scholarly journals QUALITATIVE PROPERTIES OF VIBRATIONS OF ELASTICALLY SUPPORTED RIGID BODY

2020 ◽  
Vol 2 (2) ◽  
pp. 85-94
Author(s):  
S Bekshaev ◽  
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Free Vibrations ◽  
Natural Vibrations ◽  
Qualitative Properties ◽  
Engineering Structures ◽  
Natural Oscillations ◽  
Geometric Characteristics ◽  
Operating Modes

The paper investigates free vibrations of an absolutely rigid body, supported by a set of linearly elastic springs and performing a plane-parallel motion. The proposed system has two degrees of freedom, which makes it elementary to determine the frequencies and modes of its natural oscillations by using exact analytical expressions. However, these expressions are rather cumbersome, which makes it difficult to study the behavior of frequencies and modes when the characteristics of the model change. Therefore, the aim of the work was to find out the qualitative properties of the modes of free vibrations depending on the elastic, inertial and geometric characteristics of the system, as well as to study the effect of changing the position of elastic supports on its natural frequencies. The main qualitative characteristic of the mode of natural vibrations of the system in consideration is the position of its node – a point that remains stationary during natural vibrations. For the practically important case of a system with two supports, it has been established in the work that, in the general case, of two modes corresponding to two different natural frequencies, one has a node located inside the gap between the supports, and the other – outside this gap. Analytical conditions are found that must be satisfied by the inertial and geometric characteristics of the system, which make it possible to determine which of the two modes corresponds to the internal position of the node. It is noted that these conditions do not depend on the stiffness of the supports. Analytical results were also obtained, allowing to determine a more accurate qualitative localization of the node. To clarify the behavior of natural frequencies when the position of the supports changes, an explicit expression is obtained for the derivative of the square of the natural frequency of the system with respect to the coordinate defining the position of the support. This expression can be used to solve a variety of problems related to the control and optimization of the operating modes of engineering structures subjected to dynamic, in particular periodic, effects. The results of the work were obtained using qualitative methods of the mathematical theory of oscillations. In particular, the theorem on the effect of imposing constraints on the natural frequencies of an elastic system is systematically used.

scholarly journals QUALITATIVE PROPERTIES OF VIBRATIONS OF ELASTICALLY SUPPORTED RIGID BODY

2020 ◽  
Vol 2 (2) ◽  
pp. 85-94
Author(s):  
S Bekshaev ◽  
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Free Vibrations ◽  
Natural Vibrations ◽  
Qualitative Properties ◽  
Engineering Structures ◽  
Natural Oscillations ◽  
Geometric Characteristics ◽  
Operating Modes

The paper investigates free vibrations of an absolutely rigid body, supported by a set of linearly elastic springs and performing a plane-parallel motion. The proposed system has two degrees of freedom, which makes it elementary to determine the frequencies and modes of its natural oscillations by using exact analytical expressions. However, these expressions are rather cumbersome, which makes it difficult to study the behavior of frequencies and modes when the characteristics of the model change. Therefore, the aim of the work was to find out the qualitative properties of the modes of free vibrations depending on the elastic, inertial and geometric characteristics of the system, as well as to study the effect of changing the position of elastic supports on its natural frequencies. The main qualitative characteristic of the mode of natural vibrations of the system in consideration is the position of its node – a point that remains stationary during natural vibrations. For the practically important case of a system with two supports, it has been established in the work that, in the general case, of two modes corresponding to two different natural frequencies, one has a node located inside the gap between the supports, and the other – outside this gap. Analytical conditions are found that must be satisfied by the inertial and geometric characteristics of the system, which make it possible to determine which of the two modes corresponds to the internal position of the node. It is noted that these conditions do not depend on the stiffness of the supports. Analytical results were also obtained, allowing to determine a more accurate qualitative localization of the node. To clarify the behavior of natural frequencies when the position of the supports changes, an explicit expression is obtained for the derivative of the square of the natural frequency of the system with respect to the coordinate defining the position of the support. This expression can be used to solve a variety of problems related to the control and optimization of the operating modes of engineering structures subjected to dynamic, in particular periodic, effects. The results of the work were obtained using qualitative methods of the mathematical theory of oscillations. In particular, the theorem on the effect of imposing constraints on the natural frequencies of an elastic system is systematically used.

