processes in a nonlinear elastic body is considered. A method of constructing an analytical solution of the corresponding boundary-value problems for nonlinear partial differential equations is proposed, which is based on the use of Ateba functions, the Van der Pol method, ideas of asymptotic integration, and the principle of single-frequency oscillations. For "undisturbed" analogues of the model equations, single-frequency solutions were obtained in an explicit form, and for "perturbed" ‒ analytical dependences of the basic parameters of the oscillation process on a small perturbation. The dependence of the main frequency of oscillations on the amplitude and non-linearity parameter of elastic properties in the case of single-frequency oscillations of "unperturbed motion" is established. An asymptotic approximation of the solution of the autonomous "perturbed" problem is constructed. Graphs of changes in amplitude and frequency of oscillations depending on the values of the system parameters are given.

Synthesis of uniformly distributed optimal control with nonlinear optimization of oscillatory processes

In the article the problem of synthesizing uniformly distributed optimal control for nonlinear optimization of oscillatory processes described by integro-differential partial differential equations with the Volterra integral operator was explored. The study was conducted according to the Bellman-Egorov scheme and an algorithm for constructing a uniformly distributed optimal control in the form of a functional from the state of the controlled process was developed. Sufficient conditions for the solvability of the synthesis problem in nonlinear optimization were established.

Study of the State Primary Measurement Standard of the Unit of Phase Shift Angle Between Two Voltages

Phase measurements are necessary for determining main parameters of the oscillatory process in complex electrical networks. Most often, it is precisely the phase shift angle (PSA) between two oscillatory processes of the same frequency that is measured. An essential indicator of the quality of electrical energy is the coefficient of asymmetry in a three-phase electrical network, which depends on the load of consumers in this network. This indicator is affected by a short circuit between two phase voltages. Phase measurement standards, phase meters, and phase converters are included in the measuring equipment for phase measurements. They are widely used in such fields as radiolocation, radio navigation, non-destructive testing, radio engineering, telecommunications, acoustics, metallurgy, machine and aircraft industry, space industry, as well as in scientific research and defence. The State Measurement Standard of Ukraine of the PSA unit between two voltages in the frequency range from 0.01 Hz to 10 MHz is maintained at the State Enterprise “UKRMETRTESTSTANDARD”, Kyiv. It provides metrological traceability of phases measured in the country. The main components of the standard were calibrated at the PTB, the National Metrology Institute of Germany. In Ukraine, numerous measurement standards and measurement instruments for phase measurements (more than 500.000 units) are used, in particular, phase calibrators, phase meters, phase shifters, synchronoscopes etc. Regular study of metrological characteristics of the DETU 09-07-11 measurement standard is conducted both in the main (from 5 Hz to 200 kHz) and in the extended (from 0.01 Hz to 10 MHz) frequency range. The PSA values obtained as a result of the research in the main frequency range do not exceed 0.001° (which is maximum according to measurements at all calibration points 0.00015°), and in the extended frequency range – 0.01° (which is maximum according to measurements at all calibration points 0.0053°). To eliminate the systematic measurement uncertainty component of the phase measurement standard, a special calibration is regularly performed using a set of resistive and capacitive phase bridges.

Динамическая модель харвестера, оснащенного канатной анкерной системой, при проведении лесозаготовительных работ на крутом склоне

The efficiency of using logging machines for work in mountainous or hilly areas characterized by the presence of steep slopes depends on many factors, among which the quantitative parameters of the dynamic state of both the harvester itself and the anchor system play a priority role to ensure the safe operation of these technological machines. This article considers a complex spatial dynamic model that combines into a common interconnected system all the main components of the simulated phenomenon, including directly a harvester with a hydraulic manipulator mounted on it, a movable assortment in space, an anchor system consist-ing of an anchor rope and a winch, an anchor tree for attaching an anchor rope and the soil of the support surface. The dynamic mathematical model of such a six-component system includes 35 generalized coordinates that determine the linear and angular displacements of the mass centers of the listed system components. A system of 35 differential equations constructed using the Lagrange’s equation was solved by the 4-th-order Runge-Kutta method. For this purpose, a computer program has been developed, the description of which is contained in the article. In relation to the basic version of the simulated system with quantitative initial characteristics focused on the characteristics of a three-axle wheeled harvester with a 6K6 wheel formula, calculations of oscillatory processes for dynamic parameters determining the loading of the anchor system and the safety of harvester operation in the process of assortment manipulation were carried out.

