Study of localized modes in steelpans via a vector landscape function

The steelpan is a pitched percussion instrument in the form of a concave shell with several regions of lower curvature, called notes. Each note can be made to vibrate independently, an example of mode localization in an elastic shell. We investigate how the strength of localization in steelpans depends on the geometry, and find that it is determined by the change in curvature at the boundary of the note regions. In our analysis, we use a new generalization of the localization landscape theory which can be used to predict localized modes in general shells. The landscape allows us to estimate the localization regions by solving a Poisson problem instead of the full eigenvalue problem.