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Numerical simulations of aeroelastic instabilities in turbine blade cascade by modified Van der Pol model at running excitation
Pešek, Luděk ; Šnábl, Pavel ; Prasad, Chandra Shekhar ; Delanney, Y.
Apart from rotary test rig for evaluation of structural dynamics of the bladed wheels, the control flutter experiments has been performed on the linear cascade model in the subsonic wind tunnel in the Institute of Thermomechanics, of CAS, in Prague. These experiments are aimed at stability evaluation of the cascade at running waves or at stability limit testing by flow speed changes or by force impulses of blades. The onset of flutter and its spreading in the cascade are observed, too. The linear cascade model consists of five NACA010 blades. All the blades can be separately excited with electromagnetic torque excitation mechanism and all of them are instrumented to measure the aerodynamic moments which can be used to calculate the aerodynamic work. A more details about the linear blade cascade experimental set up can be found in [1-2]. To predict a dynamic behaviour in the blade cascade, we have been dealing with simplified theoretical modelling of the aeroelastic instability in turbine blade cascade [3-5]. Due to the application of the reduced cascade model consisting of simple elements – springs, rigid bodies, linear dampers – and aeroelastic forces introduced by analytical Van der Pol model, it facilitates to study the dangerous states of vibration of such complicated turbine parts [6-9]. This study is aimed at examination of aeroelastic instabilities of 10-blade cascade at running excitation that arises due to the wakes flowing from stator the blades to the rotating blades. They cause forced excitation in the narrow frequency range.
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Construction of the Lyapunov function reflecting the physical properties of the model
Náprstek, Jiří ; Fischer, Cyril
Practical experience shows that the random excitation component can affect the system response and its dynamic stability not only negatively but also positively. Such mechanisms are usually developed heuristically and are often not sufficiently justified theoretically. The paper presents a possibility of using the properties of first integrals for the construction of a Lyapunov function for the analysis of a dynamic system stability in the stochastic domain. In such case, the Lyapunov function itself contains information on the examined system and, consequently, it is able to provide a more detailed insight into the system stability properties. The procedure is illustrated by a nonlinear SDOF example.
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Analysis of van der Pol equation on slow time scale for combined random and harmonic excitation
Náprstek, Jiří ; Fischer, Cyril
Vortex shedding represents one of the most important processes that constantly attract the attention of experimental and theoretical research. A number of non-linear effects arise from the fluid-structure interaction. The non-stationary response in the vicinity of the lock-in region has a quasi-periodic character, beating frequency of which varies considerably with the distance from the lock-in frequency. This property is significantly affected by the assumption of combined random and harmonic excitation. This paper describes several details that contribute to the probabilistic characteristics of the system on a time-slow scale using partial response amplitudes.
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