The Medium-Frequency Range in Computational Acoustics: Practical and Numerical Aspects

Abstract

The upper frequency limit of vibroacoustic calculations with finite element methods is usually concluded from resolution rules for the minimal wavelength encountered in the problem. Here, we derive general resolution rules that account for the pollution effect in finite element solutions of time-harmonic equations. These rules are given for the Helmholtz equation and the Bernoulli beam equation. The latter are based on an analysis of numerical dispersion for finite difference solutions. The theoretical results are given in the broader context of industrial vibroacoustic computations in the medium-frequency range. The governing equations of deterministic vibroacoustic computations and statistical energy analysis are reviewed with the goal to indicate, respectively, upper and lower frequency bounds for the applicability of either model. From the discussion of priorities in industrial application, open questions for theoretical investigations are deduced.