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Consistency of mathematical and experimental model of the autoparametric system
Fischer, Cyril ; Náprstek, Jiří
This paper presents a long-overdue comparison of data obtained from experimental investigation of a spherical vibration absorber with the results of two mathematical models of the motion of a heavy sphere in a spherical surface. It shows that the danger posed by the potentially unstable self-parametric nature of the mathematical system is not too great in the case of realistic configurations, and that the values of the parameters describing the realistic structures remain within intervals corresponding to the stable behaviour of the absorber.
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Experimental verification of resonance behaviour of a damped spherical pendulum
Fischer, Cyril ; Pospíšil, Stanislav ; Náprstek, Jiří
Theoretical, experimental and numerical analysis of a spherical pendulum is carried out. The stability of the response in a vertical plane is analysed in the theoretically predicted resonance region. Mathematical model respects the non-linear character of the pendulum and allows to introduce asymmetrical damping. Experimental pendulum is hanging from the Cardan joint and placed to carriage. Uni-directional harmonic excitation is applied to the system. The pendulum is damped by two magnetic units. These units are able to reproduce linear viscous damping independently in both principal response components. Response in in-plane and out-of-plane directions is measured and analyzed.
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Experimental and theoretical stability analysis of damped auto-parametric pendulum
Pospíšil, Stanislav ; Fischer, Cyril ; Náprstek, Jiří
The article describes an experimental and theoretical treatment of the auto-parametric pendulum damper modelled as a double-degree-of-freedom (DDOF) system. It is strongly non-linear, with the harmonic excitation being applied in the suspension point and interpreted for instance as an excitation by wind. The stability of the motion in a vertical plane is analysed in the meaning of semi-trivial vibration. This effect of stability loss and possible stability regain is very important from practical point of view, because the motion of an damper beyond the stability limits may act negatively and thus endanger the structure itself. Special experimental frame was developed.The stability of the system is analysed experimentally and compared with theoretical results.
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Dynamic stability and post-critical processes of pendulum related auto-parametric systems
Náprstek, Jiří ; Fischer, Cyril
The existence and stability of the semi-trivial solution of the auto-parametric system is analyzed. Individual types of post-critical states are discussed (limit cycles, quasi-periodic response types, chaotic processes, transition processes). General considerations are demonstrated on particular DDOF and MDOF cases in both classes mentioned above. Sensitivity of several systems to stability loss with respect to their parameters, excitation amplitudes and other factors are evaluated. Bifurcation mechanism and diagrams are developed and analyzed. Important transition effects together with physical interpretation are investigated. Some open problems and possible future research strategy are outlined.
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Some properties of non-linear resonance of the pendulum damper
Fischer, Cyril ; Náprstek, Jiří
The pendulum damper modelled as a two degree of freedom strongly non-linear auto-parametric system is investigated using an approximate differential system. Uni-directional harmonic external excitation at the suspension point is considered. The resonance phenomenon cannot be described using the semi-trivial solution. In this contribution, nature of the numerical solution in the state of resonance is thoroughly investigated as a preliminary work for the detailed analytical study. Stationary and non-stationary (quasiperiodic) character of the resonance solution is determined and characterised. General form of a solution is proposed
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Dvě rovnice popisjící kyvadlový tlumič
Fischer, Cyril ; Náprstek, Jiří
The pendulum damper modelled as a two degree of freedom strongly non-linear auto-parametric system is investigated using two approximate differential systems. Uni-directional harmonic external excitation at the suspension point is considered. Semi-trivial solutions and their stability are analyzed. The thorough analysis of the non-linear system using less simplification than it is used in the previous paper is performed. Both approaches are compared and conclusions are drawn.
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