The goal of the present work is to control the modal dynamics of a piezo-electric loudspeaker in order to reach directivity of efficiency criteria. In this context, we study the dynamics and sound radiation of a piezoelectric plate biased by a static pressure on one side. This pressure inflates the plate and its forced dynamics around this equilibrium position are then studied. With the help of von Karman plate theory, the static equilibrium position of a plate of any shape is sought for before writing its linear dynamics around this equilibrium position. This two-step problem is solved numerically using a finite elements software (Freefem++). This results in a series of eigenmodes and eigenfrequencies for each value of the static pressure difference. Next the modal forces due to the piezoelectric coupling are calculted. By considering a baffled plate, the acoustical radiation is computed using the Rayleigh integral. The numerical model is used to perform a parametric optimisation of the system.