Oscillations Of Mechanical Systems Research Articles

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.

Nonlinear feedback synthesis and control of periodic, quasiperiodic, chaotic and hyper-chaotic oscillations in mechanical systems

Nonlinear feedback synthesis and control of periodic, quasiperiodic, chaotic and hyper-chaotic oscillations in mechanical systems

Системный подход в оценке динамических состояний технических объектов: элементы концепции динамических инвариантов

The scientific and methodological base is being developed within the framework of systems theory and system analysis in application to the tasks of assessment, control and formation of dynamic states of technical objects, the design schemes of which are mechanical oscillatory systems with concentrated parameters. In the context of the fundamental problems of the theory of system studies of forced movements under deterministic disturbances there are considered the problems, whose solutions are aimed at developing a methodological approach to assessing the dynamic states of technical objects operating under coherent vibration loads. The purpose of the study is to develop a method for evaluating, controlling and forming dynamic states of the objects under harmonic force loads. It is assumed that mechanical oscillatory systems formed by a solid body performing small steady-state oscillations relative to the position of the static equilibrium can be used as calculation schemes of the technical objects. To construct mathematical models, Lagrange formalism, Laplace integral transformations taking into account zero conditions and structural methods are used, which make it possible to consider mechanical oscillatory systems as dynamically equivalent structural schemes of automatic control systems. The dynamic state of an object is assessed by using a transfer function, which in the physical sense represents the interpretation of a dynamic compliance. The amplitude-frequency characteristics used to assess the dynamic state of the object present a parametric family, for which the first parameter is the coefficient of connectivity of external force disturbances, and the second parameter is the coordinate of the point for which the dynamic accuracy is defined. An infinite family of amplitude-frequency characteristics is regularized due to the introduction of dynamic invariants, which can be considered as generalized dynamic states of mechanical oscillatory systems. To determine the dynamic invariants of a family of amplitude-frequency characteristics, taking into account two parameters, a map of dynamic invariants is constructed, which divides the plane of parameters into disjoint sets using boundaries. A theorem is proved to determine the explicit analytic expressions of these boundaries.

РАЗВИТИЕ РЫЧАЖНЫХ ПРЕДСТАВЛЕНИЙ В ОЦЕНКЕ ДИНАМИЧЕСКИХ СОСТОЯНИЙ МЕХАНИЧЕСКИХ КОЛЕБАТЕЛЬНЫХ СИСТЕМ В УСЛОВИЯХ СВЯЗНЫХ ВИБРАЦИОННЫХ НАГРУЖЕНИЙ

The article presents a frame of a systematic approach to assessment, control, and formation of dynamic states based on the concept of level ties of elements of technical objects subjected to connected vibrational loadings. The methodological basis of the study comprises structural mathematical modeling that allows for a comparison of mechanical oscillatory systems, which are used as computational models for tech-nical objects, with structural schemes of automated operating systems that are equivalent to dynamic relations. A level interpretation of total generalized dynamic states is designed for mechanical oscillatory systems created with solid body with three degrees of freedom. Their significant features are reflected in the number of reso-nances, modes of oscillation amplitude setting to zero, and definite form of dynamic interactions. Based on the level ties, a system of general concepts is developed to depict the role of connection of vibrational loadings in creating border dynamic states of mechanical oscillatory systems. The results consist of analytical equations, graphical images, and numerical experiments.

Application of modern interactive technologies for the analysis of complex mechanical processes and oscillatory systems

Application of modern interactive technologies for the analysis of complex mechanical processes and oscillatory systems

Maps of dynamic invariants in the estimation of modes of motion of mechanical oscillatory systems

Maps of dynamic invariants in the estimation of modes of motion of mechanical oscillatory systems

A technology of structural mathematical modelling for engineering objects under vibrational loading: Interaction forms and dynamic invariants

