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1
Content available remote Road to chaos in a Duflng oscillator with time delay loop
Borkowski Łukasz
Mechanics and Mechanical Engineering
|
2021
|
Vol. 25, nr 1
84--87
EN
This article examines a single Duffing oscillator with a time delay loop. The research aims to check the impact of the time delay value on the nature of the solution, in particular the scenario of transition to a chaotic solution. Dynamic tools such as bifurcation diagrams, phase portraits, Poincaré maps, and FFT analysis will be used to evaluate the obtained results.
2
Content available Steady state vibration of the periodically forced and damped pure nonlinear two-degrees-of-freedom oscillator
Cveticanin Livija, Zukovic Miodrag, Cveticanin Dragan
Journal of Theoretical and Applied Mechanics
|
2019
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Vol. 57 nr 2
445--460
EN
In the paper, a pure nonlinear and damped two-mass oscillator excited with a periodical force is considered. The oscillator is modelled with a system of two coupled second order nonlinear and non-homogenous equations. Using the model, two problems are investigated: one, identification of the excitation force for the known vibrating response of the system, and the second, determination of vibrations of the system excited with the known periodical force. Using the steady-state motion of the nonlinear oscillator, a method for identification of the excitation force is developed. For the pure nonlinear oscillator, it is obtained that the forcing function has the form of the Ateb function. However, if the excitation force is known, the procedure for computing the steady-state vibration of the system is introduced. The solution corresponds to steady-state vibrations of the free oscillator, but the amplitude and phase are assumed to be time variable. The averaged solutions are obtained for the pure nonlinear oscillator with an additional linear elastic force and for the van der Pol oscillator. Analytically obtained solutions are compared with numerical ones. They are in good agreement.
3
Content available remote Prediction of solutions of the Duffing system with tuned mass damper
Mnich K.
Mechanics and Mechanical Engineering
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2018
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Vol. 22, nr 4
983--989
EN
In this work we analyze the behavior of a nonlinear dynamical system using a probabilistic approach. We focus on the coexistence of solutions and we check how the changes in the parameters of excitation influence the dynamics of the system. For the demonstration we use the Duffng oscillator with the tuned mass absorber. We mention the numerous attractors present in such a system and describe how they were found with the method based on the basin stability concept.
4
Content available Synchronization of an uncertain Duffing oscillator with higher order chaotic systems
Kabziński J.
International Journal of Applied Mathematics and Computer Science
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2018
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Vol. 28, no. 4
625--634
EN
The problem of practical synchronization of an uncertain Duffing oscillator with a higher order chaotic system is considered. Adaptive control techniques are used to obtain chaos synchronization in the presence of unknown parameters and bounded, unstructured, external disturbances. The features of the proposed controllers are compared by solving Duffing–Arneodo and Duffing–Chua synchronization problems.
5
Content available Periodic signal detection with using duffing system poincare map analysis
Martynyuk V, Fedula M, Balov O
Advances in Science and Technology. Research Journal
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2014
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Vol. 8, nr 22
26--30
EN
In this article the periodic signal detection method on the base of Duffing system chaotic oscillations analysis is presented. This work is a development of the chaos-based signal detection technique. Generally, chaos-based signal detection is the detection of chaotic-to-periodic state transition under input periodic component influence. If the in¬put periodic component reaches certain threshold value, the system transforms from chaotic state to periodic state. The Duffing-type chaotic systems are often used for such a signal detection purpose because of their ability to work in chaotic state for a long time and relatively simple realization. The main advantage of chaos-based signal detection methods is the utilization of chaotic system sensitivity to weak signals. But such methods are not used in practice because of the chaotic system state control problems. The method presented does not require an exact system state control. The Duffing system works continuously in chaotic state and the periodic signal detection process is based on the analysis of Duffing system Poincare map fractal structure. This structure does not depend on noise, and therefore the minimum input signal-to-noise ratio required for periodic signal detection is not limited by chaotic system state control tolerance.
6
Content available The dynamics of the cutting process with Duffing nonlinearity
Weremczuk A., Kęcik K., Rusinek R., Warmiński J.
Eksploatacja i Niezawodność
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2013
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Vol. 15, no. 3
209-213
EN
The paper presents the nonlinear one degree of freedom model of cutting process. To describe the dynamics the Duffing model with time delay part is used. The model is solved analytically by using the multiple time scale method. The stability lobe diagrams are determined numerically and analytically. The obtained results show that stability region depends on initial conditions of the system.
