Radomil Král

Experimental Set-Up for Advanced Aeroelastic Tests on Sectional Models

This article describes an original and multipurpose experimental set-up for the analysis of complex linear and non-linear aspects of aero-elastic behaviour of beam cross-sections. The apparatus meets rigorous theoretical assumptions and allows very precise and quick adjustment of stiffness and mass of a cross-section, which is not always possible with the traditional “parallel spring-supported bridge” approach used by many researchers. The principal advantages are described together with key construction details. Examples of the large amplitude non-linear response are presented, to illustrate the capacity and usefulness of the stand.

Finite element method analysis of Fokker–Plank equation in stationary and evolutionary versions

Abstract The problems that often arise in stochastic dynamics can be investigated using the Fokker–Planck (FP) equation. The response of a such systems being subjected to additive and/or multiplicative random noise is represented by probability density function (PDF) that gives the full information about a response random character. Various analytic and semi-analytic solution methods have been developed for various systems to obtain results requested. However numerical approaches offer a powerful alternative. In particular the Finite Element Method (FEM) seems to be very effective. A couple of single dynamic linear/non-linear (Duffing and Van Der Pol type) systems under additive and multiplicative random excitations are discussed using FEM as a solution tool of the FP equation. The resulting PDFs are analyzed and if the analytic results exist mutually compared.

Theoretical background and implementation of the finite element method for multi-dimensional Fokker–Planck equation analysis

Abstract Fokker–Planck equation is one of the most important tools for investigation of dynamic systems under random excitation. Finite Element Method represents very effective solution possibility particularly when transition processes are investigated or more detailed solution is needed. However, a number of specific problems must be overcome. They follow predominantly from the large multi-dimensionality of the Fokker–Planck equation, shape of the definition domain and usual requirements on the nature of the solution which are out of a conventional practice of the Finite Element employment. Unlike earlier studies it is coming to light that multi-dimensional simplex elements are the most suitable to be deployed. Moreover, new original algorithms for the multi-dimensional mesh generating were developed as well as original procedure of the governing differential and algebraic systems assembling and subsequent analysis. Finally, an illustrative example is presented together with aspects typical for the problem with large multi-dimensionality.

Influence of Stationary Vehicles on Bridge Aerodynamic and Aeroelastic Coefficients

AbstractThis study focuses on modifications in bridge aerodynamic and aeroelastic behaviors due to stationary (nonmoving) vehicles for various arrangements of vehicles on a bridge deck. Dimensionless aerodynamic force and moment coefficients, as well as flutter derivatives, are analyzed experimentally in a wind tunnel in the model of a bridge with a semibluff cross section. A comparison is provided for stationary vehicles placed in leeward, windward, and all traffic lanes, as well as for an empty bridge-deck section. Drag, lift static forces, and moment coefficients are determined for various wind incidence angles. Flutter derivatives are obtained using the free-vibration technique for both one- and two-degrees-of-freedom systems. Stationary vehicles on the bridge deck are generally observed to change aerodynamic coefficients of the bridge. This is particularly exhibited for the pitch moment. Galloping sensitivity of the bridge does not change considerably in the presence of vehicles, as all studied confi...

Climatic wind tunnel for wind engineering tasks

this paper introduces a new climatic wind tunnel laboratory, which is one of the laboratories of the institute of theoretical and applied mechanics (itam) of the academy of Science of the Czech republic. the tunnel is used for fundamental research in civil engineering, architecture, and heritage care and in other fields where wind effects appear along with other factors. the paper includes essential information about the interior layout of the tunnel, descriptions of the principal parts of the tunnel which were designed taking into account both the optimal flow characteristics together with the description of some facilities serving for the simulation of a strong wind, rain, freeze and heat radiation, and the modelling of the atmospheric boundary layer. a design for a rectangular contraction nozzle, based on a parabolic profile and extending the capacity of the wind tunnel is presented.

