A random vibrational response study of a dynamical system is presented. In particular, suspension bridge stability analysis in the presence of turbulence is addressed. The effects of turbulence on the well-understood deterministic stability of section models using aerodynamic functions are explored emphasizing governing physical mechanisms. For this purpose, the primary emphasis is placed on the nonlinear control parameter (square of the upstream flow velocity) and the resulting nonlinear noise term. To this end, it is pointed out that the introduction of “nonwhite” nonlinear noise for the excitation forces is of paramount importance. Further, it is concluded that this invoking of nonwhite noise is necessary to avoid inconsistencies involved with the usual assumption of Gaussian white noise. Finally, numerical simulation of nonwhite, nonlinear noise and subsequent integration of the single-degree-of-freedom torsional equation of motion involving varying “time scales” are carefully carried out. The numerical tests for sample stability provide some new results that are consistent with existing experimental observations.

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