Effect of spanwise correlation of turbulence field on the motion stability of long-span bridges

Abstract

Motion stability of long-span bridges is investigated, taking into consideration imperfect spanwise correlation in the turbulent wind flow. The study is based on a linear mathematical model for the structure-fluid system. Two types of structural modes are considered, the torsional modes and the vertical bending modes. The motion stability is defined in terms of the statistical moments, in particular the second-order moments of the state variables of the system. Turbulence is known to play two opposite roles in affecting the stability of a dynamical system. On the one hand, it destabilizes individual modes if each of these modes acts independently; on the other hand, it facilitates the transfer of energy from the least stable mode to more stable modes, thus increasing the stability margin of the entire system. It is shown in the present paper that in the ideal case of a perfectly correlated turbulence field, this transfer of energy can only occur between modes of different types (from a torsion mode to a bending mode or itvice versa), but not between modes of the same type. The lack of spanwise uniformity in the turbulence field renders the transfer of energy between modes of the same type possible, and yet at the same time, it reduces the generalized parametric random forces in the lower order modes. The analytical algorithm developed in this paper permits the assessment of the overall effect of a turbulence field, which can be either stabilizing or destabilizing, depending primarily on whether or not favorable aerodynamic coupling exists between different types of modes for a particular bridge. A computationally efficient procedure is developed to calculate stability boundaries for linear systems involving a large number of state variables. The procedure reduces the calculation to within a smaller state space including only those state variables which describe the essential system behavior near the stability boundary. The approximate results are found to be very accurate while reducing the computer time significantly.