scholarly journals SOME PROBLEMS OF OPTIMIZATION AND CONTROL OF THE NATURAL FREQUENCIES OF AN ELASTICALLY SUPPORTED RIGID BODY

2021 ◽  
Vol 3 (2) ◽  
pp. 88-102
Author(s):  
S. Bekshaev ◽  
Keyword(s):  
Rigid Body ◽  
Fundamental Frequency ◽  
Natural Frequencies ◽  
Optimization Problems ◽  
Free Vibrations ◽  
The Body ◽  
Natural Vibrations ◽  
Natural Oscillations ◽  
Optimal Position ◽  
Elastic Supports

The article analytically investigates the behavior of the frequencies and modes of natural vibrations of a rigid body, based on point elastic supports, when the position of the supports changes. It is assumed that the body is in plane motion and has two degrees of freedom. A linear description of body vibrations is accepted. The problems of determining such optimal positions of elastic supports at which the fundamental frequency of the structure reaches its maximum value are considered. Two groups of problems were studied. The first group concerns a body supported by only two supports. It was found that in the absence of restrictions on the position of the supports to maximize the fundamental natural frequency, these supports should be positioned so that the basic natural vibrations of the body are translational. Simple analytical conditions are formulated that must be satisfied by the corresponding positions of the supports. In real practical situations, these positions may be unreachable due to the presence of various kinds of restrictions due to design requirements. In this paper, optimization problems are considered taking into account a number of restrictions on the position of supports, typical for practice, expressed analytically by equations and inequalities. For each of the considered types of constraints, results are obtained that determine the optimal positions of the supports and the corresponding maximum values of the main natural frequencies. The approach applied allows us to consider other types of restrictions, which are not considered in the article. In the second group of problems for a body resting on an arbitrary number of supports, the optimal position of an additional elastic support introduced in order to maximize the fundamental frequency in fixed positions and the stiffness coefficients of the remaining supports was sought. It was found that this position depends on the value of the stiffness coefficient of the introduced support. Results are obtained that qualitatively and quantitatively characterize this position and the corresponding frequencies and modes of natural oscillations, including taking into account practically established limitations. The research method uses a qualitative approach, systematically based on the well-known Rayleigh theorem on the effect of imposing constraints on the free vibrations of an elastic structure.

scholarly journals THE CONTACT INTERACTION DYNAMICS OF THE WORKING TOOL OF THE MOLE PLOWSHARE WITH THE SOIL DURING FORMING PROSESS A CHANNEL FOR AN ANTI-FILTRATION SCREEN

2020 ◽  
pp. 81-89
Author(s):  
Olena Solona ◽  
Vladimir Kovbasa ◽  
Igor Kupchuk
Keyword(s):  
Rigid Body ◽  
Contact Interaction ◽  
Large Scale ◽  
Geometric Parameters ◽  
Theoretical Development ◽  
Maximum Efficiency ◽  
Industrial Complex ◽  
Engineering Structures ◽  
Operating Modes ◽  
Working Bodies

Today's realities of agriculture are increasingly prompting the need for the introduction of technologies for subsoil irrigation, as a possible tool to obtain maximum efficiency indicators of agricultural activities of agricultural enterprises. At the same time, the large-scale introduction of intra-soil irrigation technologies at the enterprises of the agro-industrial complex is significantly complicated due to the poor practical and theoretical development of its methods, as well as the lack of extensive experimental verification of this method of irrigation. The development of many processes in the construction of irrigation and engineering structures requires substantiation of the geometric parameters and operating modes of the working bodies that are used to implement these processes. One of the working bodies that is used to form the cavity along which communication is stretched is a mole plow, which, depending on the expected working conditions, may have a different geometric configuration and size. The results of investigations of the interaction of the mole ploughshare with the soil in cavity formation for laying the anti-filtration screen are describe in this article. The authors propose to consider the soil in the form of an elastic-viscous model. By solving the contact problem of the interaction of a rigid body with a deformed medium, the stress components in the soil on the contact surface with the ploughshare are determined, and soil compaction is determined. The components of forces that appear on the surface of the ploughshare because of its interaction with the soil are determined depending on its geometric parameters and the mechanical properties of the soil. This solution is a general approach for the analytical solution of the class of problems of the contact interaction of a rigid body with a deformable medium possessing the properties of elasticity and viscosity.

