In this study, the harmonic oscillations of gas-filled axisymmetric acoustic cavities near resonance conditions are considered. This problem has gained considerable interest during the last decade when compression ratios of up to 340% have been achieved.
The objective of this project is to develop theoretical models that can predict the performance of resonators of complex geometries in a straightforward manner to enable the selection of optimal resonator configurations that yield high compression ratios. With this goal in mind, a mathematical model is developed based on the equations of conservation of mass, linear momentum, and state equation for ideal gas. The model accounts for the full nonlinear behavior of the gas oscillations. The equations are cast in a weighted residual form which can be solved provided that the exact mode shapes for the linear problem can be determined. The model is proved to be accurate in capturing experimental phenomena such as the formation of shock waves at large excitations.
However, it is solvable only for resonators with simple geometries. In order to overcome these deficiencies, a finite element model is developed based on the weak form of the governing equations. The finite element model enables the prediction of resonators of complex geometries with either body or boundary excitation sources at different flow conditions. Furthermore, the model is integrated with the dynamics of axisymmetric piezoelectric bimorphs that are used to actuate the acoustic cavity instead of the conventional actuation systems.
The coupling between the cavity and piezoelectric bimorph models is achieved by considering their mutual interactions. The validity of the coupled model is validated experimentally and against the predictions of a commercial finite element software (ANSYS) that deals with linear acoustic equations. Close agreement is obtained between theory and experiment indicating that the developed analytical and experimental tools can be confidently used in the design of axisymmetric acoustic resonators that possess a high potential of applicability in designing smart structures and vibration control.
Source: University of Maryland
Author: El-Sabbagh, Adel