An Energy Diffusion Model for Interior Acoustics with Structural Coupling Using the Laplace Transform Boundary Element Solution

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Virginia Tech


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.



Acoustic diffusion, boundary element method, Laplace transform, numerical inverse Laplace transform, structural-acoustic coupling