Abstract:

The Helmholtz equation--least-squares (HELS) method developed by Wang and Wu [J. Acoust. Soc. Am. (to be published)] is extended to reconstruction of acoustic pressure fields inside a vibrating cavity. In this method, the acoustic pressures are reconstructed through an expansion of acoustic modes, or a set of independent functions generated via an orthonormalization with respect to the particular solutions to the Helmholtz equation on the particular surface under consideration. The coefficients associated with these acoustic modes are determined by requiring the assumed form solution to satisfy the pressure boundary condition at the measurement points. The errors incurred in this process are minimized by the least-squares method. Numerical examples of partially vibrating spheres and cylinders with various half-length to radius ratios and dimensionless frequencies are demonstrated. The results thus obtained are compared with the numerical solutions obtained by using a direct boundary-element method (BEM). Results show that the HELS method enables one to reconstruct the radiated acoustic pressure fields much more effectively and accurately than BEM does. [Work supported by the Institute for Manufacturing Research at Wayne State University.]