Trapped modes in a cylindrical elastic waveguide with a damping gasket

An infinite cylindrical body containing a three-dimensional heavy rigid inclusion with a sharp edge is considered. Under certain constraints on the symmetry of the body, it is shown that any prescribed number of eigenvalues of the elasticity operator can be placed on an arbitrary real interval $(0,l)$ by choosing suitable physical properties of the inclusion. In the continuous spectrum, these points correspond to trapped modes, i.e., to exponentially decaying solutions to the homogeneous problem. The results can be used to design filters and dampers of elastic waves in a cylinder.