Sathej G, Adhikari R
Department of Biotechnology, Indian Institute of Technology Madras, Chennai, India.
J Acoust Soc Am. 2009 Feb;125(2):831-8. doi: 10.1121/1.3058632.
In a family of drums used in the Indian subcontinent, the circular drum head is made of material of nonuniform density. Remarkably, and in contrast to a circular membrane of uniform density, the low eigenmodes of the nonuniform membrane are harmonic. In this work the drum head is modeled as a nonuniform membrane whose density varies smoothly between two prescribed values. The eigenmodes and eigenvalues of the drum head are obtained using a high-resolution numerical method. The mathematical model and the numerical method are able to handle both concentric and eccentric nonuniformities, which correspond, respectively, to the dayan and the bayan drums. For a suitable choice of parameters, which are found by optimizing the harmonicity of the drum, the eigenspectra obtained from the model are in excellent agreement with experiment. The model and the numerical method should find application in numerical sound synthesis.
在印度次大陆使用的一系列鼓中，圆形鼓面由密度不均匀的材料制成。值得注意的是，与密度均匀的圆形膜相反，这种非均匀膜的低阶本征模是谐波的。在这项工作中，鼓面被建模为一种非均匀膜，其密度在两个规定值之间平滑变化。使用高分辨率数值方法获得鼓面的本征模和本征值。该数学模型和数值方法能够处理同心和偏心的非均匀性，它们分别对应于塔杨鼓和巴杨鼓。对于通过优化鼓的谐波性找到的合适参数选择，从模型获得的本征谱与实验结果非常吻合。该模型和数值方法应可应用于数值声音合成。