We present a system approach to evaluating dynamic forms of interactions between elements of mechanical oscillatory systems, which can be applied as design diagrams of engineering objects used for transport or technology purposes. The approach of structural mathematical modelling was used, where a mechanical oscillatory system (with the finite number of freedom degrees) is compared to the block diagram of a dynamically equivalent automatic control system. The research object was represented by a family of mechanical oscillatory systems with the finite number of freedom degrees under the action of connected force harmonic disturbances. The main research focus was on a set of dynamic states of an engineering object, which are caused by the application of common-phase external force disturbances at various frequencies and characterised by a connection coefficient. For a family of chain mechanical oscillatory systems with two degrees of freedom, a method for interpreting a set of dynamic states in the form of oriented graphs was developed. A method for constructing a population graph of dynamic states based on the frequency response of system transfer functions was developed. Within the framework of the developed interpretation, the graphs of dynamic states can be considered as peculiar invariants that persist on sets of mechanical oscillatory system parameters. Using the methodology of structural mathematical modelling, a concept of dynamic invariants was developed, according to which the totality of dynamic invariants can be used to provide a general evaluation of the variety of dynamic states and forms of dynamic interactions between the elements of mechanical oscillatory systems. The proposed concept of dynamic invariants extends the methodology of structural mathematical modelling in relation to the problems of system analysis for ensuring the safety of engineering objects for transport and technology purposes under the conditions of connected vibrational loading.

Factor relationship of kinetics of nonequilibrium processes in vegetable oil when cleaning the filter installation surface for regeneration of vegetable oil

When processing oilseeds, technologies are needed to obtain valuable vegetable oils by pressing with a long shelf life. Existing technologies for cleaning vegetable oils in small enterprises do not allow cleaning the oil from all undesirable substances and therefore the oils have a short shelf life, quickly oxidize and lose their presentation. The article theoretically substantiates the design parameters of a directional ultrasonic and mechanical oscillatory system for cleaning the filtration surface of the installation from accumulated solid particles in the oil.

Problem of Vibration Damping in Mechanical Systems: System Analysis, Modeling, Control

System approaches are being developed in the problems of dynamics of transport and technological machines related to the provision of dynamic vibration damping modes and the identification of a number of specific effects characteristic of technical objects with working bodies representing solids. The methods of structural mathematical modeling are used, in which a mechanical oscillatory system, considered as a design scheme of a technical object, is compared with a structural scheme, equivalent in dynamic terms, of an automatic control system. It is shown that the modes of dynamic damping are realized through the fixation of fixed points called centers of rotation (or oscillations). A method is proposed for the analytical evaluation of the possibilities of forming dynamic states based on the use of generalized feedback transfer functions, coefficients of motion connectivity by coordinates, forms of dynamic interaction of system elements under the simultaneous action of two harmonic excitations. Within the framework of the interpretation under consideration, the key characteristic of a mechanical oscillatory system is the characteristic frequency equation and its transformations. The development of ideas about the form of dynamic interactions of elements of a mechanical oscillatory system is proposed. The concept of form generalizes ideas about the directions of change in time of the coordinate of a system element in relation to a change in an external force or kinematic excitation. The methodology for displaying a set of dynamic states and forms of dynamic interaction of elements of a mechanical oscillatory system based on oriented graphs is proposed.

Системные подходы в оценке динамических состояний механических колебательных систем: технология структурных преобразований

A scientific and methodological base is being developed in the direction of systems analysis and systems theory as applied to the problems of assessing the dynamic states of technical objects, the design schemes of which are represented by mechanical oscillatory systems with one or more degrees of freedom. Within the framework of the proposed approach, a mechanical oscillatory system is compared with a dynamically equivalent structural diagram of an automatic control system. Based on the concepts of objects, whose dynamic properties are estimated, on the external force and kinematic influences, typical elementary links, negative feedbacks, transfer functions and dynamic modes of mechanical oscillatory systems, a new technique is proposed, taking into account the motion transformation devices. On the basis of the developed approach there are obtained the new data on the dynamic properties of systems that include links with reduced elastic characteristics. The possibilities of creating a number of new dynamic effects in mechanical oscillatory systems reflecting the specificity of the vibration interaction of the elements of oscillatory structures are considered

Mathematical Modeling of Stress in Circuit Cards Represented by Mechanical Oscillatory Systems

Mathematical Modeling of Stress in Circuit Cards Represented by Mechanical Oscillatory Systems

