The vibration and the sound radiation of cylindrical shells are analyzed and controlled. Shunted piezoelectric rings are placed periodically along the shell length to act as sources of impedance mismatch. The resulting periodic structure features a behavior which is characterized by frequency bands, 'stop bands', where the vibrations are attenuated and wave propagation is impeded. The location and the width of the stop bands are controlled by the impedance mismatch introduced along the structure. In the considered configuration, the stop bands can be tuned by proper selection of the shunting circuit.