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

概要

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Nagado-daiko, the most common type of traditional Japanese drum, is known for its unique diaphragm, which is stretched to a relatively high tension compared to other types of drums. The diaphragm is primarily made of cow skin. Once the cow skin is chemically treated, it exhibits Young’s modulus of approximately 3.5×109 Pa, suggesting that the diaphragm should be treated as a stretched plate, or a stiff membrane. This paper reviews the method for obtaining eigenvalues and eigen-frequencies of a membrane with stiffness. Eigenvalues of the 15 lowest modes are given as functions of tension vs. bending stiffness ratios. A double exponential function with four constants is also presented so that eigenvalues (and then resonance frequencies) of the 15 lowest modes can be simply obtained by common calculators. Measured results of a nagado-daiko with a 48 cm diameter show that the effect of stiffness on the spacing of resonance frequencies is negligible in the lowest several modes, contradicting theoretical prediction. A more precise experimental study is necessary to determine the effectiveness of the diaphragm stiffness on the resonance frequencies especially in the mid to high frequency region.
2009-09-01