A coupled nonlinear model for axisymmetric acoustic resonators driven by piezoelectric bimorphs

The fundamentals governing the operation of actively controlled, gas-filled, axisymmetric resonators are presented. In this class of resonators, a piezoelectric diaphragm is used to harmonically excite the gas inside the resonator's cavity. Under resonant conditions, high pressure standing waves can be generated that make the resonator act as an acoustic compressor. A finite element model is developed to describe the non-linear interaction between the dynamics of the gas inside the resonator and the piezoelectric diaphragm. The coupled-field model is used to predict the pressure profiles which are generated inside the resonator cavity as influenced by the geometry of the cavity and the gas flow through the boundaries. The predictions of the model are validated for simple cavity configurations, for which the exact solutions are available, and against published experimental results. It is found that the model accurately predicts the dynamics of this class of resonators over a broad range of excitation amplitudes and frequencies. This accuracy will allow the proposed model to be used as an effective design tool of piezoelectric acoustic resonators for a wide range of applications.