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.

Analysis and manipulation of modal ratios of cylindrical drums

“…4 Research into the coupling between the two heads of a Japanese drum, a wadaiko, has been performed by Suzuki and Hwang. 10 Their research concludes, "depending on the tension ratio of the membranes, the frequency and amplitude ratios of the coupled resonances change".…”

A finite-element analysis on the free vibration of Japanese drum wood barrels under material property uncertainty

“…The wood barrel is much more rigid and massive than the diaphragms. Previous study on the coupling between the two membranes of a Japanese drum through the air inside the wood barrel, concentrating on the resonance frequency changes due to the coupling, has been investigated using semi analytical method [1]. In that study, the wood barrel wall was treated rigid, and the membrane bending stiffness was neglected.…”

Theoretical and experimental studies on the resonance frequencies of a stretched circular plate: Application to Japanese drum diaphragms

“…Very few studies have been reported on the resonance frequencies of Japanese drums [7][8][9]. Even though the structure of the nagado-daiko is very simple, the coupling of the two diaphragms complicates the distribution of the resonance frequencies [10,11]. To avoid this problem, one of the two diaphragms of a 0.48 m diameter nagado-daiko was removed and the resonance frequencies of the remaining diaphragm were compared to those of numerically-calculated frequencies.…”