Modeling of High Frequency Broadband Acoustic Fields Inside Cylindrical Enclosures Using an Energy Intensity Boundary Element Method

Abstract

High frequency broadband acoustic fields inside three-dimensional enclosures are modeled through an energy-intensity boundary element method (EIBEM). Derived from first principles, this novel approach uses uncorrelated and spreading energy sources as building blocks to solve for steady state interior mean-square pressure distributions. The enclosure boundary is replaced with a distribution of energy intensity sources and discretized into constant strength radiating panels. The directivity function of the radiating panel is expanded into a series of half-space orthogonal spherical harmonics that accounts for both diffuse and specular reflections. Energy transfer between boundary panels and interior sources are formulated into an influence matrix that satisfies the prescribed reflecting boundary conditions and is inverted to solve for the panel powers. The diffuse solution is straightforward while the specular solution is computed through an iterative Lagrangian optimization technique. Refinements to the energy method are introduced to model reflections in enclosures with more generalized geometries. These include a numerical quadrature scheme which uses interpolating polynomial functions to approximate panel interactions, along with a boundary panel image source procedure for improving specular convergence. The new energy method is verified with a benchmark solution in three rectangular enclosures and compared against a more exact EIBEM algorithm developed specifically for rectangular geometries. The absorption scaling solution, which decomposes the mean-square pressure response into a power series that scales with the average room absorption, is formulated through the panel influence matrices and is shown to produce quick and accurate diffuse solutions for various levels of absorption.Once verified in a well-understood rectangular geometry, the energy method is then applied to model mean-square pressure fields inside cylindrical enclosures. The curved boundary is discretized into trapezoidal energy intensity panels and examined for its effect on panel radiation. An analytical benchmark solution is derived for a cylindrical enclosure with rigid flat end caps and a uniform impedance assigned to the cylindrical wall. Through an innovative approach which combines a linear image source array with a modal scattering decomposition, the pressure field is solved at a given frequency which is then numerically band averaged to obtain the broadband solution. Results are computed for both a high and low aspect ratio cylindrical enclosure with an interior dipole source. Excellent agreement is observed when compared with the specular EIBEM solution for three different absorption cases at various trajectories, however the diffuse solution is found to produce substantially incorrect pressure distributions which do not capture the specular focusing effects of the curved geometry. The EIBEM is also experimentally verified inside of a large cylindrical tank with absorption placed along the cylindrical wall in the form of modular absorbing panels. A custom-built broadband source with monopole and dipole configurations is placed inside the tank and used to generate the steady state response. The normal incidence reflection coefficients of the absorbing materials are measured through both an impedance tube and a free-field panel method. Interior sound pressure levels are recorded along an axial trajectory for six different one-third octave bands ranging from 3kHz to 10kHz, and are compared with the diffuse and specular EIBEM results for an equivalent enclosure. Comparison of the experimental pressure levels for different center frequencies reveals the transition from the mid frequency region to the uncorrelated high frequency limit which produces smooth mean-square pressure variations that show agreement with the diffuse EIBEM predictions.