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Steady-State and Time-Decaying Sound Fields in Enclosures Using Energy-Intensity Boundary Elements with Time Delay Analysis and Absorption Scaling
| Content Provider | Semantic Scholar |
|---|---|
| Author | Bliss, Donald B. Franzoni, Linda P. Michalis, Krista A. |
| Copyright Year | 2007 |
| Abstract | An Energy-Intensity Boundary Element Method is used to predict the spatial-temporal variation of mean-square pressure at mid-to-high frequencies. Enclosure boundaries are replaced by uncorrelated broadband directional sources, which provide constituent fields in terms of fast average mean-square pressure and intensity variables. For time-dependent problems, an interpolation method is used to re-express the actual delays as a discrete set of integer-multiple delays, facilitating solution. Temporal behavior is formulated as a higher-dimensional eigenvalue problem, with boundary source strengths expressed as eigenmodes. Decaying solutions exhibit rapid short-time spatial redistribution, followed by long-time decay of the slowest eigenmode. Short-time adjustment and decay depends on initial conditions and the relative distribution of absorbing material. The short-time behavior of the rapidly decaying eigenmodes is primarily due to energy redistribution, not absorption. These methods are used in conjunction with an absorption-based perturbation analysis to show that sound fields obey certain overall scaling laws in terms of a spatially averaged absorption parameter. Spatial variation is dependent on absorption distribution, but is insensitive to the overall absorption. Although developed assuming small absorption, the scaling method works well up to large absorptions, and provides insight into the behavior of acoustic spaces. (Sponsor: NSF) INTRODUCTION This research utilizes an energy based boundary element method for computational room acoustics. Previous work has shown that the steady-state time-averaged intensity and meansquare pressure in broadband high frequency sound fields can be calculated accurately using formally derived energy-intensity boundary sources. These sources are added in an uncorrelated manner, but they utilize a directivity function that accounts for correlation effects and specular reflection at boundaries. For steady-state sound fields this approach has been implemented in a boundary element method and demonstrated to give excellent agreement with computationally intensive exact solutions obtained by modal methods. The energy-intensity boundary element approach, formally developed in refs. [1-4], does not require computation at each individual frequency and uses boundary elements that are much larger than a wavelength. Thus accurate results are obtained for orders-of-magnitude less computational effort. This paper work to further understand, extend, and simplify this problem. The first goal is to better understand a specific physical behavior that is observed in numerical simulations of enclosures with steady-state broad-band sound fields. In many enclosures, both 2-D and 3-D, spatial variations in mean-square pressure are observed to be nearly identical as wall absorption coefficients are scaled up and down. For example, in a room with fixed power input if all the wall absorption coefficients are doubled, halved, or changed in any proportional manner, the spatial variation in mean-square pressure, p, is virtually unchanged although the average level may be considerably higher or lower. The theory demonstrating that the |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.sea-acustica.es/WEB_ICA_07/fchrs/papers/rba-05-010.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
