BBAA VI International Colloquium on: Bluff Bodies Aerodynamics & Applications Milano, Italy, July, 20–24 2008 SELF-EXCITED NONLINEAR RESPONSE OF A BRIDGE-TYPE CROSS SECTION IN POST-CRITICAL STATE Jiˇ r´ ıN´ aprstek ? , Stanislav Posp´ ıˇ sil ? ,R¨ udiger H ¨ offer † , Joerg Sahlmen † ? Institute of Theoretical and Applied Mechanics, v.v.i. Academy of Sciences of the Czech Republic, Proseck´ a 76, 19700 Prague, Czech Republic e-mails: naprstek@itam.cas.cz, pospisil@itam.cas.cz † Building Aerodynamics Laboratory Faculty of Civil Engineering, Ruhr University Bochum Building IA 0/58, D-44780 Bochum, Germany e-mails: ruediger.hoeffer@rub.de, joerg.sahlmen@rub.de Keywords: aeroelastic system, self-excited vibration, limit cycles, instability, post-critical be- haviour Abstract: Long slender civil-engineering structures exposed to wind, especially decks of sus- pension bridges, their supporting elements, masts, towers and tall buildings are susceptible to vibrations under certain circumstances due to pure wind load action or due to special aeroelas- tic effects. Interaction between structural response and wind load, having the influence on the stability, is nowadays of basic importance in advanced technical design of such structures. Finding the stationary points and determining stability characteristics of a system is an im- portant undertaking in any attempt to understand or to modify its dynamical properties. We demonstrate the importance with an example describing the aeroelastic system with gyroscopic (non quadratic in the velocities) as well as with non-conservative terms. In the article we con- sider a non-linear system with two degrees of freedom representing an interaction of bending and torsion of a slender beam vibrating in a cross flow. The shape makes possible to separate principal effects and the coupling of aeroelastic modes is caused solely by the flow around the structure. Conditions of existence of stationary points and their types are investigated using primar- ily the Lyapunov function and center manifold theory. The procedure presented is applicable for Hamiltonian holonomic systems which are conservative, or nonconservative with certain limitations on the generalized forces. The singular points are to be classified with respect to their asymptotically stable or unstable character together with adequate physical interpretation. Attention is paid to attractive and repulsive areas surrounding these points. Using this back- ground several types of post-critical response in non-linear formulation will be presented, such as stable/unstable limit cycles with various ratio of amplitudes of both components, or quasi- periodic response processes having a form of symmetric or asymmetric beating effects with strong energy trans-flux between degrees of freedom. 1