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Study of aeroelastic interference effect among four cylinders arranged in rectangular configuration
Hračov, Stanislav ; Macháček, Michael ; Michálek, Petr
The paper describes the analysis of the destructive oscillation of a skewed steel rod with the length 21 m. The steel rod is a part of roof supporting bundle (rectangular array) of cylindrical hangers at the airport building; it is therefore exposed to frequent moderate and sometimes strong winds with the low turbulence. The vibration is analyzed from the aeroelastic perspective, i.e. the cause of the oscillation is analyzed as wake-induced vibration because the collapse was observed at the bottom downwind hanger in that array configuration. The normalized distance of hangers in horizontal and vertical directions is equal to 3.15D, and 3.8D, respectively, where D is the diameter of the hanger cross section. Experimental testing of 1:1 scaled sectional model of four-cylinder array in the wind tunnel indicates, that the cause of the high level vibration is most probably the interference galloping. The unstable behavior was detected both for the downwind hanger as a part of rectangular array and for the hanger as a part of a two hangers in a row only. The results indicate the strong influence of the top pair of the hangers on the decrease of the critical wind velocity, which is even below the value of the critical wind velocity obtained for two hangers only. The strong hysteresis effect resulting in the preservation of the high vibration amplitudes even after the decrease of wind speed far below the critical one, was observed.
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Sensitivity of the generalized van der Pol equation to sub- or super-harmonic resonance
Fischer, Cyril ; Náprstek, Jiří
Vortex induced vibrations in aeroelasticity of slender structures are often described using the generalized van der Pol equation. This equation provides a good analytical model which is able to reproduce the complex non-stationary behaviour of the structure. Due to the non-linear character of the underlying physical system, the effect of sub- or super-harmonic synchronization can be encountered. The contribution presents results of a numerical study aimed at detailed identification of sub- or super-harmonic resonance effects in the model. This way it supplements the previous works by the authors.
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Rapid research with computer algebra systems
Fischer, Cyril
Computer algebra systems (CAS) are gaining popularity not only among young students and scholars but also as a tool for serious work. These highly complicated software systems, which used to just be regarded as toys for computer enthusiasts, have reached maturity. Nowadays such systems are available on a variety of computer platforms, starting from freely-available on-line services up to complex and expensive software packages. The aim of this review paper is to show some selected capabilities of CAS and point out some problems with their usage from the point of view of 25 years of experience.
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Local stabilization of the quasiperiodic response of the generalized van der Pol oscillator
Fischer, Cyril ; Náprstek, Jiří
The generalized van der Pol equation is often used for description of various effects originating in the aero-elasticity of large slender engineering structures. This applies mainly to the quasiperiodic beatings that can be encountered especially in lock-in regimes when the vortex frequency becomes close to the structure eigenfrequency with a small detuning. The current paper presents numerical analysis of influence of the subor superharmonic excitation on the character of the response of a generalized van der Pol oscillator. This way it complements two previous papers of the authors dealing with stability analysis of certain types of the stationary periodic or quasiperiodic response of the system under study.
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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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Probability density determination by means of Gibbs entropy probability density
Náprstek, Jiří ; Fischer, Cyril
A method of random response investigation of a nonlinear dynam-ical system is discussed. In particular, the solution of the probability density of a single/multi-degree of freedom (SDOF/MDOF) system response is investigated. Multiple stable equilibrium states with possible jumps of the snap-through type among them are considered. The system is Hamiltonian with weak damping excited by a set of non-stationary Gaussian white noises. The solution, which is based on the Gibbs principle of the maximum entropy of probability, can be employed in various branches of engineering. The search for the extreme of the Gibbs entropy functional is formulated as a constrained optimization problem. The secondary constraints follow from the Fokker-Planck equation (FPE) for the system considered or from the system of ordinary di_erential equations for the stochastic moments of the response derived from the relevant FPE
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