Balanced data assimilation for highly oscillatory mechanical systems

Data assimilation algorithms are used to estimate the states of a dynamical system using partial and noisy observations. The ensemble Kalman filter has become a popular data assimilation scheme due to its simplicity and robustness for a wide range of application areas. Nevertheless, the ensemble Kalman filter also has limitations due to its inherent Gaussian and linearity assumptions. These limitations can manifest themselves in dynamically inconsistent state estimates. We investigate this issue in this paper for highly oscillatory Hamiltonian systems with a dynamical behavior which satisfies certain balance relations. We first demonstrate that the standard ensemble Kalman filter can lead to estimates which do not satisfy those balance relations, ultimately leading to filter divergence. We also propose two remedies for this phenomenon in terms of blended time-stepping schemes and ensemble-based penalty methods. The effect of these modifications to the standard ensemble Kalman filter are discussed and demonstrated numerically for two model scenarios. First, we consider balanced motion for highly oscillatory Hamiltonian systems and, second, we investigate thermally embedded highly oscillatory Hamiltonian systems. The first scenario is relevant for applications from meteorology while the second scenario is relevant for applications of data assimilation to molecular dynamics.

Influence of inertial links on the distribution of vibration amplitudes of points of the working body of a technological vibrating

Features of problems of dynamics and formation of dynamic states of working bodies of vibrating technological machines are considered. The purpose of the work is to develop a method for constructing mathematical models of vibration machines that provide the ability to evaluate, control and adjust the forms of movement of working bodies by introducing additional links into the structure of the system, forming a closed internal contour. Methods of structural mathematical modeling are used in the construction of original structural formations of their typical elements. The direction of constructive and technical solutions in the implementation of approaches to configure and adjust the structure of the vibration field of the working body is proposed. The method is implemented using the analytical apparatus of the automatic control theory. The features of dynamic states formation based on the application of transfer functions of structural mathematical models of mechanical oscillatory systems are studied. The use of transfer functions of interpartial connections for the formation of vibration fields of working bodies is proposed. Analytical relations are obtained that determine the possibility of implementing specific dynamic modes, including the decoupling of movements by individual coordinates, taking into account the features of the connectivity of movements by characteristic points of the working body, the manifestation of oscillation nodes or modes of dynamic damping. Features of using structural mathematical modeling methods in problems of dynamics of mechanical oscillatory systems with additional connections are discussed. The work is aimed at specialists in the field of theoretical and applied mechanics, machine science and mechanical engineering.

Особенности системных представлений о динамике механических колебательных структур при несимметричных связях

The paper is devoted to a new approach to the formation of the methodological basis of system analysis in application to problems of the dynamics of mechanical oscillatory systems taking into account the forces of viscous friction. A mechanical oscillatory system with two mass-inertia elements connected to the support surfaces and to each other by elastic-dissipative elements is considered. A method for estimating the free movements of a mechanical oscillatory system is developed based on the characteristics expressed in terms of the parameters of the lever connections between the partial blocks in the form of a gear ratio. Mathematical models are built on the basis of Lagrange formalism, algebraic methods, and the theory of functions of a complex variable. A matrix method is proposed for constructing frequency functions and damping functions for mechanical oscillatory systems with two degrees of freedom based on the ratio of the potential and kinetic energy of the system, taking into account the forces of viscous friction. For a mechanical system in which the connection of elements with a single reference surface is reset, a graphic analytic analysis of the extreme properties of the corresponding frequency functions and damping functions is performed. A topological approach is proposed.

