Experimental investigation of shell modes in two-dimensional phononic crystal consisting of hollow cylinders

We experimentally demonstrate the flexural shell modes of thin-walled hollow steel cylinders immersed in water. For a two-dimensional square-arranged phononic crystal consisting of such hollow cylinders, two flat bands are created because of the coupling of the shell modes among neighboring cylinders. The narrow bands associated with shell-modes are first validated by experiment. In particular, by analyzing the transmission spectra, band-structure, and eigen-pressure field distribution, we give detailed discussion on the anisotropic coupling behavior of the two flat bands with external incident plane waves.