  Micro- and nano-resonators have important applications including sensing,
navigation, and biochemical detection. Their performance is quantified using
the quality factor $Q$, which gives the ratio of the energy stored to the
energy dissipated per cycle. Metallic glasses are a promising materials class
for micro- and nano-scale resonators since they are amorphous and can be
fabricated precisely into complex shapes on these lengthscales. To understand
the intrinsic dissipation mechanisms that ultimately limit large $Q$-values in
metallic glasses, we perform molecular dynamics simulations to model metallic
glass resonators subjected to bending vibrations. We calculate the vibrational
density of states, redistribution of energy from the fundamental mode of
vibration, and $Q$ versus the kinetic energy per atom $K$ of the excitation. In
the linear and nonlinear response regimes where there are no atomic
rearrangements, we find that $Q \rightarrow \infty$ (since we do not consider
coupling to the environment). We identify a characteristic $K_r$ above which
atomic rearrangements occur, and there is significant energy leakage from the
fundamental mode to higher frequencies, causing finite $Q$. Thus, $K_r$ is a
critical parameter determining resonator performance. We show that $K_r$
decreases as a power-law, $K_r\sim N^{-k},$ with increasing system size $N$,
where $k \approx 1.3$. We estimate the critical strain $\langle \gamma_r
\rangle \sim 10^{-8}$ for micron-sized resonators below which atomic
rearrangements do not occur, and thus large $Q$-values can be obtained when
they are operated below $\gamma_r$. We find that $K_r$ for amorphous resonators
is comparable to that for resonators with crystalline order.