The cognitive triad network - oscillation - behaviour links individual differences in EEG theta frequency with task performance and effective connectivity

We reconcile two significant lines of Cognitive Neuroscience research: the relationship between the structural and functional architecture of the brain and behaviour on the one hand and the functional significance of oscillatory brain processes to behavioural performance on the other. Network neuroscience proposes that the three elements, behavioural performance, EEG oscillation frequency, and network connectivity should be tightly connected at the individual level. Young and old healthy adults were recruited as a proxy for performance variation. An auditory inhibitory control task was used to demonstrate that task performance correlates with the individual EEG frontal theta frequency. Older adults had a significantly slower theta frequency, and both theta frequency and task performance correlated with the strengths of two network connections that involve the main areas of inhibitory control and speech processing. The results suggest that both the recruited functional network and the oscillation frequency induced by the task are specific to the task, are inseparable, and mark individual differences that directly link structure and function to behaviour in health and disease.

The study of forced oscillations in the non-linear system of an individual traction drive

BACKGROUND: The processes taking place in the ‘traction electric drive – wheel – road’ system during acceleration and braking cause increased dynamic loads on drive components, which may lead to a breakdown. Therefore, it is important to control the drive in a way to minimize and to suppress the given processes. To make it possible, the control system is to be equipped with a resistance torque observer at the electric motor shaft. In addition, in any system, there is a heighten interest in study of arise of resonances, which come with abrupt increase of oscillations amplitudes. Therefore, the features of oscillation phenomena in the given non-linear system are to be studied. AIM: Identification of the peculiarities of oscillatory processes, resonance phenomena in the systems of electromechanical drive of vehicles, which are nonlinear technical systems. METHODS: The study of features of the oscillating processes and the study of capabilities of arise of resonant phenomena were conducted using analysis of the differential equations system describing the operation of the non-linear system. RESULTS: The features of the oscillating phenomena in non-linear systems of interaction between an elastic wheel and road as well as capabilities of arise of resonant phenomena were considered. It is defined that arise of the resonant phenomena in the considered systems is not possible due to breakdown of them. The behavior of modes of interaction between an elastic wheel and road during intensive acceleration and braking was analyzed. The abrupt shock behavior of change rate of wheel torque and current consumed by a drive as well as features of lowering of them when using the self-oscillating phenomena suppression were found. CONCLUSION: The practical value of the study lies in ability of using the proposed conclusions at development of units of a traction electric drive and at synthesis of vehicle motion control systems.

Study of the Synchronization and Transmission of Intracellular Signaling Oscillations in Cells Using Bispectral Analysis.

The oscillation synchronization analysis in biological systems will expand our knowledge about the response of living systems to changes in environmental conditions. This knowledge can be used in medicine (diagnosis, therapy, monitoring) and agriculture (increasing productivity, resistance to adverse effects). Currently, the search is underway for an informative, accurate and sensitive method for analyzing the synchronization of oscillatory processes in cell biology. It is especially pronounced in analyzing the concentration oscillations of intracellular signaling molecules in electrically nonexcitable cells. The bispectral analysis method could be applied to assess the characteristics of synchronized oscillations of intracellular mediators. We chose endothelial cells from mouse microvessels as model cells. Concentrations of well-studied calcium and nitric oxide (NO) were selected for study in control conditions and well-described stress: heating to 40 °C and hyperglycemia. The bispectral analysis allows us to accurately evaluate the proportion of synchronized cells, their synchronization degree, and the amplitude and frequency of synchronized calcium and NO oscillations. Heating to 40 °C increased cell synchronization for calcium but decreased for NO oscillations. Hyperglycemia abolished this effect. Heating to 40 °C changed the frequencies and increased the amplitudes of synchronized oscillations of calcium concentration and the NO synthesis rate. The first part of this paper describes the principles of the bispectral analysis method and equations and modifications of the method we propose. In the second part of this paper, specific examples of the application of bispectral analysis to assess the synchronization of living cells in vitro are presented. The discussion compares the capabilities of bispectral analysis with other analytical methods in this field.

Kinematic mechanics study of silicon wafers and glass particles oscillatory separation based on friction coefficient differences

In this paper, the static friction coefficient of different particle sizes silicon wafers, glass particles and separation platform are measured by the plane method. Based on the force analysis of particle oscillatory separation process, the kinetic equation of particle oscillatory separation process is established, and the influence of factors such as particle size and friction coefficient on the motion trajectory of particle oscillatory separation process is analyzed. The research results indicate that the range of static friction coefficients between silicon wafers, glass particles, and separation platforms is different, but there are also overlapping parts. The kinetic equation indicates that the motion speed of particle oscillatory separation process is affected by factors such as the friction coefficient between particles and separation platforms, the inclination angle of separation platforms, and the amplitude of separation platforms. During the oscillatory separation process of silicon wafer glass mixed particles, silicon wafer particles with friction coefficients of 0.33–0.39 will become silicon wafer products, glass particles with friction coefficients of 0.22–0.31 will become glass products, and silicon wafer glass particles with overlapping friction coefficients of 0.310.33 will become intermediate products. To achieve better separation of silicon wafer and glass particles in the oscillatory separation process, it is necessary to take control measures to reduce the friction coefficient between the separation platform and silicon wafer and glass particles as much as possible.

