In this paper, piezoelectric patches and electrical circuits are associated to attenuate vibration of a flat panel. The resulting electrical network is equivalent to a resistor-inductor-capacitor circuit performing as a tuned vibration absorber, denoted by piezoelectric resonator. The choice of design parameters, such as the correct placement for piezoelectric patches and the optimal electrical circuit elements, is assisted by finite element simulation and theoretical analysis. Measurements of sound transmission loss and modal analysis are conducted to demonstrate the structural vibration control and its resulting sound insulation performance. It is shown that, despite its reduced mass, the piezoelectric resonator can be more effective than conventional damping in low frequencies, which enables the overall sound insulation system to perform, with lower mass, in a wider frequency range.