Knowledge of the indoor propagation of sound has many important applications including acoustic prediction in homes, office buildings, stores, and schools, and the design of concert halls, auditoriums, classrooms, and factories. At low frequencies, interior acoustics are analyzed with the wave equation, but significant computational expense imposes an upper frequency limit. Thus, energy methods are often sought for high frequency analysis. However, conventional energy methods are significantly limited by vast simplifications or computational costs. Therefore, new improvements are still being sought. The basis of this dissertation is a recently developed mathematical model for interior acoustics known as the acoustic diffusion model. The model extends statistical methods in high frequency acoustics to predict the spatial distribution of acoustic energy in the volume over time as a diffusion process. Previously, solutions to the acoustic diffusion model have been limited to one dimensional (1-D) analytical solutions and to the use of the finite element method (FEM). This dissertation focuses on a new, efficient method for solving the acoustic diffusion model based on a boundary element method (BEM) solution using the Laplace transform. First, a Laplace domain solution to the diffusion model is obtained using the BEM. Then, a numerical inverse Laplace transform is used to efficiently compute the time domain response. The diffusion boundary element-Laplace transform solution (BE-LTS) is validated through comparisons with Sabine theory, ray tracing, and a diffusion FEM solution. All methods demonstrate excellent agreement for three increasingly complex acoustic volumes and the computational efficiency of the BE-LTS is exposed. Structural coupling is then incorporated in the diffusion BE-LTS using two methods. First, a simple transmission coefficient separating two acoustic volumes is implemented. Second, a structural power flow model represents the coupling partition separating acoustic volumes. The validation of these methods is successfully performed in an example through comparisons with statistical theory, a diffusion FEM solution, ray tracing, and experimental data. Finally, the diffusion model and the BE-LTS are shown to possess capabilities beyond that of room acoustics. The acoustic transmission through a heat exchanger, acoustic foam, and mufflers is successfully modeled using the diffusion BE-LTS and compared to experimental data. / Ph. D.

This thesis studies interactions between coupled acoustic domain(s) and enclosing rigid or elastic boundary. Boundary element-finite element (BE-FE) sound-structure interaction models are developed by coupling frequency domain BE acoustic and FE structural models using linear inviscid acoustic and elasticity theories. Flexibility in analyses is provided by discontinuous triangular and quadrilateral elements in the BE method (BEM), and a rectangular plate and a triangular shell element in the FE method (FEM). An analytical formulation is developed for an extended fundamental sound-structure interaction problem that involves locally reacting sound absorptive treatment on interior elastic boundary. This new formulation is built upon existing analytical solutions for a configuration known as the cavity-backed-plate problem. Results from developed analytical formulation are compared against those from independent BE-FE analyses. Analytical and BE-FE analysis results for a selection of cavity-plate(s) interaction cases are given. Single- and multi-domain BE analyses of cavity-Helmholtz resonator interaction are provided as an alternative to modal method of acoustoelasticity. A discrete-form of the existing BE acoustic particle velocity formulation is presented and demonstrated on a basic case study. Both the existing and the discretized BE acoustic particle velocity formulations could be utilized in acoustic studies. A selection of case studies involving fundamental configurations are studied both analytically and computationally (by BE or BE-FE methods). These studies could provide a basis for benchmark case development in the field of acoustics.

Optical membranes are currently pursued for their ability to replace the conventional mirrors that are used to correct wave front aberration and space-based telescopes. Among some of the many benefits of using optical membranes, is their ability to considerably reduce the weight of the structure. As a secondary effect, the cost of transportation, which is of great interest in space applications, is reduced as well. Given the low density of these thin-film membranes, the lower end dynamics play a greater significant role than their rigid plate-like counterparts in achieving functional mirrors. Space-based mirrors are subjected to a series of disturbances. Among those encountered are thermal radiation, debris impact, and slewing maneuvers. Thus, dynamic control is essential for the adequate performance of thin-film membrane mirrors. With this in mind, the work described herein aims to improve the performance of optical membranes with an innovative, acoustical control approach to suppress vibration of optical membranes backed by an air cavity. This is achieved by using a centralized acoustic source in the cavity as the method of actuation. The acoustic actuation is of great interest since it does not mass load the membrane in the conventional way, as most methods of actuation would. To achieve this end goal, two structural-acoustic coupled models are developed to describe the dynamics of a pressurized optical membrane system. This is done through an impedance based modeling approach where the subsystems are modeled individually, and then coupled at the interface. The control of the membrane is implemented using a positive position feedback approach. The theory is also extended to positive velocity and positive acceleration feedback. Three experiments are carried out to validate the models previously mentioned. Successful implementation of a control experiment is also accomplished leading to considerable attenuations in the coupled membrane's dynamics. / Ph. D.