On the Modeling of an Emitting Cylindrical Transducer With a Piezoelectric Polymer Membrane

This work aims at providing a theoretical description of an ultrasonic emitting transducer, which consists of a cylindrical Polyvinylidene fluoride (PVDF) membrane coupled to an air-filled back-cavity. Based on the fundamental equations of piezoelectricity and linear acoustics, and assuming axisymmetrical geometry, an analytical model which describes the coupling of the displacement field of the membrane with the pressure fields on both of its sides is presented. Solutions are obtained using modal expansion theory for the displacement field of the membrane and for the acoustic pressure field in the axial-direction of the back-cavity. This model permits to predict the resonances of the system, which are not taken into account in an earlier work. A lumped elements network is then derived from the analytical solution, valid in the lowest frequency range, when keeping only one mode and when considering two levels of approximations. Comparison between measurement results and theoretical ones of the pressure radiated by two prototypes of emitter shows an overall good agreement.