Analysis and manipulation of modal ratios of cylindrical drums

Abstract

This paper uses modal analysis to investigate the effect of manipulating drumhead tension on the modal frequency ratios of a cylindrical drum with two drumheads. This analysis evaluates a drum's free vibration after excitation. It is shown that the frequency of the (01) mode of the drum is the same on both heads, whereas the frequency of each (11) mode has a decreased dependence on that of the opposite drumhead. This allows manipulation of the ratios for the (11) modes of the batter and resonant heads with respect to the overall (01) mode. This manipulation is shown to allow a range of tunings such that the (11) mode of the batter head can be tuned to a ratio of 1.5× that of the (01) mode.