PL
W artykule przedstawiono jednowymiarowy nieliniowy model skrawania. Do opisu procesu przyjęto model Duffinga z opóźnieniem czasowym. Model rozwiązano analitycznie za pomocą metody wielu skal czasowych. Wykres stabilności otrzymano numerycznie i analitycznie. Wykazano, że obszary stabilności zależą od warunków początkowych układu.
7
Content available remote Magnetorheological Damping of a System with a Pendulum Vibration Absorber
Kęcik K., Mitura A.
Machine Dynamics Research
|
2012
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Vol. 36, No. 2
49-56
EN
This paper presents a numerical study of a nonlinear two-degrees-of-freedom system consisting of the Duffing oscillator with an attached pendulum absorber. The system is excited close to the principal parametric resonance. By applying numerical simulation we show the influence of viscous and a magnetorheological damping (MR) on the vibration absorption effect. The absorber can be highly efficient for slightly damped systems, if it is correctly tuned. A new element in this work is to use the MR damper, modelled with the effect of hysteretic loop in the nonlinear damper.
8
Content available remote Nieliniowe układy dynamiczne – problem nadal otwarty
Chudzik A. A.
Mechanik
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2011
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R. 84, nr 7(CD)
89-94
PL
W pracy przedstawiono zjawisko wystąpienia synchronizacji oscylatorów typu Duffing podwieszonych do elastycznej belki. Zbadano wpływ zmiany modelu belki na zachowanie oscylatorów. Wykazano, że dla danych warunków początkowych wzbudzenia, początkowo nieliniowe, chaotyczne oscylacje struktury stają się okresowe i synchroniczne.
EN
The paper presents the phenomenon of synchronization of Duffing oscillators suspended on a flexible beam. This article presents the results of changes in the beam model on the behavior of oscillators. It was shown that for the initial conditions of excitation, initially nonlinear, chaotic oscillations of structures become periodic and synchronous.
9
Chaotic behavior description in technical systems
Houfek L., Kratochvil C., Krejsa J., Houfek M., Navrat Τ.
Modelling and Optimization of Physical Systems
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2007
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z. 6
77--80
EN
Chaotic behavior of technical systems is lately under great interest of researchers. The paper describes a possibility to analyze system which exhibits chaotic oscillations. For simplicity the model of Duffing oscillator was selected as analyzed case, as the chaotic oscillations occur in this model. Bifurcation diagram and phase plane analysis are used as analysis tool.
10
Content available remote Numerical analysis of Duffing oscillator with dry friction damper
Stefański A., Wojewoda J., Wiercigroch M
Mechanics and Mechanical Engineering
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2000
|
Vol. 4, nr 2
127--137
EN
Mathematical modelling and numerical analysis of the classical Duffing oscillator with four different dry friction dampers is presented. Then the influence of the different types of friction characteristics on the system dynamic responses is systematically examined pointing out a necessity of proposing a new dry friction model, which is constructed based on the non-reversible approach [4,8]. A comparison between the dynamic responses for all models including the new one is provided.
11
Content available Statistical and equivalent linearization techniques with probability density criteria
Socha L.
Journal of Theoretical and Applied Mechanics
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1999
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nr 2
369-382
EN
The concept of statistical and equvalent linearization with probability density criteria for dynamic systems under Gaussian excitation is considered in the paper. New criteria of linearization and two approximate approaches are proposed. In the first one (statistical linearization) in order to establish the linearization coefficients and response characteristics the output probability density functions of statistic nonlinear element and the corresponding static linearized element are used in an iterative procedure. In the second approach (equivalent linearization) the direct minimization of a criterion based on output probability density functions of dynamic nonlinear system is proposed. The detailed analysis and numerical results are given for the Duffing oscillator.
PL
W pracy zaproponowano metodę statystycznej i równoważnej linearyzacji dla układów dynamicznych z wymuszeniami o charakterze białych szumów Gaussowskich i kryteriami w przestrzeni funkcji gęstości prawdopodobieństw. Przy wyznaczaniu współczynników linearyzacji i charakterystyk rozwiązań układu dynamicznego za pomocą metody statystycznej linearyzacji korzysta się z minimalizacji kryterium uwzględniającego różnicę wyjściowych funkcji gęstości prawdopodobieństw odpowiednio elementu nieliniowego zlinearyzowanego oraz pewnej procedury iteracyjnej. W przypadku równoważnej linearyzacji przeprowadza się bezpośrednią minimalizację kryterium uwzględniającego różnicę wyjściowych funkcji gęstości prawdopodobieństw odpowiednio układów dynamicznych nieliniowego i zlinearyzowanego. Szczegółową analizę i obliczenia numeryczne przeprowadzono dla oscylatora Duffinga.
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