  Given the flexibility of choosing negative elastic parameters, we construct
material structures that can induce two resonance phenomena, referred to as the
elastodynamical resonances. They mimic the emerging plasmon/polariton resonance
and anomalous localized resonance in optics for subwavelength particles.
However, we study the peculiar resonance phenomena for linear elasticity beyond
the subwavelength regime. It is shown that the resonance behaviours possess
distinct characters, with some similar to the subwavelength resonances, but
some sharply different due to the frequency effect. It is particularly noted
that we construct a core-shell material structure that can induce anomalous
localized resonance as well as cloaking phenomena beyond the quasi-static
limit. The study is boiled down to analyzing the so-called elastic
Neumann-Poinc\'are (N-P) operator in the frequency regime. We provide an
in-depth analysis of the spectral properties of the N-P operator beyond the
quasi-static approximation,and these results are of independent interest to the
spectral theory of layer potential operators.
