Vibrating structures are often mounted on or located near a passive plane surface with finite acoustic impedance, and hence the acoustic pressures measured in a half-space bounded by the surface consist of both the direct radiation from the structure and the reflection from the boundary surface. In order to visualize the direct radiation from the source into free space, a reconstruction method based on expansion in half-space spherical wave functions is proposed. First, the series of half-space spherical wave functions is derived based on the analytical solution of the sound field due to a multipole source located near an impedance plane. Then the sound field in the half-space is approximated by the superposition of a finite number of half-space expansion terms. The expansion coefficients are determined by solving an overdetermined linear system of equations obtained by matching this assumed solution to the total acoustic pressures in the half-space. The free-space radiation can finally be reconstructed via multiplying the free-space spherical wave functions by the corresponding coefficients. Numerical simulation examples of a vibrating sphere and a vibrating baffled plate are demonstrated. The effects of specific acoustic impedance of the boundary and the locations of the measurement points on the accuracy of reconstruction are examined.

This paper presents a study of intentionally induced acoustic mode complexity in rigid-walled ducts of separable geometry and with uniform mean flow. An intermediately located perforated plate conceptualized as an impedance discontinuity is employed to maximize the acoustic mode complexity, in turn producing a unidirectional traveling wave from the source to the impedance discontinuity. The impedance of the perforated plate for realization of a unidirectional traveling wave is derived analytically and is found to be a function of the modal wavenumbers, the Mach number of the mean flow, the position of the perforated plate, and the termination impedance. The conditions derived analytically are verified computationally by finite element analysis. A measure of acoustic mode complexity is defined and also evaluated from the finite element analysis. It is found that the realization of a unidirectional traveling wave is robust at low Mach number mean flows, except at the occurrence of resonances. The method presented in this work provides a strategy to control the transmission of acoustic energy in rigid-walled ducts of separable geometry in the presence of uniform mean flow.

When implementing the reconstruction of the sound field directly radiated from a source located in a half-space, the half-space basis functions with boundary impedance as a parameter, need to be formulated. And the boundary impedance is usually obtained via <i>in situ</i> sound impedance measurement techniques. In the reconstruction method based on the expansion in half-space spherical wave basis functions, a hologram surface and a single reference microphone placed in the near-field are used to collect sound pressures. The sound pressure at the reference microphone is first reconstructed and the error of the reconstructed pressure relative to the measured pressure is then calculated. The sound pressure reflection coefficient corresponding to the minimum error is chosen as the measure of the reflection coefficient at the measurement point. Thus, this method is applicable to reconstructing the directly radiated sound pressures without the knowledge of boundary impedance, free from the in situ sound impedance measurement techniques necessary for conventional methods. The purpose of this work is to discuss the various parameters affecting the accuracy of reconstruction. Moreover, the boundary impedance is reconstructed based on the estimation of the reflection coefficient, so that a sound impedance measurement technique implemented via the near-field acoustical holography is proposed. By taking the spherical source for example, numerical simulations are conducted to verify the proposed method of reconstructing the boundary impedance and the directly radiated sound pressures. The influences of reference microphone coordinate, the effective flow resistivity of the boundary, and the rate of decrease of porosity with depth of the boundary on the accuracy of reconstruction are quantitatively analyzed.

When implementing the reconstruction of the acoustic field directly radiated from a source located in a half-space, the half-space basis functions with boundary impedance as a parameter, need to be formulated. And the boundary impedance is usually obtained via in situ acoustic impedance measurement techniques. The reconstruction method based on the expansion in half-space spherical wave basis functions, uses a hologram surface and a single reference microphone placed in the near-field to collect acoustic pressures. The acoustic pressure at the reference microphone is reconstructed firstly and the error of the reconstructed pressure relative to the measured pressure is then calculated. The acoustic pressure reflection coefficient corresponding to the minimum error is chosen as the estimation of the reflection coefficient at the measurement points. Thus, this method is applicable to reconstruct the directly radiated acoustic pressures without the knowledge of boundary impedance, free from the in situ acoustic impedance measurement techniques necessary for conventional methods. The purpose of this thesis is to discuss the various parameters affecting the accuracy of reconstruction. Moreover, the boundary impedance is reconstructed based on the estimation of the reflection coefficient, so that an acoustic impedance measurement technique implemented via the near-field acoustical holography is proposed. By taking the spherical source as an example, numerical simulations are conducted to verify the proposed method in reconstruction of the boundary impedance and the directly radiated acoustic pressures. The impacts of reference microphone coordinate, the effective flow resistivity of the boundary, and the rate of decrease of porosity with depth of the boundary on the accuracy of reconstruction are quantitatively analyzed.

Analytical mathematical models and solutions for spatial localization of acoustic waves through an impedance discontinuity produced by an intermediate damped side branch are studied in stationary media in ducts with varying cross sections. Three specific geometries, namely, with polynomial, sinusoidal, and exponential longitudinal variations, are investigated. The sound fields inside the ducts are modeled by Webster's horn equation. Traveling-wave solutions are obtained by appropriate transformations. The side-branch impedances required for spatial localization (confinement) of traveling and standing waves are found analytically and verified numerically using three-dimensional finite element analysis. The impact of the longitudinal variation of the duct's cross-sectional area (CSA) on the side-branch impedance is examined. It was found that the required side-branch resistance changes more than the reactance with the variation of the duct CSA. A measure of a traveling wave is defined to quantitatively examine the spatial localization of acoustic waves. It was found that the CSA corrections on the side-branch impedances are important. The results of this study reveal the quantitative relationships between the side-branch impedance and the CSA variations for zero reflection from the impedance discontinuity. The mathematical approach presented is potentially helpful for a design of a full anechoic termination and energy localization in duct systems.