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Analysis of eigen-values of viscously damped two degrees of freedom system due to changes of parameters of secondary subsystem
Hračov, Stanislav ; Náprstek, Jiří ; Pospíšil, Stanislav
The paper deals with an analysis of non-classically damped two degrees of freedom system from the point of view of eigen-values. The theoretical relations between the system parameters for the case of multiple complex eigen-values were derived. The parametric problem was carried out analytically and graphically. The influence of the relative frequency tuning on the overdamping of individual eigen-values with increasing of the secondary damping was studied. The overdamping intervals were defined with respect to the mass ratio and the frequency tuning. The boundaries between respective overdamping intervals represent among others the frequency tuning of system with multiple complex eigen-values. The phase between components of eigen-modes and its relation to the eigen-values were examined with respect to the secondary damping increase.
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Multipurpose experimental rig for aeroelastic tests of bridge girders and slender beams
Pospíšil, Stanislav ; Král, Radomil ; Náprstek, Jiří
The bridges, footbridges and broadcast towers create an important subset of infrastructure subjected to dynamic loading of various origins. Especially, exposed to wind, they are susceptible to vibrations under certain circumstances due to pure load action or aero-elastic effects. This means that once an element or a structure starts to vibrate, a complex interaction between the moving boundary and the airflow takes place. Because of the complexity, the research has been in progress for several decades in both theoretical and experimental way. The article describes an original and multi-purpose experimental frame for the analysis of complex linear and non-linear aspects of aero-elastic behavior of the slender beams. The apparatus meets the rigorous theoretical assumptions and allows very precise and quick adjustment of the stiffness and mass of the structure, which is not always possible with a traditional "parallel spring-supported bridge" approach used by many researchers.
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Dynamics of a vibration damperworking on a principle of a heavy ball rolling inside a spherical dish
Náprstek, Jiří ; Fischer, Cyril ; Pirner, Miroš
Wind excited vibrations of slender structures such as towers, masts or certain types of bridges can be reduced using passive or active vibration absorbers. If there is available only a limited vertical space to install such a device, a ball type of absorber can be recommended. In general, it is a semispherical horizontal dish in which a ball of a smaller diameter is rolling. Ratio of both diameters, mass of the rolling ball, quality of contact surfaces and other parameters should correspond with characteristics of the structure. The ball absorber is modeled as a holonomous system. Using Lagrange equations of the second type, governing non-linear differential system is carried out. The solution procedure combines analytical and numerical processes. As the main tool for dynamic stability investigation the 2nd Lyapunov method is used. The function and effectiveness of the absorber identical with those installed at the existing TV towers was examined in the laboratory.
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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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