Employing numerical techniques in the analysis and design of musical instruments
Katherine Legge, J. Petrolito · The Journal of the Acoustical Society of America · 2012
In the simplest of terms, a musical instrument consists of a source of oscillation coupled to a resonating body. The exception to this is an idiophone such as a triangle or gong, where the vibrating source is able to be its own radiator of sound. Whatever the configuration, the radiating structure is generally not a simple shape easily represented by a mathematical formulation, and analytical solutions to the governing equations of even a simplified model are often not obtainable. Working with Neville Fletcher in the 1980’s a personal computer was employed to undertake a time-stepping routine through the equations of a simplified model of a kinked metal bar, to depict nonlinear coupling of its modes of vibration. Similar analysis of a gong modelled by a spherical shell with a kinked edge was well beyond the available computing power. In this paper we illustrate how the development of computers and numerical techniques over the intervening thirty years means that we are now able to describe and analyse complex shapes and are encroaching on the domain of the instrument maker through the use of numerical optimisation for instrument design.