Periodic structures exhibit special dynamical characteristics of passbands and stopbands that enable one to design filters and control the propagation of waves and vibration with particular frequencies through the structures. The finite element and transfer matrix methods are combined to develop a model of wave propagation in a beam bonded with periodical piezoelectric patches using Timoshenko beams theory considering the effect of shear deformation and rotary inertia. The effects of geometric dimensions and material parameters on the wave propagation characteristics of the periodic structure are analyzed and compared with some results from Bernonlli-Euler beam theory. Research indicates that when the thickness ratio of base beam layer and piezoelectric layer reaches 40, the width of a stop band is reduced by 54%, so it is necessary to use the model based on Timoshenko theory rather than Bernonlli-Euler theory when the thickness of base layer is large and shear and rotational inertia become more important. For different configurations of the periodic piezoelectric beam, the frequency bands are very different. The characteristics of frequency bands and wave propagation in the structure can be altered by tuning different structural parameters. The investigation provides the basic guidelines to design periodic piezoelectric structures to achieve desired filtering characteristics.