A team of researchers from the Harvard School of Engineering and Applied Sciences (SEAS) and the Department of Physics
The geometry of the musical saw, as notedresearchers, creates what musicians call the sweet spot, and physicists call localized vibrational modes. This is a limited area on the sheet that resonates without losing energy at the edges.
Using the mathematics of topological systems,The researchers found that the localized vibrational modes in the sweet spot of a singing saw are controlled by a topological parameter that can be calculated and is based on the existence of two opposing curves in the material. The researchers also found that they can tune the mode localization by changing the shape of the S-curve, which is important in applications like sensing where you need a resonator tuned to very specific frequencies.
Using experiments, theoretical and numericalanalysis, we have shown that S-curvature in a thin shell can localize topologically protected modes in the "sweet spot" or inflection line, similar to exotic edge states in topological insulators. This phenomenon is independent of the material, i.e. it appears in steel, glass or even graphene.
Pieture Bride, co-author of the study at the Harvard School of Engineering and Applied Sciences
The sound of the musical saw since the spreadcheap and affordable steel has become popular in folk music in different countries. Created by bending a metal hand saw and tilting it like a cello, the instrument, according to the authors of the work, reached its peak on the vaudeville stages of the early 20th century and experienced a resurgence thanks to social networks.
"The way the musical saw sings is based onamazing effect,” says Bride. - When you strike a flat elastic sheet, such as a metal sheet, the whole structure vibrates. Energy is quickly lost, resulting in a dull sound that quickly dissipates. The same result is observed if you bend it into a J-shape. But if you bend the sheet into an S-shape, you can make it vibrate over a very small area, and that gives a clear, sustained sound."
The authors of the work believe that the discovery offersa reliable design principle for high quality resonators regardless of size and material, from macroscopic musical instruments to nanoscale devices, simply by combining geometry and topology. This technology, the researchers say, could replace the use of complex, carefully structured, periodic arrays of nanomembranes that are now used to drive local modes.
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