The paper studies the performance of a novel generator, consisting of a ball tightly sandwiched between two dielectric elastomeric membranes for energy harvesting. The membranes are built into a housing subjected to external ambient random vibrations, so that the relative motion between the ball and the membranes deforms the latter allowing energy conversion. A dynamic model of the nonlinear mechanical and electrical behaviour of the device is presented, and a novel approach for estimating the mean output energy of the device is developed. An explicit analytical formula for the mean output power, derived and presented for the first time, allows comparing the generator performance depending on the level of nonlinearity and the membranes deformation rate. A comparison of the generator performance for the linear and nonlinear device properties is demonstrated. The numerical results of the Monte-Carlo simulations are presented and agreed well with the derived analytical estimation.