Control of torsional vibrations in piezolaminated rods

This paper is concerned with active control of torsional vibrations in laminated rods by piezoelectric shear sensors and actuators. A piezoelectric layer can be used as a sensor by utilizing the direct piezoelectric effect, measuring either the charge on short-circuited electrodes or the voltage on open electrodes. On the other hand, the converse piezoelectric effect enables actuation by applying an electric potential difference to the electrodes of a piezoelectric layer. The sensor and actuator equations are formulated in the framework of an extended Saint-Venant torsion theory considering additional cross-sectional warping due to piezoelectric eigenstrains. A solution of the shape control problem for torsional vibrations is presented, i.e. the necessary distribution of actuation strains in order to completely compensate vibrations caused by external excitations. For the case, in which the external excitations are not known exactly, a feedback control solution is presented using one piezoelectric layer as a sensor and a second one as an actuator. For the examples of a rectangular and a circular cross-section, the theoretical results are validated by three-dimensional finite element computations, showing a very good coincidence.