The damping of a truss structure with a piezo­electric transducer

This paper re-examines the classical problem of active and passive damping of a piezoelectric truss. The active damping strategy is the so-called IFF (integral force feedback) which has guaranteed stability; both voltage control and charge (current) control implementations are examined; they are compared to resistive shunting. It is shown that in all three cases, the closed-loop eigenvalues follow a root-locus; closed form analytical formulas are given for the poles and zeros and the maximum modal damping. It is shown that the performances are controlled by two parameters: the modal fraction of strain energy νi in the active strut and the electromechanical coupling factor k. The paper also examines the damping via inductive shunting and the enhancement of the electromechanical coupling factor by shunting a synthetic negative capacitance. In the second part, a numerical example is examined and the analytical formulae are compared with predictions based on more elaborate models, including a full FE representation of the truss, the transducer, the electrical network and the controller. The limitations of the analytical formulae are pointed out. © 2007 Elsevier Ltd. All rights reserved.