The effects of unsteady motions of flapping flat plates and corrugated structures in different parameters are studied using fluid-solid coupling and overlapping grid methods. Based on the dragonfly's right forewing and right hindwing model, these actions include sweeping and pitching, take-off acceleration, and tandem wings cruising in the reverse phase at 180°. The results show that when the advance ratio J =0.36, the “inflow deflection” improves the aerodynamic force in two degrees of freedom compared to simple flapping. When considering only the impact of flexibility, the aerodynamic forces of flexible flat plates and corrugated structures are better than that of the rigid wing models. Considering the effect of corrugated structures, the lift of flexible corrugated wings diminishes, but more thrust is generated. From the perspective of vortex street, chain vortices materialize only in the downstroke stage, while the attachment effect of leading edge vortices is noticeable in several models. In the same phase flutter, the two wings combine to form a giant wing, which generates significant forward flight momentum. In anti-phase flapping mode, the series wings generate two lifts and two or three thrust peaks to attain the required forward flight speed while sustaining a high lift.