  Propagation of a longitudinal wave through the periodic structure composed of
alternating elastic and piezoelectric layers is considered. The faces of each
piezoelectric layer are electroded and connected via a circuit with the
capacity $C$. It is shown that if $C<0$ then the Floquet-Bloch spectrum $
\omega(K)$ in a certain range of negative $C$ may possess a quasistatic
absolute stopband starting at $\omega =0$. Other unusual features of the
spectrum occurring at certain fixed values of $C<0$ are the infinite group
velocity of the first branch at the origin point $\omega =0$, $K=0$ and the
flat bands $\omega={\rm const}$.
