In this paper we revive classical methods (i.e. those needed to synthesize analog circuits for designing direct computers) in order to conceive novel devices which we call piezo-electro-mechanical (PEM) structural members. By means of two independent synthesis procedures, new circuital analogs for the uniformly damped Elastica and Kirchhoff–Love plate are found. These circuits are used as electrical wave guides gyroscopically coupled to the corresponding mechanical members to design electrically dissipative PEM systems. The concept on which these systems are based exploits piezoelectric transducers––uniformly distributed on the member––to transform strain energy into capacitive energy: this last will be subsequently dissipated using resistors, the optimal value of which is determined by a pole placement criterion. We underline that in PEM structures PZT transducers can be regarded, at the same time, as sensors and actuators. By means of analytical methods and numerical simulations, the electro-mechanical constitutive parameters of some PEM structures are determined and it is shown that they can be designed and may be technically feasible. Moreover it is shown that in PEM structures, also when mechanical dissipative phenomena are negligible, mechanical vibrations are efficiently damped by means of completely passive electrical circuits.