scholarly journals Фазовая кластеризация в иерархическом ансамбле связанных осцилляторов ван дер Поля

2021 ◽  
Vol 47 (9) ◽  
pp. 14
Author(s):  
О.С. Темная ◽  
G.P. Tsironis
Keyword(s):  
Natural Frequencies ◽  
Coupling Parameter ◽  
Hierarchical Level ◽  
Hierarchical Network ◽  
Synchronous State

We demonstrate phase clusterization in a hierarchical network of mutually coupled van der Pole oscillators. We find that in the system with random initial phases there is a coupling parameter, which corresponds to intermittent transition from non-synchronous state to synchronous. Clusterization does not decay if oscillators have non-identical natural frequencies or randomly distributed initial phases. In this structure, those elements that are placed on the same hierarchical level have equal phases.

TRACKING PHASE SYNCHRONIZATION OF TWO COUPLED RÖSSLER OSCILLATORS WITH INTERNAL RESONANCE

2009 ◽  
Vol 23 (23) ◽  
pp. 4809-4816 ◽  
Author(s):  
YONG LIU
Keyword(s):  
Coupling Strength ◽  
Internal Resonance ◽  
Natural Frequencies ◽  
Phase Synchronization ◽  
Coupling Parameter ◽  
Primary Resonance ◽  
Coupled Systems ◽  
Nonlinear Coupling ◽  
Linear Coupling ◽  
Phase Dynamics

Phase synchronization between linearly and nonlinearly coupled systems with internal resonance is investigated in this paper. By introducing the conception of phase for a chaotic motion, we tune the linear coupling parameter to obtain the two Rössler oscillators in a synchronized regime and analyze the effect of a nonlinear coupling on the phase synchronized state. It demonstrates that the detuning parameter σ between the two natural frequencies ω1and ω2affects phase dynamics, and with the increase of the nonlinear coupling strength, for the primary resonance, the effect of phase synchronization between two sub-systems was decayed, while increasing with frequency ratio 1:2. Further investigation reveals that the transition of phase states between the two oscillators are related to the critical changes of the nonlinear coupling strength.

Efficient Theoretical and Numerical Methods for Solving Free Vibrations and Transient Responses of a Circular Plate Coupled With Fluid Subjected to Impact Loadings

2021 ◽  
Vol 143 (5) ◽  
Author(s):  
Ming Ji ◽  
Kazuaki Inaba
Keyword(s):  
Finite Element ◽  
Numerical Methods ◽  
Circular Plate ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Coupling Parameter ◽  
Coupled System ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Transient Responses

Abstract This paper presents an easy-to-use theoretical method and an efficient numerical method for solving free vibrations and transient responses of a circular plate coupled with fluid subjected to impact loadings and provides insights into various coupling cases with these developed methods. The Kirchhoff plate theory, Mindlin–Reissner plate theory, and the linear velocity potential function are used. The wet mode of the coupled system is described as the superposition of dry modes of the plate, which has been considered in few studies. The natural frequencies and corresponding mode shapes are solved using the orthogonality of dry modes. The transient responses of the plate are then solved using the superposition of the wet modes and the orthogonality of dry modes. To validate the theoretical results, an efficient and flexible finite element method is proposed and verified by comparing with commercial software. The four-node mixed interpolation of the tensorial component quadrilateral plate finite element (MITC4) and the eight-node acoustic pressure element are used to model the plate and the fluid, respectively. The theoretical and numerical methods provide reliable and accurate results. Parametric studies are performed to investigate the influence of geometric sizes, plate material properties, and fluid properties on the natural frequencies of the coupled system. A coupling parameter of fluid–structure interaction is proposed. The nondimensional added virtual mass incremental (NAVMI) factor decreases as the coupling parameter increases. Besides, the influence of fluid on wet modes of the plate decreases with the order.

Development of the method for detecting natural frequencies of blocks in seismic noise before small seismic events

2020 ◽  
Author(s):  
Alina Besedina ◽  
Dmitry Pavlov
Keyword(s):  
Seismic Noise ◽  
Natural Frequencies ◽  
Active Regions ◽  
Natural Oscillation ◽  
Ore Deposits ◽  
Hierarchical Level ◽  
Seismic Events ◽  
Natural Oscillations ◽  
Spectral Centroid ◽  
Iron Ore Deposits

<p><strong>Previous studies of microseismic noise before earthquakes in seismically active regions showed the possibility of detecting the preparation processes of seismic events. This effect manifests itself as decrease of the frequency of natural oscillations before earthquakes. In this work, the method for detecting the natural frequencies of blocks in seismic noise is adapted to a lower hierarchical level. Using known empirical relations for faults with a characteristic length of less than 500-1000 m, the characteristic natural oscillation frequencies that can be used to diagnose a fault zone are estimated. For small seismic events with magnitudes Mw from -2 to -1, we calculated the expected frequencies of natural vibrations of 350-1100 Hz, and for events with Mw from 0 to 1,  - below 35 Hz. For analysis, we used the recording data of high-frequency accelerometers at a depth of 300 m from the free surface in the area of the city of Gubkin (Russia) within iron ore deposits. Before small events with an amplitude of more than 0.01 m/s<sup>2</sup>. The intervals of decrease in the spectral centroid in the range of 20-1200 Hz were identified. The minimum values of the spectral centroid obtained on the basis of experimental data are generally in a good agreement with theoretical estimates. This work was supported by RFBR (project # 18-05-00923).</strong></p>