scholarly journals AIMED CONTROL OF THE FREQUENCY SPECTRUM OF EIGENVIBRATIONS OF ELASTIC PLATES WITH A FINITE NUMBER OF DEGREES OF FREEDOM OF MASSES BY SUPERIMPOSING ADDITIONAL CONSTRAINTS

2021 ◽  
Vol 17 (2) ◽  
pp. 76-82
Author(s):  
Leonid Lyakhovich ◽  
Pavel Akimov
Keyword(s):  
Finite Number ◽  
Frequency Spectrum ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Elastic Plates ◽  
Natural Vibrations ◽  
Design Constraint ◽  
Elastic Systems ◽  
The Masses ◽  
Additional Constraints

As is known, for some elastic systems with a finite number of degrees of freedom of masses, for which thedirections of motion of the masses are parallel and lie in the same plane, methods have been developed for creatingadditional constraints that purposefully change the spectrum of natural frequencies. In particular, theory and algorithm forthe formation of aimed additional constraints have been developed for the rods, the introduction of each of which doesnot change any of the modes of natural vibrations, but only increases the value of only one frequency, without changingthe values of the remaining frequencies. The distinctive paper is devoted to the method of forming a matrix of additionalstiffness coefficients corresponding to such aimed constraint in the problem of natural vibrations of rods. This method canalso be applied to solving a similar problem for elastic systems with a finite number of degrees of freedom, in which thedirections of motion of the masses are parallel, but not lie in the same plane. In particular, such systems include plates.However, the algorithms for the formation of aimed additional constraints, developed for rods and based on the propertiesof rope polygons, cannot be used without significant changes in a similar problem for plates. The method for the formationof design constraint schemes that purposefully change the spectrum of frequencies of natural vibrations of elastic plateswith a finite number of degrees of freedom of masses, will be considered in the next work.

Calculation of the frequency of own oscillations of polyurethane shock absorbers used in shipbuilding

2020 ◽  
pp. 152-157
Author(s):  
Ю.Ф. Титова ◽  
С.Н. Яковлев
Keyword(s):  
Vibration Isolation ◽  
Shock Absorber ◽  
Free Vibrations ◽  
Empirical Dependence ◽  
Natural Vibrations ◽  
Natural Oscillations ◽  
Rubber Material ◽  
Shape Coefficient ◽  
Calculated Dependence ◽  
Shock Absorbers

В работе приведено обоснование необходимости применения амортизаторов и замены традиционного эластомерного материала резины на более совершенный материал – полиуретан. Целью работы является экспериментальное исследование деформативности полиуретанового виброизоляционного массива амортизатора и получение расчетной зависимости для определения собственной частоты колебаний системы «агрегат-амортизатор». В работе представлен подробный анализ зависимости коэффициента виброизоляции от соотношения частот вынужденных и свободных колебаний. Отмечено, что эффективность виброизоляции тем выше, чем больше это соотношение частот. Учитывая, что частота вынужденных колебаний - величина заданная, для повышения эффективности виброизоляции следует понижать частоту собственных колебаний амортизатора благодаря применению новых виброизоляционных материалов. В качестве эластомерного материала предложен полиуретан фирмы «Synair» (Великобритания) твердостью 40,45 и 50 ShA. Приведено описание нагружающего устройства для исследования деформативности виброизоляционного массива амортизатора серии КАС (корабельный амортизатор сварной). Получена эмпирическая зависимость коэффициента ужесточения в зависимости от коэффициента формы виброизоляционного массива амортизатора. Представлена эмпирическая зависимость по определению модуля упругости эластомерного материала виброизоляционного массива амортизатора в зависимости от условий контактирования на торцах и фактора формы массива. Представлена расчетная зависимость по определению частоты собственных колебаний амортизатора в зависимости от величины статической деформации. Представленная зависимость позволяет на стадии проектирования определить собственную частоту колебаний и предупредить возникновение такого опасного явления, как резонанс. The paper substantiates the need for the use of shock absorbers and the replacement of the traditional elastomeric rubber material with a more advanced material - polyurethane. The aim of the work is an experimental study of the deformability of a polyurethane vibration-isolating array of a shock absorber and obtaining a calculated dependence for determining the natural frequency of oscillations of the aggregate-shock absorber system. The paper presents a detailed analysis of the dependence of the vibration isolation coefficient on the ratio of the frequencies of forced and free vibrations. It is noted that the effectiveness of vibration isolation is higher, the greater the ratio of the frequencies of forced and natural vibrations. Taking into account the fact that the frequency of forced vibrations is a given value, to increase the efficiency of vibration isolation, it is necessary to reduce the frequency of natural vibrations of the shock absorber due to the use of new vibration insulation materials. The work describes the loading device for studying the deformability of the vibration-isolating array of the KAS series shock absorber (welded ship shock absorber). An empirical dependence of the tightening coefficient is obtained depending on the shape coefficient of the vibration-isolating array of the shock absorber. The paper presents a calculated dependence on determining the frequency of natural oscillations of the shock absorber depending on the magnitude of the static deformation.

