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Stochastic version of the arc-length method
Náprstek, Jiří ; Fischer, Cyril
The solution of a nonlinear algebraic system using the incremental method, based on pre-defined loading steps, fails in the vicinity of local extrema as well as around bifurcation points. The solution involved the derivation of the so-called ’Arc-Length’ method. Its essence lies in not incrementing the system parameter or any of the independent variables but rather the length of the response curve. The stochastic variant of this method allows for working with a system where system parameters include random imperfections. This contribution presents a variant that tracks the first two stochastic moments. Even in this simple case, interesting phenomena can be observed, such as the disappearance of the energy barrier against equilibrium jump due to random imperfections in the system.
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Galloping of insulated bundled overhead line - nonlinear numerical analysis in time domain
Macháček, Michael ; Hračov, Stanislav
Our contribution focuses on a 3D numerical nonlinear analysis of galloping in a specific bundled overhead line with ice accretion. We studied the susceptibility to this self-excited oscillation, critical onset wind speeds, and global dynamic response of a very low-tensioned line with simulated icing observed on similar real conductors. Due to the highly nonlinear mechanical behavior of such a flexible cable, we employed the Newmark integration method combined with the iterative Newton-Raphson method. We analyzed two numerical models of the overhead line loaded by the wind: one assuming nonlinearity only in the wind load, while retaining the linearity of the mechanical system itself, and the other representing a fully nonlinear system including geometrical nonlinearity. Our analysis revealed that the determined critical wind speeds for the onset of galloping are in relatively close ranges for both models. However, numerical simulations with the fully nonlinear system indicated significantly lower amplitudes of limit cycle oscillations, especially at higher wind speeds, compared to the linear model of the line. This underscores the necessity of using fully nonlinear models during the design stage of such low-tensioned aerial conductors.
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LES simulations of airflow around rectangle with side ratio 2:1 and their comparison with experiments
Ledvinková, Blanka ; Hračov, Stanislav ; Macháček, Michael
Our contribution is focused on the comparison of the experimental investigations and of the numerical 3D LES simulations of the airflow around sharply edged rectangle with side ratio 2:1. The rectangle object was exposed to the airflow having a given velocity at different angles of the wind attack in the wind tunnel with the aim to obtain the curves of the aerodynamic coefficients and Strouhal number depending on the impact angle. The comparative numerical 3D simulations of the wind tunnel testing were performed using COMSOL Multiphysics and OpenFoam both incorporating the Large Eddy Simulation (LES) method.
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Galloping of insulated bundled overhead line simplified analysis
Hračov, Stanislav ; Macháček, Michael
Our paper provides an analysis of the susceptibility of a particular bundled overhead line to galloping. It presents a case study of an aerial bundled cable, consisting of four conductors insulated by polyethylene, and used for low-voltage power lines. The susceptibility to loss of stability is analyzed for cable without and with simulated icing observed on similar real conductors. In the first case, the proneness to galloping was excluded based on the results of CFD simulation and the Den Hartog criterion. In latter case, the possible occurrence of galloping was confirmed. The critical wind velocity for the ice-covered cable was calculated utilizing quasi-steady theory. Finally, the amplitudes of limit cycle oscillation for supercritical wind speeds were estimated based on simplified numerical analysis.
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Solution methods for an aeroelastic problem with combined harmonic and stochastic excitation
Fischer, Cyril ; Náprstek, Jiří
Assessing responses in slender engineering structures facing both deterministic harmonic and stochastic excitation is often based on an approximation by the single-degree-of-freedom van der Pol-type nonlinear model. Determining the response probability density function involves solving the Fokker-Planck equation, which is generally a challenging task. Hence, semi-analytical and numerical methods come into play. This contribution reviews several possible techniques and spotlights the exponential-polynomial-closure method. The shown results are limited, as the paper reflects an early stage of the relevant research direction.
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