  Exceptional points (EPs) are singular points on a parameter space at which
some eigenvalues (scattering poles) and their corresponding eigenmodes
coalesce. This study shows the existence of second- and third-order EPs in
cylindrical elastic systems with radiation loss. We consider multilayered
cylindrical solids under the plane-strain condition placed in a background
elastic or acoustic medium. Elastic and acoustic waves propagating in the
background media are subject to the radiation loss. We optimize the radii and
the material constants of the multilayered solids, such that some scattering
poles coalesce on the complex frequency plane. Some numerical experiments are
performed to confirm that the coalescence originates from EPs. We expect that
this study provides a new approach for enhancing mechanical sensors.
