A minimal model of the bar-resonator vibroacoustic interaction in mallet percussion instruments

Abstract

In some mallet percussion instruments, such as vibraphones and marimbas, tubular acoustic resonators are placed beneath the tuned bars to enhance acoustic radiation at their fundamental frequency. This work deals with the formulation of a minimal physical model describing the vibro-acoustic interaction occurring in these instruments. The fundamental bar mode is modelled as a disk-shaped oscillator and the resonator as a cylindrical acoustic waveguide, described in terms of its acoustic modes. The three-dimensional effects associated with sound radiation and the interaction between the two elements are calculated using a 2-D axisymmetric finite element (FE) model, whose numerical results are then fitted to dimensionless analytical expressions, which encapsulate the complex physics of the vibro-acoustic interaction in a simplified manner. This can pragmatically be used to formulate a lumped-parameter model of the coupled system. Illustrative numerical results are presented and qualitatively validated, demonstrating the ability of the proposed modelling approach to capture the essential features of the coupled dynamics occurring in real instruments.