Multimode vibration control using several piezoelectric transducers shunted with a multiterminal network

In this paper a new approach is presented to reduce 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 of the whole system are coupled to each othe...

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Bibliographic Details
Published in:Archive of applied mechanics (1991) 2009-09, Vol.79 (9), p.859-879
Main Authors: Giorgio, Ivan, Culla, Antonio, Del Vescovo, Dionisio
Format: Article
Language:English
Subjects:
Beams (structural)
Clamping
Classical Mechanics
Engineering
Engineering Sciences
Mathematical analysis
Mathematical models
Mechanical engineering
Mechanics
Original
Physics
Piezoelectric transducers
Piezoelectricity
Theoretical and Applied Mechanics
Vibration
Vibration mode
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Summary:In this paper a new approach is presented to reduce 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 of the whole system are coupled to each other through the direct and converse piezoelectric effect. More in detail, the mechanical equations are expressed in accordance with the modal theory considering n vibration modes 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 degrees of freedom (dof’s) 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 a better performance. 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. Laboratory experiments carried out in real time on a beam clamped at both ends consent to validate the proposed technique.
ISSN:0939-1533
1432-0681
DOI:10.1007/s00419-008-0258-x