Damping of bending waves in truss beams by electric transmission lines with PZT actuators

A new device to damp mechanical waves in modular truss beams has been proposed in [1]. It is based on the electro-mechanical coupling of the truss beam with an electrical transmission line by a line distribution of PZT actuators. It has been proved in [1] that extensional and torsional waves can be damped using a standard second-order transmission line, and that such a line is not suitable to damp bending waves. In the present paper, we propose to couple the beam with a fourth-order transmission line, obtained from the standard one by adding a voltage-driven current generator, thus electrically paralleling the structure of the bending wave equation. As a detailed description of the system would require huge numerical programming, to test qualitatively the efficiency of the proposed electro-mechanical coupling we consider a coarse continuum model of PiezoElectro-Mechanical (PEM) beams, using an identification procedure based on the principle of virtual power [4]. We define the critical value for line impedance maximizing the electro-mechanical energy exchange for every wave frequency, thus proving that the electric damping of bending waves by distributed PZT control is technically feasible.