印度鼓的本征谱
The eigenspectra of Indian musical drums
摘要：
在印度次大陆使用的鼓族中，圆形鼓头由密度不均匀的材料制成。值得注意的是，与均匀密度的圆形膜相反，非均匀膜的低本征模是谐波的。在这项工作中，我们的鼓头模型的非均匀膜的密度在两个规定的值之间平滑变化。利用傅里叶-切比雪夫谱配置法，我们得到了鼓头的本征模和本征值。对于一个合适的选择的参数，我们发现通过优化成本函数，从我们的模型得到的本征谱与实验值非常吻合。我们的模型和数值方法应该在数值声音合成中找到应用。
英文摘要：
In a family of drums used in the Indian subcontinent, the circular drum head is made of material of non-uniform density. Remarkably, and in contrast to a circular membrane of uniform density, the low eigenmodes of the non-uniform membrane are harmonic. In this work we model the drum head by a non-uniform membrane whose density varies smoothly between two prescribed values. Using a Fourier-Chebyshev spectral collocation method we obtain the eigenmodes and eigenvalues of the drum head. For a suitable choice of parameters, which we find by optimising a cost function, the eigenspectra obtained from our model are in excellent agreement with experimental values. Our model and the numerical method should find application in numerical sound synthesis.
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