Modelling a Drum by Interfacing 2-D and 3-D Waveguide Meshes
Marc-Laurent Aird, Joel Laird, John ffitch · The University of Bath Online Publications Store (The University of Bath) · 2000
The Digital Waveguide Mesh is an extension of the 1-D Digital Waveguide technique (Smith, 1992), and oers the ability t o m o d e l t w o and three dimensional wave propagation (Van Duyne & Smith, 1993;Van Duyne & Smith, 1996; Fontana & Rocchesso, 1999).So far 2-D triangular meshes have been used to model wave propagation in membranes (Fontana & Rocchesso, 1998;Laird et al., 1998), while 3-D meshes have been proposed in room acoustics simulations (Savioja et al., 1994).In this paper we propose a model of a drum based upon a 2-D mesh for the drum skin and a 3-D mesh to model the interior air cavity.We also attach rimguides (Laird et al., 1998) to each of these structures to model correctly the circular boundary for low frequencies.Due to the dierences in wave speed through the two media, the membrane mesh will be far denser than the 3-D mesh, with non-integer ratios between mesh radii, and hence interfacing the two mesh structures is non-trivial.We consider the use of low-order approximations to pressure fronts in the air and their inverse operations on the membrane to model the contributions from one medium to the other and vice versa.We also propose extensions to the work to include higher order approximations at the interface using interpolation, and the building of an interface between the air and the drum shell.