This paper deals with the design of periodic piezoelectric structures for broadband vibration control. By shunting identical negative capacitances to the periodically distributed piezoelectric patches, a wide and continuous band gap is created so as to cover the frequency range of interest. This way the modal density of the structure is reduced and the modal shapes are localized at the boundaries. A large proportion of the energy can then be removed or dissipated by a small number of dampers or energy harvesters integrated within the negative capacitance circuits. A design process is proposed to achieve the wide band gap. The overall amount of piezoelectric materials is constrained in order to keep mass of structures low. The wave electromechanical coupling factor is proposed and used as a criterion. This allows to reach the largest width of the band gap by using a stable value of negative capacitance. The control of multiple high-order modes of a cantilever beam is considered as an example. The vibration reduction performance of the designed piezoelectric structures is presented and the influences of band gap resonance, resistor and the boundary condition are discussed. The proposed approach is fully based on wave characteristics and it does not rely on any modal information. It is therefore promising for applications at mid- and high frequencies where the access to the exact modal information is difficult.