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- W4313446871 abstract "The steelpan is a pitched percussion instrument that takes the form of a concave bowl with several localized dimpled regions of varying curvature. Each of these localized zones, called notes, can vibrate independently when struck, and produces a sustained tone of a well-defined pitch. While the association of the localized zones with individual notes has long been known and exploited, the relationship between the shell geometry and the strength of the mode confinement remains unclear. Here, we explore the spectral properties of the steelpan modeled as a vibrating elastic shell. To characterize the resulting eigenvalue problem, we generalize a recently developed theory of localization landscapes for scalar elliptic operators to the vector-valued case, and predict the location of confined eigenmodes by solving a Poisson problem. A finite element discretization of the shell shows that the localization strength is determined by the difference in curvature between the note and the surrounding bowl. In addition to providing an explanation for how a steelpan operates as a two-dimensional xylophone, our study provides a geometric principle for designing localized modes in elastic shells." @default.
- W4313446871 created "2023-01-06" @default.
- W4313446871 creator A5016218544 @default.
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- W4313446871 date "2022-12-29" @default.
- W4313446871 modified "2023-10-18" @default.
- W4313446871 title "Localization in musical steelpans" @default.
- W4313446871 doi "https://doi.org/10.48550/arxiv.2212.14465" @default.
- W4313446871 hasPublicationYear "2022" @default.
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