In this paper, a nonlinear dynamic model derived from engineering is investigated. The dynamic characteristic is analyzed by using the geometrical theory of ordinary differential equations. The Tacoma bridge is taken for example, the quantitative analysis of the nonlinear dynamical model of a flexible structural bridge under the unsteady aerodynamics from engineering by harmonic balance method is made based on the qualitative analysis of the types of fixed points and the existence of periodic motion. And the approximate periodic solution is obtained. Finally, the approximate analytical results are verified by numerical simulation. The results show that the analytic results are close to the numerical ones in accord with the qualitative analysis when the wind speed is in a certain region of parameter. Here, the results in this paper are valuable in the calculation of vibration engineering and theoretical design, since the long-time periodic oscillation is likely to cause the fatigue of structure, even probably effect severely the structural safety of bridge.