Absorption and scattering of sound wave by resonator arrays and impedance distributions

Resonator arrays have been used a lot for sound manipulation and absorption. Their sound absorption enhancement mechanism and subwavelength evaluation index are sometimes used excessively or inappropriately. The main objective of this thesis is to explore the physical and analytical model of the resonator array, starting from the physical concept.

Firstly, a mass-spring-damping system is introduced to characterize a single resonator, i.e., the Helmholtz resonator, which is regarded as a representative sound absorption component. It shows that linear vibration models yield an oscillatory-diffusive representation in the frequency domain. This kind of analysis method gives physical interpretation compared with complex and unintuitive characterization methods of model size parameters. Results reveal that the sound absorption performance of a resonator is mainly determined by its volume.

Acoustic structures consisting of inter-resonator arrays are widely analyzed theoretically and numerically. When two single resonators are connected in parallel, one needs to consider the coupling between them. A cylindrical structure consisting of two quarter-wavelength resonators is covered with a porous material. An analytical expression of mutual interaction is derived to clarify its influence on a resonance shift phenomenon and sound absorption performance. Finally, the equivalent mass-spring-damping oscillatory system is introduced to interpret the physical mechanism of inter-resonator coupling. When a parallel array of resonators are used, inter-resonator coupling gives rise to negative stiffness in the frequency range between two resonating peaks and benefits broadband absorption.

After analyzing the performance of a single resonator and resonator arrays, this thesis also explores the sound absorption of a periodical resonator array. It imposes the mode-matching method to discuss the sound properties of scattering and transmission involved in a typical inter-resonator array structure with a non-uniform distribution of surface impedance. The theoretical analysis was validated with commercial software simulation and experiments. Results can reveal information about mode shapes and amplitudes compared with numerical simulation. This allows a clear and detailed understanding of sound fields rather than just final results, such as absorption coefficients.

Then the sound wave manipulation of a periodical resonator array is fulfilled by a surface impedance approach. The analyzed geometrical model with discrete resonator arrays are simple while typical. One may replace them equivalently due to their locally-reacting nature with structures composed of a periodical pattern. The properties hold with individual special geometries as long as the same distribution of surface impedance, or more-physically mass-spring-damping equivalent, is guaranteed.

Finally, resonator arrays are used as liners in duct noise attenuation. It is shown that porous materials with a suitable flow-resistivity are more effective than resonators assembled asymmetrically in maximizing sound energy absorption. Specifically, when the sound absorption coefficients approach one, a tiny increase of absorption coefficient value may contribute to an overall improvement of several dBs in accumulative sound energy loss. Thus, it is necessary to select appropriate optimization objectives in engineering projects.

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