Using finite-difference time-domain methods with a Rayleigh approach to model low-frequency sound fields in small spaces subdivided by porous materials

Abstract

Finite-Difference Time-Domain (FDTD) models are used to predict low-frequency sound fields in small volumes containing a limp panel formed from a porous material which partially or completely subdivides the volume. This porous panel is incorporated into FDTD using a Rayleigh model as proposed by Suzuki et al. However, to accurately reproduce the low-frequency sound field it is found necessary to introduce an additional Moving Frame Model (MFM) to account for motion of the porous panel. For spaces that are completely subdivided by a porous panel, the MFM accounts for a spring-mass-spring resonance that can occur below the lowest acoustic cavity mode. The MFM assumes lumped mass behavior of the porous panel which is coupled to the FDTD update equations that incorporate the Rayleigh model. FDTD is compared against measurements using transient excitation with a pulse input to a loudspeaker in a small reverberant room under three different conditions: (1) empty room, (2) with a mineral fibre panel partially dividing the room, and (3) with a mineral fibre panel completely dividing the room. Close agreement is obtained between experimental results and FDTD incorporating the MFM; this validates the models as well as implementation of the loudspeaker as a hard velocity source.