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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.

MULTIFOLD STATIONARY SOLUTIONS OF AN AUTO-PARAMETRIC NON-LINEAR 2DOF SYSTEM