Nonlinear standing waves in miniature acoustic resonators

Abstract

The research on both fundamental mechanisms and applications in nonlinear acoustic resonances has recently become active. By using shaped resonators, the acoustic saturations occurred in straight cylindrical resonators have been removed and large amplitude pressure oscillations have been obtained. Acoustic compressors have been developed following this technology. It is of interests to investigate if the nonlinear resonance can be used to produce high pressure gas oscillations in miniature/micro scales, which would be useful in microfluidics and bio-engineering applications. In order to have nonlinear resonances in small resonators, some issues, such as viscosity effects, resonator configurations and actuating methods, need to be studied. This thesis presents a study on nonlinear resonance oscillations in shaped resonators. The main objective of the study is to investigate acoustic characteristics of nonlinear standing waves in small-size and miniature resonators. This is achieved by studying the effect of resonator geometry and driving methods on the resonance pressures theoretically and experimentally. At the end of the study, a novel design for miniature resonators is demonstrated. The theoretical study in this dissertation mainly comprises three aspects. Firstly, resonance pressures in shaped resonators driven by a shaking force are studied. The resonators are of two types of configurations: one is axisymmetric with cross sectional area being exponentially expanded; another is of a low-aspect-ratio rectangular cross section whose width is exponentially expanded. One-dimensional nonlinear wave equations are obtained by modifying equations developed by Ilinskii et al. (1998), taking into account of shear viscosity and bulk viscosity terms which are derived from I