  We present an analytical description of the large-amplitude stationary
oscillations of the finite discrete system of harmonically-coupled pendulums
without any restrictions to their amplitudes (excluding a vicinity of $\pi$).
Although this model has numerous applications in different fields of physics it
was studied earlier in the infinite limit only. The developed approach allows
to find the dispersion relations for arbitrary amplitudes of the nonlinear
normal modes. We underline that the long-wavelength approximation, which is
described by well- known sine-Gordon equation leads to inadequate zone
structure for the amplitude order of $\pi/2$ even if the chain is long enough.
The extremely complex zone structure at the large amplitudes corresponds to lot
of resonances between nonlinear normal modes even with strongly different wave
numbers. Due to complexity of the dispersion relations the more short
wavelength modes can possess the smaller frequencies. The numerical simulation
of the dynamics of the finite-length chain is in a good agreement with obtained
analytical predictions.
