Finite element modelling of steelpan acoustics

Abstract

In this paper the finite element method is used to model acoustic vibrations of steelpan shells. The steelpan surface is characterized as a three-dimensional compound shell, comprising notes (surfaces with reverse curvature) on a concave ellipsoidal surface attached to a cylindrical shell (the skirt). In this model note and inter-note surfaces are defined by geometric parameters which can be varied to define complex surface geometries. The geometric mesh model is used develop tenor, cello and bass steelpans instruments and a 3D finite element shell vibration algorithm is used to demonstrate their vibration characteristics. Modes shapes and frequencies of the composite shell structures are computed for typical configurations of note and skirt geometry. The model demonstrates that there exist many composite natural modes of a playing surface involving the interaction between two or more notes. In addition, it is found that the frequency range of mode shapes associated primarily within skirt vibration overlaps with the musical range of the notes underscoring the potential for “skirt-note” coupling. The degree of frequency overlap was found to be largely dependent on skirt length and configuration.