scholarly journals Собственные частоты изгибных колебаний углеродных нанотрубок

2021 ◽  
Vol 91 (11) ◽  
pp. 1732
Author(s):  
С.В. Дмитриев ◽  
И.Р. Сунагатова ◽  
М.А. Ильгамов ◽  
И.С. Павлов
Keyword(s):  
Carbon Nanotubes ◽  
Molecular Dynamics ◽  
Degrees Of Freedom ◽  
Electromechanical Coupling ◽  
Natural Frequencies ◽  
High Accuracy ◽  
Dynamics Model ◽  
Natural Vibrations ◽  
Bending Vibrations ◽  
Low Amplitude

Using a molecular dynamics model with a reduced number of degrees of freedom, the natural frequencies of bending vibrations of carbon nanotubes (CNTs) of various diameters are calculated under plane strain conditions. It is shown that the theory of thin cylindrical shells provides high accuracy in estimating the frequencies of low-amplitude natural vibrations even for relatively small CNT diameters. It is shown that with an increase in the amplitude, the frequency of natural vibrations decreases, which is consistent with the data available in the literature. The results obtained are necessary for the design of terahertz resonators based on CNTs and high-precision mass and force nanosensors based on the effect of electromechanical coupling that CNTs exhibit.

scholarly journals Most important results of the scientific activity of the Seismological Division GS RAS in 2016-2020 (seismic research)

2021 ◽  
Vol 3 (1) ◽  
pp. 54-74
Author(s):  
Aleksei Liseikin ◽  
Viktor Seleznev
Keyword(s):  
Seismic Data ◽  
Natural Frequencies ◽  
Low Frequency ◽  
Fold Increase ◽  
Scientific Activity ◽  
Operating Conditions ◽  
Natural Vibrations ◽  
Natural Oscillations ◽  
Moho Boundary ◽  
Seismic Impacts

The article presents the most important results of seismic studies carried out in 2016-2020 at the Seismological Division GS RAS. Work at the Chirkey’s HPP, where natural oscillations of the dam and their seasonal changes were studied in detail and a method for monitoring the natural frequencies of the structure was developed. Research at the Sayano-Shushenskaya HPP, where the processes of interaction of operating hydroelectric units with surrounding structures were studied and it was found that under certain operating conditions of the equipment, there is a 10-20-fold increase in the natural oscillations of the dam, the source of which is natural oscillations (organ vibrations) in the penstocks. A method has been developed for assessing the response of structures to seismic impacts, based on the method of coherent reconstruction of standing wave fields and allowing to calculate the vibrations of an object arising from seismic impacts at its base. The possibilities of determining the natural vibrations of large objects based on low-frequency seismological records and their monitoring are demonstrated on the example of the results of the analysis of satellite images and seismological materials when determining the causes of the landslide on the Elbashinsky dump of the Kolyvan anthracite deposit in the Novosibirsk region. The possibility of using river seismic data to study the structure of the earth’s crust at all depth, including the Moho boundary, has been substantiated using the example of data obtained during the development of the CDP-2D profile in the lower reaches of the river Lena.

scholarly journals ASSESSMENT OF THE SEISMIC SAFETY OF ENGINEERING STRUCTURES BASED ON ACOUSTIC NOISE

2021 ◽  
Vol 2 (3) ◽  
pp. 24-31
Author(s):  
Konstantin V. Fedin ◽  
Elizaveta E. Kosyakina
Keyword(s):  
Field Experiments ◽  
Natural Frequencies ◽  
Acoustic Noise ◽  
Amplitude Spectrum ◽  
Residential Building ◽  
Engineering Structures ◽  
Natural Oscillations ◽  
Change Over Time ◽  
Seismic Safety ◽  
Over Time

