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1
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.
2
Content available remote Modeling Impact of a Cantilever Beam
Kapitaniak T., Czołczyński K., Błażejczyk-Okolewska B.
Machine Dynamics Problems
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2008
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Vol. 32, No. 4
37-49
EN
A vibrating system with one degree of freedom that can be employed to predict a nature of motion with impacts of certain systems with heavy mass of elastic elements is subject to investigations. An example of such a system is a heavy cantilever beam with a mass impacting on the base, fixed at its end. The applicability limits of two ways of modelling impacts described as hard impacts and soft impacts, as well as advantages and disadvantages of both the ways have been presented below.
3
Content available remote Dynamics of an Array of Duffing Oscillators Suspended on Elastic Etructures
Czołczyński K., Stefański A., Perlikowski P., Kapitaniak T.
Machine Dynamics Problems
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2007
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Vol. 31, No. 2
57-65
EN
We consider the dynamics of externally excited chaotic oscillators suspended on the elastic structure. We show that for the given conditions of oscillations of the structure, initially uncorrelated chaotic oscillators become periodic and synchronous. In the periodic regime we observed synchronized clusters and multistability as different attractors coexist.
4
Content available remote Drgania wymuszone dwóch zderzających się oscylatorów
Czołczyński K., Błażejczyk-Okolewska B.
Vibrations in Physical Systems
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2000
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Vol. 19
86--87
5
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
6
Content available remote Impact oscillator as dynamic damper
Blażejczyk-Okolewska B., Czołczyński K.
Mechanics and Mechanical Engineering
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2000
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Vol. 4, nr 1
105--112
EN
In a large number of various machines, design or working conditions lead to collisions between the components of a system. Examples of this type include gears, bearings, vibration isolation elements, buildings during earthquakes, impact dampers and impact hammers. In recent years, many important works concern a system of two single-degree-of freedom impacting linear oscillators subjected to periodic external force. The object of my investigations is a system composed of two harmonic oscillators. During the motion, the oscillators impact each other. A special attention was paid to determine an influence of system parameters on a vibration amplitude and a character of the motion (regular or irregular). The investigations were carried out by means of numerical simulation.
7
Content available remote Dynamics of Two Independent Impacting Oscillators
Czołczyński K., Błażejczyk-Okolewska B.
Machine Dynamics Problems
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2000
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Vol. 24, No. 1
47-61
EN
In the paper we present the dynamic behavior of a mechanical system, which consists of two oscillators. When the motion of the oscillators is forced by an external forcing, they may collide each other, what causes perturbation of their motion. Because of these impacts, for many sets of the system parameters, the motion has a chaotic character. We show the influence of the damping, stiffness and mass of oscillators on the range of chaotic behavior. The object of presentation are also self-similar structures, found in bifurcation diagrams, and also super- and sub-harmonical resonances of the system. The investigations were made using the numerical method which was verifield by comparing some results of calculations with the experiment.
8
Content available remote Dynamics of the linear oscillator with impacts
Czołczyński K., Błażejczyk-Okolewska B.
Mechanics and Mechanical Engineering
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1999
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Vol. 3, nr 1
5--14
EN
A dynamical behaviour of the linear oscillator with one degree of freedom is presented. During a motion excited by an external harmonic force the oscillator impacts on the basement. A physical and mathematical model of the system, as well as bifurcation diagrams showing an effect of the excitation frequency on the character of the system motion have been discussed. Results of the analysis of an influence of the viscous damping coefficient on regularity of the oscillator motion have also been presented. The investigations have been conducted by means of numerical simulations.
9
Content available remote Chaotic motion of the impact force generator
Błażejczyk-Okolewska B., Czołczyński K., Kapitaniak T.
Mechanics and Mechanical Engineering
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1998
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Vol. 2, nr 1
49--53
EN
During the last years the interest of scientists in multibody mechanical systems in which the phenomenon of impact occurs has been still growing. In the present paper a principle of operation of the impact force generator being an element of the rotor of the heat exchanger has been presented. Step disturbances of the rotational velocity of the rotor caused by the generator are aimed at intensification of the heat exchange process.
10
Content available remote Analysis and simulation of deterministic chaos in the dynamical model of aeroplane engine mounting
Jeż M., Stefański A., Czołczyński K.
Mechanics and Mechanical Engineering
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1998
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Vol. 2, nr 2
163--173
EN
A dynamic model of a piston engine mounted in the aeroplane has been formulated. The equations of motion have been identified for 4-cylinder boxer Franklin installed in the Polish acrobatic Koliber plane. Comparision of engine body acceleration RMS values obtained by measurement and simulation has given positive results. The engine body vibrations in the plane of the reactive torque of forces have been investigeted in the Matlab-Simulink environment and with the help of the INSITE software. It has revealed relationships of system responses to its parameters and excitation values to assure a methodical approach to the suspension synthesis. The asymtotic methods have given multidimensional expressions for natural frequencies and resonance curves. The numerical methods have been applied to establish stability boundaries, chaos occurrence, routes to chaos and to identify chaos symptoms.
11
Content available remote Air Hammer Phenomenon in Rotors Supported in Elastically Mounted Gas Bearings
Czołczyński K., Kapitaniak T.
Machine Dynamics Problems
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1998
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Vol. 20
101-112
EN
When during the operation of rotors supported in gas bearings their rotational velocity reaches a sufficiently high value, loss of steady-state stability occurs. This instability is caused by the loss of damping properties of the gas film, which leads to self-excited vibrations. These vibrations are the basic obstacle to a widespread application of a gas bearings. The phenomenon of self-excited vibrations can be avoided by introducting an elastic supporting structure between the bearing bushes and the casing, characterized by properly selected stiffness and damping coefficients. In practice such a structure can have the form of an externally pressurized gas ring. In this paper we demonstrate, on the basis of selected examples, in what ranges of the frequencies of vibrations the "air hammer" phenomenon may cause the instability, and what happens on the stability thresholds - is there a sub- or supe-critical Hopf bifurcation. We also show a design of the ring structure, especially of its feeding system, which ensure the required values of stiffnes and damping coefficients (with regard to the stability). Our investigations have been carried out by means of a numerical simulation method with the use of a mathematical model of the gas bearing, verifield already many times.
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