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1
Content available remote Influence of Parameters of Two Pendulums System With an Elastic Element on Regular and Chaotic Vibrations
Sado D., Brodowska E. T.
Machine Dynamics Research
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2017
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Vol. 41, No. 2
85--96
EN
In this work, a system with two degrees of freedom is studied, consisting of the two coupled pendulums, connected by the element characterized by linear elasticity of rigidity and linear damping. One of the pendulums is subjected to harmonic horizontal excitation. The equations of motion within the studied system are derived as Lagrange’s equations. For small vibrations it was assumed that displacement of the spring element is horizontal only. Exemplary results of the energy transfer, for different parameter values of the system are presented. Numerically, it was indicated that near the internal and external resonance, except different kinds of periodic vibrations, chaotic vibration may also occur. For characterizing an irregular chaotic response, the Poincare maps and maximal exponents of Lyapunov have been constructed.
2
Content available Chaotic vibration of an autoparametrical system with the spherical pendulum
Sado D., Freundlich J., Bobrowska A.
Journal of Theoretical and Applied Mechanics
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2017
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Vol. 55 nr 3
779--786
EN
In the paper, the dynamics of a three degree of freedom vibratory system with a spherical pendulum in the neighbourhood of internal and external resonance is considered. It has been assumed that the spherical pendulum is suspended to the main body which is then suspended to the element characterized by some elasticity and damping. The system is excited harmonically in the vertical direction. The equation of motion has been solved numerically. The influence of initial conditions on the behaviour of the spherical pendulum is investigated. In this type of the system, one mode of vibration may excite or damp another one, and for different kinds of periodic vibrations there may also appear chaotic vibrations. For characterization of an irregular chaotic response, time histories, bifurcation diagrams, power spectral densities, Poincar´e maps and the maximum Lyapunov exponents have been calculated.
3
Content available The dynamics of a coupled mechanical system with spherical pendulum
Sado D., Freundlich J., Dudanowicz A.
Vibrations in Physical Systems
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2016
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Vol. 27
309--316
EN
The nonlinear response of a three degree of freedom vibratory system with spherical pendulum in the neighbourhood internal and external resonance is investigated. It was assumed that spherical pendulum is suspended to the main body which is suspended by the element characterized by elasticity and damping and is excited harmonically in the vertical direction. The equation of motion have bean solved numerically. In this type system one mode of vibration may excite or damp another one, and for except different kinds of periodic vibrations there may also appear chaotic vibration.
4
Content available remote Oscillations of an Autoparametrical Systems with the Spherical Pendulum
Sado D., Bobrowska A.
Machine Dynamics Research
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2016
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Vol. 40, No. 2
155--163
EN
Dynamic properties of the three degrees of freedom autoparametric system with spherical pendulum in the neighbourhood internal and external resonance are investigated. It was assumed that the spherical pendulum is suspended in the main body which is suspended by the element characterized by elasticity and damping and is excited harmonically in the vertical direction. The spherical pendulum is similar to the simple pendulum, but moves in 3-dimensional space, so the model with spherical pendulum is more similar to the real systems than the model with simply pendulum. In this paper the position of the main body is described by coordinate z and position of the pendulum is describe by the coordinate z and two angles: θ and φ in the vertical planes. This system has three degrees of freedom. Dynamic properties of the system described by three differential equations containing strongly nonlinear terms are investigated numerically. In autoparametric system one mode of vibration may excite or damp another one, and for except periodic or quasi-periodic vibrations there may also appear chaotic vibration. For characterizing an irregular chaotic response, time histories, bifurcation diagrams, power spectral densities, Poincaré maps and maximal exponents of Lyapunov have been developed.
5
Content available Metamorphoses of resonance curves in systems of coupled oscillators
Kyzioł J., Okniński A.
Journal of Theoretical and Applied Mechanics
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2016
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Vol. 54 nr 4
1197--1204
EN
We study dynamics of two coupled periodically driven oscillators in a general case and compare it with two simplified models. Periodic steady-state solutions to these system equations are determined within the Krylov-Bogoliubov-Mitropolsky approach. Amplitude profiles are computed. These two equations, each describing a surface, define a 3D curve – intersection of these surfaces. In the present paper, we analyse metamorphoses of amplitude profiles induced by changes of control parameters in three dynamical systems studied. It is shown that changes of the dynamics occur in the vicinity of singular points of these 3D curves.
6
Content available Compound-combination synchronization of chaos in identical and different orders chaotic systems
Ojo K. S., Njah A. N., Olusola O. I.
Archives of Control Sciences
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2015
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Vol. 25, no. 4
463--490
EN
This paper proposes a new synchronization scheme called compound-combination synchronization. The scheme is investigated using six chaotic Josephson junctions evolving from different initial conditions based on the drive-response configuration via the active backstepping technique. The technique is applied to achieve compound-combination synchronization of: (i) six identical third order resistive-capacitive-inductive-shunted Josepshon junctions (RCLSJJs) (with three as drive and three as response systems); (ii) three third order RCLSJJs (as drive systems) and three second order resistive-capacitive-shunted Josepshon junctions (RCSJJs (as response systems). In each case, sufficient conditions for global asymptotic stability for compound-combination synchronization to any desired scaling factors are achieved. Numerical simulations are employed to verify the feasibility and effectiveness of the compound-combination synchronization scheme. The result shows that this scheme could be used to vary the junction signal to any desired level and also give a better insight into synchronization in biological systems wherein different organs of different dynamical structures and orders are involved. The scheme could also provide high security in information transmission due to the complexity of its dynamical formulation.
