  We consider a classical system of two-dimensional (2D) charged particles,
which interact through a repulsive Yukawa potential $exp(-r/\lambda)/r$,
confined in a parabolic channel which limits the motion of the particles in the
$y$-direction. Along the $x$-direction, the particles are also subject to a
periodic potential substrate. The ground state configurations and the normal
mode spectra of the system are obtained as function of the periodicity and
strength of the periodic potential ($V_0$), and density. An interesting set of
tunable ground state configurations are found, with first and second order
structural transitions between them. A magic configuration with particles
aligned in each minimum of the periodic potential is obtained for V_0 larger
than some critical value which has a power law dependence on the density. The
phonon spectrum of different configurations were also calculated. A
localization of the modes into a small frequency interval is observed for a
sufficient strength of the periodic potential. A tunable band-gap is found as a
function of $V_0$. This model system can be viewed as a generalization of the
Frenkel and Kontorova model.
