This paper presents a numerical investigation on the aeromechanical performance of dynamically actuated membrane wings made of dielectric elastomers. They combine the advantages of membrane shape adaptability, which produces increased lift and delayed stall, with the benefits of simple, lightweight but high-authority control mechanism offered by integral actuation. High-fidelity numerical models have been developed to predict their performance and include a fluid solver based on the direct numerical integration of the unsteady Navier-Stokes equations, an electromechanical constitutive material model and a non-linear membrane structural model. Numerical results show that harmonic actuation can either increase or reduce the overall aerodynamic efficiency of the wing, measured as the mean lift-to-drag ratio, depending on the ratio between the actuation frequency and the natural frequency of the membrane. In addition, the definition of a reduced-order model based on POD modes of the complete high-fidelity system provides an insight of the main characteristics of the dynamics of the coupled system.