Multimode collocated vibration control with multiple piezoelectric transducers

In this thesis a new approach is presented to control vibrations for one and two-dimensional mechanical structures, as beam or thin plates, by means of several piezoelectric transducers shunted with a proper electric network system. The governing equations for the whole system are coupled to each other through the direct and converse piezoelectric effect. The mechanical equations are expressed in accordance with the modal theory considering n vibration modes, that in need of control, and the electrical equations reduce to the one-dimensional charge equation of electrostatics for each of n considered piezoelectric transducers. In this electromechanical system, a shunting electric device forms an electric subsystem working as multi-degree of freedom damped vibration absorber for the mechanical subsystem. Herein, it is introduced a proper transformation of the electric coordinates in order to approximate the governing equations for the whole shunted system with n uncoupled, single mode piezoelectric shunting systems that can be readily damped by the methods reported in literature. A further numerical optimisation problem on the spatial distribution of the piezoelectric elements allows to achieve an effective multi-mode damping. Numerical case studies of two relevant systems, a double clamped beam and a fully clamped plate, allow to take into account issues relative to the proposed approach for vibration control. Laboratory experiments carried out in real time on a beam clamped at both ends consent to validate the proposed technique.