Об идентификации характеристик неоднородных вязкоупругих тел в рамках модели дробного порядка

Nowadays, the development of models of viscoelastic materials with complex inhomogeneous structure is one of the hottest problems of continuum mechanics. Along with classical models, fractional-differential models of viscoelasticity have become increasingly popular. In this paper, we present a model for describing steady-state oscillations of inhomogeneous viscoelastic bodies in terms of fractional-order differential operators. Taking into account the fractional order of the model operators, the corresponding form of the complex module describing the material properties is constructed. The module includes four characteristics: instantaneous and long-term elastic moduli (in the case of material inhomogeneity, they are the functions of coordinates), relaxation time and fractionality parameter. The properties of the complex module are studied, and the ranges of the model parameters, at which the rheological properties are most pronounced, are identified. A general formulation of the inverse problem (IP) on the identification of function-parameters of the model based on the acoustic sounding data is proposed. In the framework of this formulation, the inverse problems for specific objects , namely, an inhomogeneous rod and a round plate, are considered. In both model problems, the influence of the fractionalization parameter on the amplitude-frequency characteristics is analyzed. It has been found that in the vicinity of viscoelastic resonances the fractionality parameter affects the parameters of the oscillatory process most significantly, which is typical for such problems. A solution to the nonlinear IPs under consideration is constructed based on the linearization method, which also serve as basis for the iterative processes supplemented with the elements of the projection approach. This allows one to determine corrections to the required functions in the specified classes of functions using regularization. For both IPs, a series of computational experiments were carried out. The analysis of the experimental results made it possible to formulate recommendations for the selection of optimal sensing modes.

Математическое моделирование волнового поля методом конечных разностей

The system of differential equations of hydrodynamics is reduced to the inhomogeneous wave equation, for which a discrete model is constructed. The computational domain is a rectangle covered with a two-dimensional uniform calculation grid. Discrete analogues of the wave equation for Dirichlet and Neumann boundary conditions were developed. The paper describes the choice of calculation grids. Analytical expressions describing the approximation error in spatial coordinate directions for the second derivative operator based on the second and fourth order of accuracy schemes were obtained and, in this range of error, the sizes of grids were estimated. The computational experiments demonstrated that, to keep the calculation error in the specified limit 0.1- 1%, it is necessary to perform calculations on grids with the number of nodes per half wavelength in the range from 9 to 30 when using the second-order of accuracy scheme, and from 4 to 6 when using the fourth-order of accuracy scheme. It is important to choose the values of the time step and the weight parameter. At the weight parameter σ =1/12, the relative error is significantly less than at σ =0 (corresponding to an explicit scheme) and at σ =1/4 (corresponding to a symmetrical setting of coefficients in a weight scheme). The optimal values of the weight parameter were calculated in the context of maintaining the propagation frequency of oscillatory processes. The analysis of the discrete model gave a condition for the stability of the difference scheme, and an expression describing the approximation error in a time variable, depending on time steps and spatial coordinate directions, was determined. It was established that the approximation of initial conditions makes a smaller contribution to the total error than the approximation of the equation for subsequent time layers. Based on the proposed algorithms and approaches, a software package was designed to simulate the propagation of vibrations in a two-dimensional computational domain. A number of computational experiments were carried out to study, for example, the propagation of acoustic waves from antennas with different directional characteristics and the scattering of waves on the obstacles of different types. To determine the farfields of an acoustic antenna, it is proposed to make the calculation window movable and to find its location in space. This significantly reduces the calculation time for the propagation of sound waves over long distances.

Modeling evolutionary power spectral density functions of strong earthquakes via copulas

This paper proposes a new approach for analyzing seismic accelerograms using the evolutionary Power Spectral Density function (EPSD). The accelerogram of an earthquake can be accurately modeled and simulated from its spectrogram, based on the oscillatory stochastic processes theory. To adequately characterize a spectrogram that is consistent with the response spectra, a parametric model with 16 parameters is proposed. This model describes the square of the amplitude spectrum, an envelope of the square of the accelerogram, and a copula that constructs a time–frequency model from the time and frequency marginals. The use of copulas to model a bivariate probability distribution is a common practice in statistics, particularly when the marginal distributions are known. The periodogram can be viewed as an unnormalized probability density function, where the total energy serves as the normalization constant, since the total energy of a seismic motion is always finite. Additionally, a reduced model consisting of only 10 parameters is presented, which may be especially valuable when only shear wave effects are relevant.

