Comparison of piezoelectronic networks acting as distributed vibration absorbers

Electric vibration absorbers made of distributed piezoelectric devices for the control of beam vibrations are studied. The absorbers are obtained by interconnecting an array of piezoelectric transducers uniformly distributed on a beam with different modular electric networks. Five different topologies are considered and their damping performance is analysed and compared. Their optimal parameters are found by adopting a criterion for critical damping of k-waves: the parameters are suitably chosen to have the quickest temporal vibration decay for a single wave number k. The analysis is based on homogenized models of the modular piezo-electromechanical systems, i.e. they are regarded as continuous systems by assuming that the number of modules per unit length is high enough with respect to the considered wave numbers. Calling k -absorbers the corresponding optimal absorbers, we show that: (i) k-waves are damped in k-absorbers with an optimal decay time which is independent of the absorber interconnecting topology, while it depends only on the piezoelectric coupling coefficient; (ii) the efficiency of k-absorbers depends significantly on the absorber interconnecting topology for k different from k; (iii) one of the proposed absorbers (which is made of a fourth-order electric transmission line with a second-order electric dissipation) equally performs for all the wave numbers and accomplishes an effective multi-modal damping for the mechanically forced response; (iv) the optimal values of the electric parameters differently depend on the number n of used circuit modules for different interconnecting topologies and, in particular, the optimal inductance per module needed in a fourth-order electric transmission line is proportional 1/ n 3 .