Dielectric elastomers are a class of smart materials capable of converting electrical energy into mechanical motion, offering great potential for lightweight and efficient actuation systems. In this work, a dielectric elastomer-transmission-wing (DETW) structure was developed to transform the in-plane vibration of a dielectric elastomer actuator into flapping motion. The static performance of the dielectric elastomer actuator was first analyzed, followed by the fabrication of a flapping-wing prototype. An energy-based model was established for DETW using the Lagrangian approach, which incorporates air load and key dissipative factors such as material viscosity. The model enables a clear understanding of how mechanical loads influence the flapping behavior and dynamic response of the structure. Experiments further confirmed the feasibility of the DETW concept and the prediction accuracy of the model.