НОВЫЕ ПОДХОДЫ К ОЦЕНКЕ СОСТОЯНИЯ ГРУЗОВЫХ ВАГОНОВ ПРИ ДВИЖЕНИИ НА СОРТИРОВОЧНЫХ УСТРОЙСТВАХ НА ОСНОВЕ СИСТЕМНОГО АНАЛИЗА И МАТЕМАТИЧЕСКОГО МОДЕЛИРОВАНИЯ

The paper develops methods of system analysis and technologies for control dynamic conditions of technical means of railway transport. Methods of structural mathematical modeling are used, within the framework of which the design scheme of the object, considered as a mechanical oscillatory system with several degrees of freedom, is interpreted as a dynamically equivalent automatic control system. The problems of the dynamics of the coupling of two freight railway carriages with two variants of its rigidity (conventional and rigid hinge-type fastening) are considered. It is shown that with a certain choice of the values of the moments of inertia of the railway carriages and the parameters of the location of the center of mass, it is possible to solve the problems of motion stabilization. Concepts are proposed for the experimental determination of the moment of inertia and coordinates of the center of mass of the railway carriage when rolling the cars off the marshalling hump and passing a special measuring station. Algorithms for determining the values of the parameters of the center of mass of the railway carriage and the values of the moment of inertia are proposed.

Possibilities of Using Frequency Energy Functions in Problems of Dynamics of Machines for Transport and Technological Purposes

New approaches to the evaluation of the dynamic properties of mechanical vibration systems are proposed, which consider as the design schemes for technical objects operating under dynamic vibration loads. The purpose of the study is to develop ideas for the use of frequency energy functions. In this case, the frequency functions represent the ratio of the potential and kinetic energies in a specific form, based on the use of the relations of the coordinates of the system in the stationary mode. The technologies of system analysis and structural mathematical modeling are used. In this approach, the mechanical oscillatory system is correspond with the block diagram of the automatic control system, which is equivalent in dynamic terms. It is proposed to use the analytical apparatus to take into account the features of interpartial relations, to evaluate the specific modes of dynamic interaction of system elements. A method for determining the natural vibration frequencies of the system based on the use of the frequency energy function is proposed. Methodological bases of approaches to solving problems of system dynamics related to the assessment of the influence of system parameters on their frequency properties are developed. The results of computational modeling are presented.

Frequency function and damping function in assessment of dynamic processes in mechanical oscillatory systems with symmetry

Introduction. A new approach to the formation of the methodological basis of system analysis in the application to the problems on mechanical oscillatory structure dynamics is considered. The study objective is to develop a method forevaluating properties of the mechanical oscillatory systems with account for viscous friction forces based on frequency functions and damping functions that depend on the so-called coefficient of connection forms, which is the ratio of characteristics of generalized coordinates. Materials and Methods. The graphoanalytical methods used for evaluating the dynamic properties of mechanical oscillatory two-degree-of-freedom systems are based on determining the extreme values of the frequency functions and the damping function, which are determined from the relations between the kinetic, potential energy and the values of the energy dissipation function. Mathematical models are based on Lagrange formalism, matrix methods, and elements of the theory of functions of a complex variable. Results. A method is proposed for constructing frequency functions and damping functions for a class of mechanical oscillatory two-degree-of-freedom systems based on the analytical expressions that reflect features of the ratio of the potential and kinetic energy of the system considering viscous friction forces represented by the dissipative function. General analytical expressions for the frequency function and the damping function are derived. Graphoanalytical analysis of extreme properties of the corresponding frequency functions and damping functions is performed for mechanical vibrational systems with elastic-damping elements with symmetry properties. The results of numerical experiments are presented. A criterion for classifying frequency functions and damping functions based on the topological features of the graphs of the corresponding functions is proposed. Discussion and Conclusions. The developed method for constructing frequency functions and damping functions can be used to display the dynamic features of mechanical oscillatory systems. The proposed matrix method for constructing a frequency-damping function for a two-degree-of-freedom system can be extended to the mechanical vibrational systems considered in different coordinate systems.

