数世紀前から伝わる民族楽器を数学的に解明、センシングやエレクトロニクスなどの高品質な共振器への道を拓くInsights on centuries-old folk instrument is underpinned by a mathematical principle that may pave the way for high-quality resonators for sensing, electronics and more
2022-04-22 ハーバード大学
The researchers clamped the saw in two configurations: a J shape (left) and an S shape (right). The S shape has an inflection point (the sweet spot) in its profile, while J shape doesn’t/ (Credit: Mahadevan Lab/Harvard SEAS)
その結果、シンギングソーのユニークな数理物理学が、さまざまな用途に向けた高品質な共振器を設計する鍵を握っている可能性があることが判明しました。
ハーバード大学ジョン・A・ポールソン工学・応用科学大学院（SEAS）と物理学科の研究チームは、新しい論文の中で、シンギングソーを使って、曲がった金属のような曲がったシートの形状を調整して、センシング、ナノエレクトロニクス、フォトニクスなどの用途で高品質で長時間の発振を実現できることを実証しています。
＜関連情報＞
- https://www.seas.harvard.edu/news/2022/04/physics-singing-saw
- https://www.pnas.org/eprint/PXCVQBKH8K8BXTIZSTJ2/full
シンギングソーにおけるトポロジカルダイナミクスの幾何学的制御 Geometric control of topological dynamics in a singing saw
Suraj Shankar, Petur Bryde, and L. Mahadevan
Proceedings of the National Academy of Sciences Published:April 21, 2022
DOI:https://doi.org/10.1073/pnas.2117241119
Abstract
The common handsaw can be converted into a bowed musical instrument capable of producing exquisitely sustained notes when its blade is appropriately bent. Acoustic modes localized at an inflection point are known to underlie the saw’s sonorous quality, yet the origin of localization has remained mysterious. Here we uncover a topological basis for the existence of localized modes that relies on and is protected by spatial curvature. By combining experimental demonstrations, theory, and computation, we show how spatial variations in blade curvature control the localization of these trapped states, allowing the saw to function as a geometrically tunable high-quality oscillator. Our work establishes an unexpected connection between the dynamics of thin shells and topological insulators and offers a robust principle to design high-quality resonators across scales, from macroscopic instruments to nanoscale devices, simply through geometry.
