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Non-linear Vibration of Planar Case of Three-blade Bundle with Dry Friction Contacts
Šnábl, Pavel ; Pešek, Luděk ; Půst, Ladislav
Using dry friction couplings (so called tie-bosses) between the blades in turbine rotors can be used to suppress dangerous resonant vibrations of turbine blades and it has been studied on our institute on various models. Experimental setup of three-blade bundle was built along with bladed wheel. The first set-up of the bundle was with blades turned 45 degrees to the disc plane. In that case the deformation of the blades causes turning of the ends of tie-bosses and edge contact together with multi-directional slip occurs. The experimental set-up was simplified herein so that the blades are parallel to the disc plane and in-line slip occurs. Although single electromagnet was used to excite the system, the first mode of vibration with no slip in tie-bosses just occurred. In case of bladed wheel, all blades have coupling through tie-bosses with neighbouring blades which stiffen them and raise their eigenfrequency. In our case, a mistuning by reducing mass of side blades caused similar behaviour. Steel to steel contact pair was used for the first tests.
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Stochastic resonance in dynamics and related disciplines
Náprstek, Jiří ; Fischer, Cyril
Stochastic resonance (SR) is a phenomenon which can be observed in some nonlinear dynamic systems under combined excitation including deterministic harmonic force and random noise. This phenomenon was observed the first in the early 1940s when investigating the Brownian motion. Later several disciplines in optics, plasma physics, biomedicine and social sciences encountered effects of this type. However, the actual discovery and start of intensive period of investigation is dated in early 1980s when the idea of SR initiated remarkable inter disciplinary interest including most areas of physics, chemistry and neuro-physiology with a significant overlap to engineering and industrial area. Promising opportunities to employ SR in mechanics emerged only recently to model certain post-critical effects in non-linear dynamics and simultaneously to develop new vibration damping devices, energy harvesting facilities, sophisticated measuring technics and others. The aim of the paper is to present information about a new challenging discipline offering a large field of basic research and possibilities for practical applications.
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Aeroelastic divergence modeled by means of the stochastic resonance
Náprstek, Jiří ; Pospíšil, Stanislav
The divergence is one of the most important and dangerous phenomenon of aeroelastic post-critical states occurring at a prismatic slender beam in a cross-flow. This phenomenon manifests by stable periodic hopping between two nearly constant limits perturbed by random noises. Experimental observation and numerical simulation motivates an idea to model this process as the effect of the stochastic resonance. Being observed and practically used in a number of disciplines in physics (optics, plasma physics, atd.) its mathematical basis follows in the most simple case from properties of the Duffing equation with negative linear part of the stiffness. The occurrence of this phenomenon depends on certain combinations of input parameters, which can be determined theoretically and verified experimentally in the wind tunnel.
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Dynamic response of a heavy ball rolling inside a spherical dish under external excitation
Náprstek, Jiří ; Fischer, Cyril
The set of a heavy metallic ball which is rolling freely inside a semispherical dish with larger diameter, being fixed to structure, is frequently used as tuned mass damper of vibration. 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 damper is modelled as a non-holonomic system. Hamiltonian functional including an adequate form of the Rayleigh function is formulated in moving coordinates using Euler angles and completed by ancillary constraints via Lagrangian multipliers. Subsequently Lagrangian differential system is carried out. Together with rolling conditions the governing system of seven equations is formulated. Later Lagrangian multipliers character is analysed and redundant motion components are eliminated. First integrals are derived and main energy balances evaluated together with their physical interpretation. Discussion of basic dynamic properties of the system is provided.
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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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Analytic model of a ball rolling on a spherical surface under harmonic kinematic excitation
Náprstek, Jiří ; Fischer, Cyril
The set of a heavy metallic ball which is rolling freely inside a semi-spherical dish with larger diameter, being fixed to structure, is frequently used as tuned mass damper of vibration. 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 damper is modeled as a non-holonomic system. Hamiltonian functional including an adequate form of the Rayleigh function is formulated in moving coordinates using Euler angles and completed by ancillary constraints via Lagrangian multipliers. Subsequently Lagrangian differential system is carried out. Together with rolling conditions the governing system of seven equations is formulated. Later Lagrangian multipliers character is analyzed and redundant motion components are eliminated. First integrals are derived and main energy balances evaluated together with their physical interpretation.
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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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