DIRECTIONS OF IMPROVING THE EFFICIENCY OF VIBRATION TECHNOLOGICAL MACHINES

The article considers the directions of increasing the efficiency of vibrating technological machines. The processing of information on the development of vibration technologies is quite diverse and is represented by numerous scientific and technical developments related to improving the efficiency of vibration machines and ensuring the reliability of their work. The analytical basis for previous research in the creation of new technology are mathematical models that reflect the properties of mechanical oscillatory systems with several degrees of freedom, which perform small oscillations under the action of a system of periodic external perturbations that create vibration fields of one configuration. The dynamic properties of the working bodies of machines in a detailed form are revealed as the distribution of the amplitudes of oscillations of the points of the working bodies. In many cases, this distribution is linear, which is due to the manifestations of the properties of the simplest movements of the working bodies. Approaches are proposed in which the possible structural mathematical modeling is realized on the idea that a linear mechanical oscillatory system with concentrated parameters and several degrees of freedom can be compared with the structural scheme of the automatic control system. Particular attention is paid to the study and evaluation of the possibility of new dynamic effects associated with the simultaneous action of several working bodies of machines, as well as - modes of dynamic damping of oscillations. An important role in ensuring such developments is played by areas of research focused on the development of methods of mathematical modeling. Based on the research it is shown that the vibration field of the vibrating technological machine is formed under the influence of several factors, which are determined by the simultaneous action of several force perturbations, asymmetry of inertial and elastic properties of the mechanical system, the presence of additional connections. The introduction of additional links in the structure of the mechanical oscillating system of the vibrating machine, can significantly affect the structure of the vibration field, providing the choice of conditions for rational organization of the technological process of vibration processing, such as vibration hardening, crushing, transportation, screening.

Factor relationship of the parameters of the harmonic oscillatory system when cleaning the filtration surface of the plant for vegetable oil regeneration

When processing oilseeds, technologies are needed to obtain valuable vegetable oils by pressing with a long shelf life. Existing technologies for cleaning vegetable oils in small enterprises do not allow cleaning the oil from all undesirable substances and therefore the oils have a short shelf life, quickly oxidize and lose their presentation. The article theoretically substantiates the design parameters of a directional ultrasonic and mechanical oscillatory system for cleaning the filtration surface of the installation from accumulated solid particles in the oil.

The Dissipative Properties Assessment of the Oscillatory System of a Serial Sample of the Coriolis Flowmeter

The quantitative estimates of the flow rate (or density) of the flowing fluid obtained by the measurements using the industrial Coriolis flowmeters are made by using the laboratory experiments previously performed with the exemplary sensor. In this case we face two limitations, such as the unavailability of the facilities because of intense laboratory schedules and little time to upgrade the sensor oscillatory system. So we suggest using the virtual prototyping approaches as an alternative to the descriptive approaches. One of the fundamental problems of creating a virtual prototype of the Coriolis flowmeter is to separate the main parameter measured by the flowmeter (the phase shift) into the parts connected to the gyroscopic and dissipative forces. To solve this problem, we need to identify the dissipative forces model of the flowmeter oscillatory system. The article discusses the experimental results determining the dissipative properties of the mechanical oscillatory system of one of the commercially available Coriolis flowmeter samples. The algorithm identifying the model of the dissipative properties of the flowmeter oscillatory system is based on studying the nonlinearity degree of the envelope of the vibrogram of free damped oscillations. The experiments were carried out at the pouring stand of the Center for Experimental Mechanics of the South Ural State University, which allows controlling the speed and phase composition of the fluid flowing through the flowmeter. The article describes the processing algorithms for vibrograms of the damped oscillations, which make it possible to isolate the contribution into the dissipated energy from the dry (Coulomb model), the linear viscous (Rayleigh model) and quadratic viscous friction. The pronounced dependence of the vibrational system dissipation of the Coriolis flowmeter on the features of the fluid flow (velocity, mode: continuous, slug) was experimentally proven, the solutions of identifying the model of the dissipative forces are presented. The identification algorithm for the model of the dissipative properties of the flowmeter oscillatory system is based on studying the nonlinearity degree of the envelope of the vibrogram of the free damped oscillations. The use of the pouring stand made it possible to control the speed and phase composition of the fluid flowing through the flowmeter. The article describes the processing algorithms for the vibrograms of the damped oscillations by isolating the contribution into the dissipated energy from the dry (Coulomb model), linear viscous (Rayleigh model) and quadratic viscous friction. The pronounced dependence of the dissipation of the vibrational system of the Coriolis flowmeter on the features of the fluid flow (velocity, mode: continuous, slug) was experimentally proved, and the results of identifying the model of the dissipative forces are presented. The experiments included water acts as a fluid medium and air acts as a dispersed phase.