  We study the elastodynamics of a periodic metastructure incorporating a
defect pair that enforces a parity-time (PT) symmetry due to a judiciously
engineered imaginary impedance elements - one having energy amplification
(gain) and the other having an equivalent attenuation (loss) mechanism. We show
that their presence affects the initial band structure of the periodic
Hermitian metastructure and leads to the formation of numerous exceptional
points (EPs) which are mainly located at the band edges where the local density
of modes is higher. The spatial location of the PT-symmetric defect serves as
an additional control over the number of emerging EPs in the corresponding
spectra as well as the critical non-Hermitian (gain/loss) strength required to
create the first EP - a specific defect location minimizes the critical
non-Hermitian strength. We use both finite element and
coupled-mode-theory-based models to investigate these metastructures, and use a
time-independent second-order perturbation theory to further demonstrate the
influence of the size of the metastructure and the PT-symmetric defect location
on the minimum non-Hermitian strength required to create the first EP in a
band. Our findings motivate feasible designs for the experimental realization
of EPs in elastodynamic metastructures.
