Coupling between two membranes of a Japanese drum

Abstract

Some drums have, typically, a hollow trunk (or a barrel) with a circular membrane at each of the two ends. In this type of drum structure, the two membranes interact with each other through the air between them inside the body. Even if the two membranes have an identical fundamental resonance frequency, the interaction results in two resonance frequencies. At the lower resonance, the two membranes vibrate in phase. Since the membranes must move the internal air, the frequency at the lower resonance is lower than that of the original resonance (without air loading). At the higher resonance, they vibrate out-of-phase, causing compression or expansion of the internal air simultaneously. The frequency at this resonance is higher than that of the original resonance since, in this case, the air works as a spring. In this paper, resonance frequencies and mode shapes of the coupled membranes are investigated using an analytical model. The membranes are assumed to be ideal (i.e., no bending stiffness) and the body is assumed to be ideally rigid. Since it is a common practice that the two membranes are slightly (intentionally) miss-tuned, the main interest of this paper is to simulate the effect of this miss-tuning on the resulting resonance frequencies and mode shapes. Numerical results for the case of a 48 cm diameter and 50 cm length Japanese drum are presented.