The capabilities of a dielectric elastomer generator formed by a hyper-electro-elastic annular membrane deforming non-homogeneously out-of-plane are investigated. The mechanical-to-electric energy conversion is determined for a four-stroke cycle, driven by an external oscillating force, that may extend within an admissible state region delimited by the typical four failure modes of dielectric elastomers: electric breakdown, electromechanical instability, maximum stretch limit, and loss of the tensile state. Performance in terms of harvested energy per unit mass and efficiency of the generator is determined in relation to: (i) initial prestretch of the membrane, (ii) external to internal radius ratio, and (iii) intensity of maximum external load. The analysis concludes with a comparison between the behaviours of two different soft materials (i.e. an acrylic elastomer and a type of natural rubber), and an estimation of the most effective generator geometry among those analysed by the authors here and in past studies.