A Revolutionary Boundary Element Approach Based on Energy Conservation for Interior Noise Predictions

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The analysis of high frequency broadband sound fields is of interest in architectural acoustics and in the aircraft and automotive industries, where interior noise prediction and reduction are important. This project will provide a computationally efficient and accurate analysis tool for the prediction of sound pressure levels in enclosures that contain broadband, high frequency sound waves. The novelty of the proposed boundary element method is that the problem and boundary conditions are recast in terms of time-averaged variables (mean-square pressure, energy, and intensity) rather than the time-varying quantities of pressure and velocity, and the infinitesimal sources that comprise each element are broadband directional uncorrelated sources. Furthermore, this method is unique among emerging energy-based boundary element or finite element methods because it does not need to assume that the acoustic medium is dissipative, nor does it assume that the boundaries are entirely diffusely reflecting. The difficulty with analyzing broadband systems in the high frequency range is that they contain a large number of modes and frequencies. Therefore, approaches based on modal analysis, as well as traditional finite element or boundary element methods, become computationally cumbersome. The proposed method is extremely efficient because each frequency in the band does not need to be considered separately and individual elements can be large compared to a wavelength. The resulting gain in computational efficiency is orders of magnitude over a traditional approach. Alternative efficient methods that have been developed for lightly damped systems are inaccurate when damping levels are not small. Typical structural-acoustic systems contain significant levels of damping, since most systems are designed to reduce vibration and interior noise levels. The method being proposed is not restricted to lightly damped situations and therefore will be applicable to more practical systems. Intellectual merit: The development of the boundary element method that was described above will provide a new tool for the analysis of high frequency broadband sound fields. This novel boundary element method will provide a much-needed alternative to traditional analyses, and represents a paradigm shift in the way that these types of sound fields are treated. Additionally, the availability of such an analysis tool will enable more efficient and accurate analyses, and thereby facilitate design of better acoustic spaces be they rooms or vehicle interiors. Broader impacts: The proposed plan of work includes theoretical, computational, and experimental components. All of these results will be disseminated broadly, published, and presented at national and international conferences. The boundary element method has the potential for commercial development and use in architectural acoustics. Another broader impact of this research project is the integration of research and education through "hands on" experiences with acoustics both in a classroom setting and in the laboratory. Students will have the opportunity to use the software developed under this grant in order to simulate sound fields in enclosures of their choosing and will be involved in performing experiments that support this research. Both undergraduate and graduate students, with particular attention being paid to underrepresented groups, will participate in this research.