7
Content available Energy balance of two synchronized self-excited pendulums with different masses
Kapitaniak T., Czołczyński K., Perlikowski P., Stefański A.
Journal of Theoretical and Applied Mechanics
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2012
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Vol. 50 nr 3
729-741
EN
We consider the synchronization of two self-excited pendulums with different masses. We show that such pendulums hanging on the same beam can show almost-complete (in-phase) and almost-antiphase synchronizations in which the difference of the pendulums displacements is small. Our approximate analytical analysis allows one to derive the synchronization conditions and explains the observed types of synchronizations as well as gives an approximate formula for amplitudes of both the pendulums and the phase shift between them. We consider the energy balance in the system and show how the energy is transferred between the pendulums via the oscillating beam allowing synchronization of the pendulums.
PL
Artykuł prezentuje analizę zjawiska synchronizacji dwóch wahadeł samowzbudnych o różnych masach. Pokazano, że jeśli takie wahadła zostaną zawieszone na wspólnej, ruchomej podstawie, zachodzi zjawisko ich (prawie) zupełnej lub (prawie) antyfazowej synchronizacji. Analiza bilansu energetycznego układu pozwala na określenie parametrów układu w stanie synchronizacji (amplitudy drgań i przesunięcia fazowe). Analiza bilansu energetycznego wyjaśnia także mechanizm synchronizowania się ruchu wahadeł: stały przepływ strumienia energii od jednego wahadła, via wspólna ruchoma podstawa, do drugiego wahadła powoduje, że ruch układu jest okresowy, a przesunięcia fazowe pomiędzy wahadłami przyjmują stałe, charakterystyczne wartości.
8
Content available remote Chaos in Autoparametric Three Degree of Freedom System with SMA Spring
Sado D.
Machine Dynamics Research
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2010
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Vol. 34, No. 2
109-120
EN
In this paper is studied a three degree of freedom autoparametric system with two pendulums connected by shape memory alloys (SMA) spring in the neighborhood internal and external resonance. The system consists of the body of mass mi which is hung on a spring and a damper, and two connected by SMA spring pendulums of the length l₁ and l₂ and masses m₂ and m₃ mounted to the body of mass m₁. It is assumed, that the motion of the pendulums are damped by resistive forces. Shape memory alloys have ability to change their material properties. A polynomial constitutive model is assumed to describe the behavior of the SMA spring (it was assumed that the uniaxial stress σ is a fifth-degree polynomial of the strain). The equations of motion have been solved numerically and there were studied pseudoelastic effects associated with martensitic phase transformations. It was assumed that SMA presents two stable phases: austenite and martensite. Solutions for the system response are presented for specific values of the parameters of system. It was shown that in this type system one mode of vibrations may excite or damp another mode, and that except different kinds of periodic vibrations there may also appear chaotic vibrations. For the identification of the responses of the system various techniques, including chaos techniques such as bifurcation diagrams and time histories, power spectral densities (FFT), Poincare maps and exponents of Lyapunov maybe use.
9
Synchronization test results of oscillator network CMOS VLSI chip
Kowalski J., Strzelecki M.
Elektronika : konstrukcje, technologie, zastosowania
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2007
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Vol. 48, nr 4
53-57
EN
This paper presents synchronization test results of CMOS VLSI ASIC integrated circuit, which implements a network of synchronized oscillators. The network chip architecture was briefly described. This circuit was designed for segmentation of binary images, which is an important issue in biomedical image analysis. The hardware realisation of oscillator network provides much faster image segmentation compared to computer simulation techniques. Oscillator's free frequency tuning idea and procedure have been proposed. Automatic oscillator's frequency tuning procedure has been implemented in LabView. Tuned chip allowed for synchronization of longer chain objects presented in the input image. Synchronization result of oscillators corresponding to a spiral image obtained using tuned oscillator network chip has been presented and discussed.
PL
Zaprezentowano wyniki testów synchronizacji oscylatorów w układzie scalonym CMOS VLSI sieci synchronicznych oscylatorów. Przedstawiono w skrócie architekturę układu scalonego sieci, zaprojektowanego do zadań segmentacji obrazów binarnych. Realizacja sprzętowa sieci synchronicznych oscylatorów pozwala na znacznie szybszą segmentację obrazów w porównaniu do metod opartych na symulacji komputerowej. Przedstawiono ideę oraz procedurę strojenia częstotliwości drgań własnych oscylatorów w sieci. Automatyczna procedura strojenia oscylatorów w sieci została zaimplementowana w środowisku LabView. Automatycznie zestrojone oscylatory w sieci umożliwiają ich synchronizację dla obrazów zawierających dłuższe łańcuchy pikseli. Zaprezentowano i przedyskutowano eksperyment synchronizacji oscylatorów przetwarzających obraz spirali.
10
Content available remote Antyfazowa synchronizacja chaosu przez nieciągłe połączenie: dwa uderzające oscylatory
Błażejczyk-Okolewska B., Brindley J., Czołczyński K., Kapitaniak T.
Vibrations in Physical Systems
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2000
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Vol. 19
62--63
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