Intermediate scattering function for polymer molecules: An approach based on relaxation mode analysis.

The theory of polymer dynamics describes the intermediate scattering function for a polymer molecule in terms of relaxation modes defined by normal coordinates for the corresponding coarse-grained model. However, due to the difficulty of defining the normal coordinates for arbitrary polymer molecules, it is generally challenging to express the intermediate scattering function for a polymer molecule in terms of relaxation modes. To overcome this challenge, we propose a general method to calculate the intermediate scattering function for a polymer molecule on the basis of a relaxation mode analysis approach [Takano and Miyashita, J. Phys. Soc. Jpn. 64, 3688 (1995)]. In the proposed method, relaxation modes defined by eigenfunctions in a Markov process are evaluated on the basis of the simulation results for a polymer molecule and used to calculate the intermediate scattering function for that molecule. To demonstrate the effectiveness of the present method, we simulate the dynamics of a linear polymer molecule in a dilute solution and apply it to the calculation of the intermediate scattering function for the polymer molecule. The evaluation results regarding the relaxation modes reasonably describe the intermediate scattering function on the length scale of the radius of gyration of the polymer molecule. Accordingly, we examine the contributions of the pure relaxation and oscillatory relaxation processes to the entire intermediate scattering function.

Determination of the characteristics of drill string vibrations during the drilling process

The object of research is vibration processes of a certain origin in the drill string with typical design deviations depending on the mode parameters of drilling. A drill string is an oscillating system with an infinite number of degrees of freedom of a multifactor system. An exhaustive study of oscillatory processes in the drill string is impossible neither analytically nor experimentally, due to the specifics of the hole deepening in various rocks, the design of the well, its shape, etc. Therefore, in practice, they try to solve the problems of the dynamics of the drill string for an idealized system and, while preserving the main oscillatory properties, solve some problems of the rod system. The work carried out was aimed at experimental studies of vibrations of the drill string during the drilling process. It is shown that the effectiveness of the use of hydrodynamic cavitation requires the development of methods and devices for intensifying the well drilling process. It is proven that the design of the cavitation generator organically fits into the existing well drilling equipment and allows for the intensification of technological processes with lower specific energy consumption. It is found that all oscillatory processes that occur in the drill string are random in nature and must be considered using the mathematical apparatus of the theory of random oscillations. The study of vibrations during well drilling shows that vibrations can be considered as random stationary processes, since transient modes have a sufficiently short duration for homogeneous rocks with fixed drilling modes. The analysis of the vibrations of the drill string elements based on random oscillations in a number of cases allows to increase the reliability of determining the vibration reliability of the drill string elements. It has been proven that the response of drill string elements to broadband random vibration can be defined as the combined effect of several narrowband random vibrations.

Assessment of Dynamic States of Railway Vehicles: Structural Mathematical Modeling

Introduction. The speed rise of railway transport and an increase in the loads on the axles of wheelsets necessitate the modernization of the existing fleet. Scientific studies in the field of rolling stock dynamics are aimed at taking into account the oscillatory processes that occur during the movement of railway vehicles in a traditional design. The attachment of supplementary elements was considered at the coupling level of two cars and the attachment of a third trolley in the center of gravity of the railway platform. The scientific literature has not paid enough attention to the construction of mathematical models that make it possible to assess the dynamic states of such constructive solutions. The objective of this study is to create a method for evaluating the dynamic conditions of a car. The situation is considered when an additional set of mass-inertial and elastic elements is introduced into its structure, and the general dynamic condition of the vehicle depends on the adjustment of their parameters.Materials and Methods. The basic research tool is the structural mathematical modeling, which is based on an approach where the source design scheme is a mechanical oscillatory system in the form of a solid body on elastic supports with supplementary typical elements introduced into its structure. The dynamic analogue of the calculation scheme used is the block diagram of the automatic control system, the use of which provides detailing the connections between typical elastic and mass-inertia elements.Results. A method for estimating the dynamic states of railway vehicles is proposed. It is based on the construction of mathematical models, taking into account the introduction of an additional structure of mass-inertia and elastic elements. The impact of additional parameters on the dynamic condition of the vehicle is investigated. Analytical relations have been obtained that provide reducing the dynamic loads on the major structural elastic elements when changing the corresponding parameters of a technical object. The transfer function of interpartial relations is given, which provides controlling the interaction between the coordinates of the vehicle movement under the action of two kinematic disturbances of the in-phase type.Discussion and Conclusion. The generated mathematical model provides for assessment, monitoring and control of the dynamic state of the vehicle under conditions of kinematic disturbances. The research results can be used to modernize existing vehicles and create new ones with improved dynamics.