Finite element modeling of the nonlinear oscillations in axisymmetric acoustic resonators

Oscillation of a gas in closed resonators has gained considerable interest in the past years. In this paper, the nonlinear equations governing the behavior of the gas oscillations inside the resonator are formulated in a weak form and then modeled using the finite element method. The pressure ratios, predicted by the proposed model, are in close agreement with the exact solutions available for simple geometries such as cylindrical, exponential and linearly varying area resonators. The presented comparisons validate the accuracy of the finite element model and emphasize its potential for predicting the performance or resonators of more complex geometries which are necessary for generating high pressures from the standing waves. Also, gas flow through the boundaries of the resonator is implemented in the proposed model. The presented finite element model presents an invaluable tool for designing a new class of acoustic compressors which can be used, for example, in refrigeration and vibration control applications.