Vibration analysis of a musical drum head under nonuniform density and tension using a spectral method

Abstract

This paper develops a numerical method to analyze the membrane vibration of a membranophone with nonuniform heads, in which the density and tension vary smoothly. A spectral method is applied to numerically analyze the wave equation governing a membrane with spatially varying areal density and tension. An Indian drum tabla, representing nonuniform density, and a typical drum tom tom with several tension rods, representing nonuniform tension, are analyzed using the proposed numerical method to determine their eigenfrequencies and eigenmode shapes.