This study proposes a model of a circular, non-symetrically laminated, piezoelctric plate, subjected to non-linear large amplitude vibrations. This model is built to simulate the behavior of aMEMS bio-sensor, designed to detect, automatically and autonomously, the presence of a given molecule present in an aqueous solution. Because of both the laminated strcuture and the fabrication process, prestresses are observed, with different signs and intensities from one layer to another. This is responsible of a non-plane deformed geometry of the plate at rest. Moreover, experimental results show that it is necessary to make the system vibrating in a large amplitude non-linear regime to obtain a large enough signal-to-noise ratio. A continuous nonlinear model of the von-Kármán type is used and discretized by an expansion of the solution onto the mode shape basis of the plate without prestresses.