Tire Vibrations

1977 ◽  
Vol 5 (4) ◽  
pp. 202-225 ◽  
Author(s):  
G. R. Potts ◽  
C. A. Bell ◽  
L. T. Charek ◽  
T. K. Roy
Keyword(s):  
Natural Frequencies ◽  
Standing Waves ◽  
Resonant Mode ◽  
Mode Shapes ◽  
Resonant Vibrations ◽  
Resonant Frequencies ◽  
Radial Tire ◽  
Analysis Techniques ◽  
Thin Ring ◽  
Good Agreement

Abstract Natural frequencies and vibrating motions are determined in terms of the material and geometric properties of a radial tire modeled as a thin ring on an elastic foundation. Experimental checks of resonant frequencies show good agreement. Forced vibration solutions obtained are shown to consist of a superposition of resonant vibrations, each rotating around the tire at a rate depending on the mode number and the tire rotational speed. Theoretical rolling speeds that are upper bounds at which standing waves occur are determined and checked experimentally. Digital Fourier transform, transfer function, and modal analysis techniques used to determine the resonant mode shapes of a radial tire reveal that antiresonances are the primary transmitters of vibration to the tire axle.

Analyzing the Russian tool-making industry within the sustainable development concept

2020 ◽  
Vol 16 (4) ◽  
pp. 662-677 ◽  
Author(s):  
T.N. Ryzhikova ◽  
V.G. Borovskii
Keyword(s):  
Sustainable Development ◽  
Hierarchical Level ◽  
Economic Systems ◽  
Resource Use Efficiency ◽  
The Sustainable Development ◽  
Case Methods ◽  
Hierarchical Levels ◽  
Use Efficiency ◽  
Intensive Development

Subject. The article explores the economic component of sustainable development through the classification of industries from the perspective of assigning the output goods to fixed or current assets, using different types of resources and assessing their condition. It considers factors of production affecting the achievement of the result and determining the development of economic systems at the meso- and micro-hierarchical level. Objectives. The aim is to assess the function of economic systems of different hierarchical levels on the tool-making facilities case. Methods. We apply an approach using general and special methods of comparative and statistical analysis, synthesis and analogies. Results. The paper analyzes the development of the Russian tool-making industry on the basis of resource-oriented approach to assess the functioning of economic systems at various levels. We review interrelations between resource use efficiency, types of sustainable development of economic systems at various hierarchical levels and strategic security of the country. Conclusions. Any development can be considered sustainable, if there is an increment in the intensive development of economic systems at all three levels.

DRAINAGE BASIN AS A COMPLEX SOCIO-NATURAL HIERARCHICAL SYSTEM

2020 ◽  
Vol 42 (3) ◽  
pp. 293-303
Author(s):  
VALERIY BONDAREV
Keyword(s):  
Drainage Basin ◽  
Temporal Analysis ◽  
Large River ◽  
Hierarchical Level ◽  
Effective Management ◽  
Drainage Basins ◽  
Time Intervals ◽  
Natural Systems ◽  
Spatial And Temporal Analysis ◽  
Entire Complex

The theoretical and methodological basis of the systems hierarchical spatial and temporal analysis of a drainage basin, which addresses the problems of effective management in socio-natural systems of different ranks, is considered. It is proposed to distinguish 9 orders of forms that are relevant to the analysis of drainage basins, where the first level is represented by individual aggregates and particles, and the last - by basins of large and the largest rivers. As part of the allocation of geological, historical and modern time intervals, the specificity of the implementation of processes in basins of different scales from changing states, through functioning to evolution is demonstrated. The interrelation of conditions and factors that determine the processes occurring within the drainage basins is revealed. It is shown that a specific combination of conditions and factors that determine processes in the drainage basin is associated with the hierarchy of the objects under consideration, i.e. the choice of a spatial-temporal hierarchical level is crucial for the organization of study within drainage basins. At one hierarchical level, some phenomenon can be considered as a factor, and at another - as a condition. For example, tectonic processes can be considered as an active factor in the evolution of large river basins in the geological perspective, but for small drainage basin, this is already a conservative background condition. It is shown that at the historical time the anthropogenic factor often comes to the fore, with the appearance of which in the functioning of the drainage basin, there is a need to take into account the entire complex of socio-environmental problems that can affect the sustainable state of various territories, especially in the field of water and land use. Hierarchical levels of managing subjects are identified, which are primarily responsible for effective management at the appropriate hierarchical level of the organization of the socio-natural system within the catchment area, starting from an individual to humankind as a whole.

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