  We investigate non-Hermitian degeneracies, also known as exceptional points,
in continous elastic media, and their potential application to the detection of
mass and stiffness perturbations. Degenerate states are induced by enforcing
parity-time symmetry through tailored balanced gain and loss, introduced in the
form of complex stiffnesses and may be implemented through piezoelectric
transducers. Breaking of this symmetry caused by external perturbations leads
to a splitting of the eigenvalues, which is explored as a sentitive approach to
detection of such perturbations. Numerical simulations on one-dimensional
waveguides illustrate the presence of several exceptional points in their
vibrational spectrum, and conceptually demonstrate their sensitivity to point
mass inclusions. Second order exceptional points are shown to exhibit a
frequency shift in the spectrum with a square root dependence on the perturbed
mass, which is confirmed by a perturbation approach and by frequency response
predictions. Elastic domains supporting guided waves are then investigated,
where exceptional points are formed by the hybridization of Lamb wave modes.
After illustrating a similar sensitivity to point mass inclusions, we also show
how these concepts can be applied to surface wave modes for sensing crack-type
defects. The presented results describe fundamental vibrational properties of
PT-symmetric elastic media supporting exceptional points, whose sensitivity to
perturbations goes beyond the linear dependency commonly encountered in
Hermitian systems. The findings are thus promising for applications involving
sensing of perturbations such as added masses, stiffness discontinuities and
surface cracks.
