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Aeroelastic instability of differently porous U-profiles in crosswind direction
Hračov, Stanislav ; Macháček, Michael
Flow-induced vibrations of the flexibly mounted slender U-shaped beams allowed to oscillate in the crosswind direction only are studied experimentally in the wind tunnel. All beams are characterized by a cross section having a side ratio of along-wind to across-wind dimension equal to two. The effects of two depths of U profiles and two porosities of their flanges ( 0 % and 75 %) onto a loss of aeroelastic stability are investigated under the smooth flow conditions and for low Scruton numbers. The results indicate almost similar proneness of the non-porous beams to galloping-type oscillations to a rectangular prism with the same side ratio regardless their depth. The onset of across-wind galloping occurred in these cases at wind velocity very close to von-Kármán-vortex-resonance flow speed, even though the critical velocity predicted by the quasisteady theory is much lower. For porous and shallower U profile this asynchronous quenching also takes\nplace. However, the higher flange porosity reduces significantly not only the vortex-shedding effect, but also causes an increase in the onset galloping velocity above the critical speed determined for non-porous profiles. In the case of deeper U-shaped beam, the effect of higher porosity even suppresses the proneness to galloping
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Aerodynamic wind tunnel testing of U-beams
Hračov, Stanislav ; Macháček, Michael
The paper presents the outcomes from the experimental testing of the set of slender U-beams in the climatic wind tunnel. All analysed beams have identical basic geometry with the U-shaped cross section given by the side ratio equal to 2 (having the short side perpendicular to the flow), but they differ in the porosity of their flanges and in the depth of their profile. Two depths of the U-profile combined with six different levels of flange porosity are analysed. The U-beams were tested in the smooth flow in order to determine their aerodynamic coefficients for various angles of wind attack. The influences of the depth and porosity onto these coefficients are studied in detail. Moreover, the susceptibility of each individual case to transversal galloping is assessed based on the classical quasi-steady theory. The comparison with the results from the aerodynamic tests of the prisms with rectangular cross-sections having side rations equal to two, four and six is also given and discussed.
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Numerical study of the air flow around the U-profile
Ledvinková, Blanka ; Hračov, Stanislav ; Macháček, Michael
Our contribution deals with the numerical simulations of the air flow around u-profiles at various angles of attack with the aim to investigate their proneness to galloping. The Unsteady Reynolds Averaged Navier- Stokes (RANS) simulations were performed in the COMSOL Multiphysics software, k-ω SST turbulence model was used. The values of the aerodynamic coefficients and Strouhal number were evaluated and the results were compared with the results obtained experimentally in the wind tunnel.
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Numerical solution of a stochastic model of a ball-type vibration absorber
Fischer, Cyril ; Náprstek, Jiří
The mathematical model of a ball-type vibration absorber represents a non-linear differential system which includes non-holonomic constraints. When a random ambient excitation is taken into account, the system has to be treated as a stochastic deferential equation. Depending on the level of simplifcation, an analytical solution is not practicable and numerical solution procedures have to be applied. The contribution presents a simple stochastic analysis of a particular resonance effect which can negatively influence efficiency of the absorber.
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Stability of a bar influenced by small and large imperfections
Náprstek, Jiří ; Fischer, Cyril
The geometrical and physical imperfections of systems can drastically reduce their critical loading. These imperfections are usually of stochastic character and, therefore, they act as random parametric perturbations of coefficients of corresponding differential equations. In this paper, the imperfections are introduced as multidimensional statistics on the set of a large number of realizations of the same system. As far as the amount of information is small or the imperfections themselves cannot be considered small, the convex analysis is preferable. The paper compares results obtained by both stochastic and convex analyses for hyperprism and demonstrates when each of them is more convenient to be used. Besides of the hyper-prism, the possibilities and properties of other modifications of convex method are considered, especially those based on the definition of imperfection zone marked as a centric hyper-ellipsoid or as an eccentric hyper-ellipsoid. The analytical background was brought up to the level when only a few configurations of imperfections are sufficient to be evaluated numerically. These configurations are obtained by means of the convex analysis as points of extreme critical loading using the Lagrange method of constrained extremes.
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Multifold stationary solutions of an auto-parametric non-linear 2DOF system
Fischer, Cyril ; Náprstek, Jiří
A non-linear 2DOF model of a bridge girder with a bluff cross-section under wind loading is used to describe the heave and pitch self-excited motion. Existence conditions of stationary auto-parametric response for both the self-excited case and an assumption of a harmonic load form a non-linear algebraic system of equations. Number of distinct solutions to this algebraic system depends on the frequencies of two principal aero-elastic modes and other system parameters. Thus, the system may possess none, one, or several stationary solutions, whose stability has to be checked using the Routh-Hurwitz conditions. If all quantities entering the system are continuous functions, individual solutions may exhibit (piecewise) continuous dependence on selected system parameters. Thus, multiple identified solutions to the system for a given set of parameters may actually belong to a single solution branch and their values can be determined from the knowledge of the solution branch. Such a situation may significantly simplify assessment of stability of the particular solutions and/or provides an applicable overall description of the system response.
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Random response of a dynamic system under polynomial of a white noise
Náprstek, Jiří ; Fischer, Cyril
Many types of external additive random excitation of dynamic systems admit to be modelled as a combination of powers of a Gaussian noise. Such a type of excitation produces a non-Gaussian response even if the dynamic system is linear and the excitation is additive only. Although the excitation as a whole is non-Gaussian, the problem can be transformed into the form of a linear system with an additive and multiplicative white noise excitation which _nally produces a non-Gaussian response. The general method of transformation, the respective FPK equation, basic stochastic moments of the response, and a demonstrative example are discussed.
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System response with random imperfections in coefficients on the space of realizations
Náprstek, Jiří ; Fischer, Cyril
The contribution is concerned with the analysis of the simultaneous effect of a random perturbation and a white noise in the coefficient of the system. The excitation of the system of the 1-st order is described by the sum of a deterministic signal and an additive white noise which is partly correlated with the parametric noise. The random perturbation in the parameter is considered as a statistics in a set of realizations. It reveals that the density of probability of perturbations must be limited in the phase space, otherwise the system would lose the stochastic stability in probability. The width of the permissible zone depends heavily on the intensity of the parametric noise, the extent of correlation with the additive excitation noise and the type of probability density. The general explanation is demonstrated on cases of normal, uniform and truncated normal densities of probability.
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