  We present a theoretical study of resonant frequencies and spatial
correlations of Josephson phases in frustrated arrays of Josephson junctions.
Two types of one-dimensional arrays, namely, the diamond and sawtooth chains,
are discussed. For these arrays in the linear regime the Josephson phase
dynamics is characterized by multiband dispersion relation $\omega(k)$, and the
lowest band becomes completely $flat$ at a critical value of frustration,
$f=f_c$ . In a strongly nonlinear regime such critical value of frustration
determines the crossover from non-frustrated ($0<f<f_c$) to frustrated
($f_c<f<1$) regimes. The crossover is characterized by the thermodynamic
spatial correlation functions of phases on vertices, $\varphi_i$, i.e.
$C_p(i-j)=\langle\cos[p(\varphi_i - \varphi_j)]\rangle$ displaying the
transition from long- to short-range spatial correlations. We find that
higher-order correlations functions, e.g. $p=2$ and $p=3$, restore the
long-range behavior deeply in the frustrated regime, $f\simeq 1$. Monte-Carlo
simulations of the thermodynamics of frustrated arrays of Josephson junctions
are in good agreement with analytical results.