COMPARISON OF NUMERICAL AND SEMI-ANALYTICAL SOLUTION OF A SIMPLE NON-LINEAR SYSTEM IN STATE OF THE STOCHASTIC RESONANCE

Stochastic resonance (SR) is a phenomenon which can be observed at some nonlinear dynamic systems under combined excitation including deterministic harmonic force and random noise. The Duffing single degree of freedom oscillator is treated and the Gaussian white noise as the random excitation component is considered. Mathematical basis of this phenomenon follows from properties of the Duffing system with negative linear part of the stiffness. Under certain combinations of the system and excitation parameters the SR can emerge. It manifests by stable periodic hopping between two nearly constant limits perturbed by random noises. SR is observed and practically used in a number of disciplines in physics, biophysics, chemistry, etc. However it seems to be promising as a theoretical model of several aeroelastic post-critical effects arising at a prismatic beam in a cross flow. Three independent theoretical solution methods have been addressed and tested in order to compare results of the system response. The first kind is semi-analytic dealing with the relevant Fokker-Planck Equation (FP). It is solved by means of the stochastic moment procedure. The multiharmonic non-stationary solution of the Probability Density Function (PDF) is expected. The Galerkin approach is adopted. The second way is based on the FEM solution of the FP equation. It is analyzed in an original evolutionary form which enables an analysis of transition effects starting the Dirac type initial conditions. The last procedure represents simulation regarding the original Duffing or relevant Ito stochastic system. Comparison of results provided by the above three methods has revealed appropriate domains of their application to particular problems regarding a preliminary analysis or careful detailed inspection in specific small domains in final stage of an engineering system design.

Multi-dimensional Fokker-Planck equation analysis using the modified finite element method

The Fokker-Planck equation (FPE) is a frequently used tool for the solution of cross probability density function (PDF) of a dynamic system response excited by a vector of random processes. FEM represents a very effective solution possibility, particularly when transition processes are investigated or a more detailed solution is needed. Actual papers deal with single degree of freedom (SDOF) systems only. So the respective FPE includes two independent space variables only. Stepping over this limit into MDOF systems a number of specific problems related to a true multi-dimensionality must be overcome. Unlike earlier studies, multi-dimensional simplex elements in any arbitrary dimension should be deployed and rectangular (multi-brick) elements abandoned. Simple closed formulae of integration in multi-dimension domain have been derived. Another specific problem represents the generation of multi-dimensional finite element mesh. Assembling of system global matrices should be subjected to newly composed algorithms due to multi-dimensionality. The system matrices are quite full and no advantages following from their sparse character can be profited from, as is commonly used in conventional FEM applications in 2D/3D problems. After verification of partial algorithms, an illustrative example dealing with a 2DOF non-linear aeroelastic system in combination with random and deterministic excitations is discussed.

Numerical Investigation of Wind Effects on the Perforated Structures

The paper deals with a numerical analysis of wind effects on structures with perforated surfaces. The solution based on FEM model is governed by the stabilized Navier-Stokes equations for incompressible fluid. Special attention is given to perforated surface. Such a partly resistance barrier always introduces considerable numerical difficulties resulting from the complexity of a flow distortion when the fluid is passing through. For simplification, the barrier is assumed as a thin screen with specific resistance parameters where the fluid flow mechanism needs not be resolved. The general influence of the barrier on the flow field is a loss in the normal momentum component and the change in the flow direction. On the other hand, the authentic simulation of the fluid mechanics requires specifying the relevant input parameters that can be determined by an experiment or by using a corresponding handbook.

Flutter Derivatives of the Kao-Pin Hsi Cable-Supported Bridge

Long-span cable-supported bridges, characterized with low natural frequencies and mechanical damping, are very sensitive to wind effects. Therefore, investigation of the aeroelastic behaviour of bridges is particularly important when designing these complex engineering structures. The focus is on evaluation of dimensionless aeroelastic coefficients, i.e. flutter derivatives, which are considered as indicators of the aeroelastic stability of bridges. A comprehensive experimental study on dynamic wind-induced behaviour of the Kao-Pin Hsi Bridge in Taiwan is carried out in the Climatic Wind Tunnel of the Centre of Excellence Telč (CET), Czech Republic. The bridge-deck section is tested at a multipurpose experimental setup originally developed in the CET. Flutter derivatives are obtained by the means of the free-vibration technique for the double-degree-of-freedom (DDOF) system. The results are compared to those of a thin flat plate with large width to height ratio, which previously proved to be stable with respect to the flutter phenomenon. While the torsional instability is observed for the Kao-Pin Hsi bridge-deck section, the flat plate proves to be aeroelastically stable.