This work deals with the damping of structural vibrations by means of Synchronized Switch Damping (SSD) techniques on piezoelectric elements. Piezoelectric patches are attached to the vibrating structure and connected to an electrical circuit that includes a switch. The latter allows to continuously switch the piezoelectric elements from an open-circuit state to a specific electric impedance, synchronously with the mechanical oscillations. The present study focuses on two goals: (i) the quantification of the added damping (ii) the optimization of the electric circuit parameters. The free and forced responses of one mode of the mechanical structure are studied in detail. The precise time response of the system is obtained with semi-analytical models for the two cases where the electrical impedance is a simple resistance or a resistance and an inductance. The added damping of the oscillations is estimated analytically. In all cases, it is found that the piezoelectric coupling coefficient has to be maximized in order to maximize the added damping. In the case of SSDI, an optimal value of the electric circuit quality factor is obtained.