Numerical and experimental solutions of self-induced instability of bridge

Abstract

The thesis is focused on a solution of self-induced oscillations and instabilities of slender beams in the wind. It uses a combination of appropriately selected numerical methods and experiments in a wind tunnel. The author deals with an elementary analysis of such an aero-elastic system where the flow-structure interaction is taking place in its entire complexity. Primary attention is paid to movement-induced excitations called flutter as a specific phenomenon which arise due to fluctuating fluid forces and a movement of the vibrating body. This is investigated on two different types of girder that enable to move in two degrees of freedom representing bending and torsion in a cross flow. The thesis presents a short introduction to the bridge aeroelasticity. It covers motion induced instability classification with definition of main features and circumstances at which such oscillation occur. Part of the thesis is devoted to the theoretical background of a numerical method adapted for a fluid-structure interaction. This employs three boundary value problems respecting the Newton's fluid, elastodynamic equations and equations of the Lagrangian-Eulerian description of motion. Numerical instabilities associated with a high Reynolds number are diminished to acceptable level with the use of a stabilisation procedure combining the Galerkin-Petrov and the Least-Square variation method. Using wind tunnel tests, the aero-elastic responses of the decks are measured. In terms of the scale model analysis, non-dimensional coefficients of the self-excited forces, also termed as flutter derivatives, are obtained to estimate the onset of aero-elastic instability in the full scale. A method of measurement assuming variable tuning of the girder frequencies for the assessment of the bridge girder stability is used. Parameters, such as phase lag, oscillation frequency at coupled motion and onset of the critical velocity with respect to the variable frequency ratio are established. Furthermore, it is shown that some instabilities can, under circumstances, be avoided due to frequency tuning of a bridge structure. The question of aero-elastic stability with regards to initial conditions is also discussed. It is demonstrated with response hysteresis and separation curves determining the bifurcation limits from the viewpoint of initial conditions. Special attention is paid to the response of the girders at onset of the critical state and in reducing wind speed. From the results of dissertation follows that a deep circumspection should be given to "strong bluff" bodies, in rectangular, for instance, for which the conventional methods of the flutter analysis, commonly based on linear formulations, did not interpret stability conditions due to non-linear effects in sufficient manner. Great caution should be given to responses in which the separation curves create very narrow sub-domains between stable and unstable response. It is shown that a hybrid approach using numerical and experimental procedures is very effective tools for examination of the aero-elastic characteristics of slender engineering structures including bridge structures.

The thesis is focused on a solution of self-induced oscillations and instabilities of slender beams in the wind. It uses a combination of appropriately selected numerical methods and experiments in a wind tunnel. The author deals with an elementary analysis of such an aero-elastic system where the flow-structure interaction is taking place in its entire complexity. Primary attention is paid to movement-induced excitations called flutter as a specific phenomenon which arise due to fluctuating fluid forces and a movement of the vibrating body. This is investigated on two different types of girder that enable to move in two degrees of freedom representing bending and torsion in a cross flow. The thesis presents a short introduction to the bridge aeroelasticity. It covers motion induced instability classification with definition of main features and circumstances at which such oscillation occur. Part of the thesis is devoted to the theoretical background of a numerical method adapted for a fluid-structure interaction. This employs three boundary value problems respecting the Newton's fluid, elastodynamic equations and equations of the Lagrangian-Eulerian description of motion. Numerical instabilities associated with a high Reynolds number are diminished to acceptable level with the use of a stabilisation procedure combining the Galerkin-Petrov and the Least-Square variation method. Using wind tunnel tests, the aero-elastic responses of the decks are measured. In terms of the scale model analysis, non-dimensional coefficients of the self-excited forces, also termed as flutter derivatives, are obtained to estimate the onset of aero-elastic instability in the full scale. A method of measurement assuming variable tuning of the girder frequencies for the assessment of the bridge girder stability is used. Parameters, such as phase lag, oscillation frequency at coupled motion and onset of the critical velocity with respect to the variable frequency ratio are established. Furthermore, it is shown that some instabilities can, under circumstances, be avoided due to frequency tuning of a bridge structure. The question of aero-elastic stability with regards to initial conditions is also discussed. It is demonstrated with response hysteresis and separation curves determining the bifurcation limits from the viewpoint of initial conditions. Special attention is paid to the response of the girders at onset of the critical state and in reducing wind speed. From the results of dissertation follows that a deep circumspection should be given to "strong bluff" bodies, in rectangular, for instance, for which the conventional methods of the flutter analysis, commonly based on linear formulations, did not interpret stability conditions due to non-linear effects in sufficient manner. Great caution should be given to responses in which the separation curves create very narrow sub-domains between stable and unstable response. It is shown that a hybrid approach using numerical and experimental procedures is very effective tools for examination of the aero-elastic characteristics of slender engineering structures including bridge structures.