RECONSTRUCTING INTERIOR ACOUSTIC PRESSURE FIELDS VIA HELMHOLTZ-EQUATION LEAST-SQUARES METHOD

This paper extends the Helmholtz equation least-squares (HELS) method previously developed by Wang and Wu [J. Acoust. Soc. Am. 102, 2020-203 2 (1997)] to reconstruction of acoustic pressure fields inside the cav ity of a vibrating object. The acoustic pressures are reconstructed th rough an expansion of the acoustic modes generated by the Gram-Schmidt orthonormalization with respect to the particular solutions to the He lmholtz equation. Such an expansion is uniformly convergent because th e selected acoustic modes consist of a uniformly convergent series of Legendre functions. The coefficients associated with these acoustic mo des are determined by requiring the assumed-form solution to satisfy t he pressure boundary condition at the measurement points. The errors i ncurred in this process are minimized by the least-squares method. Num erical examples of partially vibrating spheres and cylinders with vari ous half-length to radius aspect ratios subject to different frequency excitations are demonstrated. The reconstructed acoustic pressures ar e compared with the analytic solutions and numerical ones obtained by using the standard boundary element method (BEM) codes. (C) 1998 Acous tical Society of America. [S0001-4966(98)01110-2]