Reconstructing interior acoustic pressure fields via Helmholtz equation least-squares method

Abstract

This paper extends the Helmholtz equation least-squares (HELS) method previously developed by Wang and Wu [J. Acoust. Soc. Am. 102, 2020–2032 (1997)] to reconstruction of acoustic pressure fields inside the cavity of a vibrating object. The acoustic pressures are reconstructed through an expansion of the acoustic modes generated by the Gram–Schmidt orthonormalization with respect to the particular solutions to the Helmholtz equation. Such an expansion is uniformly convergent because the selected acoustic modes consist of a uniformly convergent series of Legendre functions. 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 aspect ratios subject to different frequency excitations are demonstrated. The reconstructed acoustic pressures are compared with the analytic solutions and numerical ones obtained by using the standard boundary element method (BEM) codes.