The analogue of quantum billiards in elasticity are resonators. If the underlying space is curved some results for the spectrum are known in the quantum case. In the curved elastic case, the situation then becomes that of shells. In general, it is expected that semiclassical methods from quantum chaos will provide an understanding of high frequency vibrations of shells.

The talk shall give an overview of shells, their classical ray limit and discuss the upcoming experiments at the Niels Bohr Institute by Clive Ellegaard and Mikkel Avlund. Further collaborators are Thomas Guhr (LTH) and Mark Oxborrow (NPL,UK).