Piezoelectric patches connected with shunting circuits are periodically placed along a base beam, forming a one-dimensional phononic crystal. Different types of shunting circuits will determine the band structure of the beam. Resistive shunting circuits can restrain the beam’s modal vibrations to some extent and the band gaps of the beam can be changed by weakening the piezoelectric effect. LC shunting circuits can produce locally resonant gaps induced by LC circuits’ electromagnetic oscillations excited by piezoelectric patches. When resistors are added to the LC circuits, the LC circuits’ oscillation will be weakened and the attenuation amplitude in the band gaps will be lowered, but the scope of band gaps are widened.