The article presents the results of field experiments on the influence of the natural frequencies in the soil and constant exposure to the outside over time for stability engineering structures. It is shown that the frequency-amplitude spectrum of the natural oscillations of the investigated multi-storey residential building does not change over time.

scholarly journals Compensatory bellows oscillations as a corrugated shell with liquid inside

2021 ◽  
pp. 31-40
Author(s):  
T. V Zinovieva ◽  
V. A Piskunov
Keyword(s):  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Elastic Shell ◽  
Free Vibrations ◽  
Forced Vibrations ◽  
Compressible Liquid ◽  
Plastic State ◽  
Material Surface ◽  
Attached Mass ◽  
Corrugated Shell

The paper deals with a relevant problem of shipbuilding, i.e. calculation of free and forced vibrations of pipeline compensatory bellows. These devices are used to reduce the vibration load caused by ship power machines. When analyzing the vibrations of the compensatory bellows, it is necessary to take into account the liquid contained in the bellows. In this work, the design model of the bellows is represented by a corrugated elastic shell as a material surface with five degrees of freedom. A variant of the classical theory of shells, built on the basis of Lagrangian mechanics, is used. The influence of the liquid is taken into account by two models. First, the liquid is considered to be ideal and incompressible and is considered through the attached mass to the shell. The shell is replaced by a cylindrical surface with a radius in the middle line of the corrugation. To account for the influence of the frequency of bellows oscillations on the attached inertia of the liquid in the calculation we also used the acoustic approximation; and derived a formula for a generalized attached mass of the ideal compressible liquid. The equations of the bellows oscillations under the periodic loading are obtained. The problem has been solved by the finite difference method. The values of natural frequencies of free vibrations are obtained for the compensatory bellows from the corrosion-resistant heat-resistant steel. It is shown that by taking account of the liquid, we significantly change the natural frequencies of the bellows. With high-frequency vibrations it is necessary to take into account the compressibility of the liquid. The problem of the forced vibrations of the bellows caused by a displacement of its end face by the harmonic law is solved. The internal forces and moments are determined, as well as occurring stresses by Mises criterion in the bellows. We found the critical value of the end face displacement at a frequency of 50 Hz, at which the bellows goes into a plastic state.

The Natural Vibration of Fluid-Structure Interaction Systems Subject to the Sommerfeld Radiation Condition

2006 ◽  
Author(s):  
Jing T. Xing
Keyword(s):  
Eigenvalue Problem ◽  
Degrees Of Freedom ◽  
Natural Vibration ◽  
Natural Frequencies ◽  
Fluid Structure Interaction ◽  
Complex Conjugate ◽  
Natural Vibrations ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Natural Modes

A fluid-structure interaction system subject to a Sommerfeld condition is defined as a Sommerfeld system in this paper. It is well known that the natural vibration of a dynamic system is defined by the eigenvalue problem of the corresponding idealized system with no material damping assumed and external forces. From the defined eigenvalue problem, the real natural frequencies and the corresponding natural modes of the system can be derived. What are the characteristics of natural vibrations of a Sommerfeld system? This paper intends to address this problem by investigating three selected fluid-structure interaction systems. The systems chosen involve the solid structures with one, two and infinite degrees of freedom coupling to an infinite fluid domain subject to a Sommerfeld condition, respectively. The governing equations describing these coupled systems are presented using the theory of continuum mechanics. The theoretical solution for each problem is derived and discussed. The analysis demonstrates that a Sommerfeld system undergoing a natural vibration behaves energy dissipative characteristics although there is no material damping in solid and fluid of the system. The natural vibrations of a Sommerfeld system are governed by a complex eigenvalue problem which has only pairs of complex conjugate natural frequencies. The number of the complex conjugate natural frequencies and corresponding natural modes of this Sommerfeld system equals to the number of the degrees of freedom of the dry solid structure in the system and it is independent of the infinite fluid domain. The natural vibration forms of the solid structure in natural vibrations do not satisfy the orthogonal relationship. The findings in this research reveal some common dynamic characteristics of Sommerfeld systems. An approach for the dynamic response analysis of a Sommerfeld system is proposed based on the orthogonal natural modes of the dry structure in the system which is more efficient for engineering analysis.

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