Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Dosch J., Inman D., Garcia E.: A self-sensing piezoelectric actuator for collocated control. J. Intell. Mater. Syst. Struct. 3, 166–185 (1992)
Anderson E.H., Hagood N.W.: Simultaneous piezoelectric sensing/ actuation: analysis and application to controlled structures. J. Sound Vib. 174, 617–639 (1994)
Hollkamp J.J., Starchville T.F.: A self-tuning piezoelectric vibration absorber. J. Intell. Mater. Syst. Struct. 5, 559–566 (1994)
Wu, S.Y.: Method for multiple-mode shunt damping of structural vibration using a single pzt transducer. In: Smart Structures and Materials. Passive Damping and Isolation, vol. 3327, pp. 159–168 (1998)
Alessandroni S., Andreaus U., dell’Isola F., Porfiri M.: A passive electric controller for multimodal vibrations of thin plates. Comput. Struct. 83, 1236–1250 (2005)
dell’Isola F., Vidoli S.: Continuum modelling of piezoelectromechanical truss beams. Arch. Appl. Mech. 68, 1–19 (1998)
Tang J., Wang K.W.: Active-passive hybrid piezoelectric networks for vibration control: comparisons and improvement. Smart Mater. Struct. 10, 794–806 (2001)
Thorp O., Ruzzene M., Baz A.: Attenuation and localization of wave propagation in rods with periodic shunted piezoelectric patches. Smart Mater. Struct. 10, 979–989 (2001)
Badel A., Sebald G., Guyomar D., Lallart M., Lefeuvre E., Richard C., Qiu J.: Piezoelectric vibration control by syncronized switching on adaptive voltage sources: Towards wideband semi-active damping. J. Acoust. Soc. Am. 119(5), 2815–2825 (2006)
Hagood N.W., Von Flotow A.: Damping of structural vibrations with piezoelectric materials and passive electrical networks. J. Sound Vib. 146, 243–268 (1991)
Wu, S.Y.: Piezoelectric shunts with a parallel R-L circuit for structural damping and vibration control. In: Proceedings of the SPIE, Smart Materials and Structure, vol. 2720, pp. 259–269 (1996)
Hollkamp J.J.: Multimodal passive vibration suppression with piezoelectric materials and resonant shunts. J. Intell. Mater. Syst. Struct. 5, 49–57 (1994)
Moheimani S.O.R., Fleming A.J., Behrens S.: Dynamics, stability, and control of multivariable piezoelectric shunts. IEEE/ASME Trans. Mechatron. 9(1), 87–99 (2004)
Andreaus U., dell’Isola F., Porfiri M.: Piezoelectric passive distributed controllers for beam flexural vibrations. J. Vib. Control 10(5), 625–659 (2004)
Maurini C., dell’Isola F., Del Vescovo D.: Comparison of piezoelectronic networks acting as distributed vibration absorbers. Mech. Syst. Signal Process. 18(5), 1243–1271 (2004)
Yang S.M., Jeng C.A.: Structural vibration suppression by concurrent piezoelectric sensor and actuator. J. Smart Mater. Struct. 5, 806–813 (1996)
Weinberg L.: Network analysis and Synthesis. Mc-Graw-Hill, New York (1962)
Tliba, S., Abou-Kandil, H.: ModTlisation et contr(le actif des vibrations d’une structure intelligente. In: Actes du 7e Colloque National en Calcul des Structures (2005)
Park C.H.: Dynamics modelling of beams with shunted piezoelectric elements. J. Sound Vib. 268, 115–129 (2003)
Maurini C., Porfiri M., Pouget J.: Numerical methods for modal analysis of stepped piezoelectric beams. J. Sound Vib. 298, 918–933 (2006)
Behrens S., Moheimani S.O.R., Fleming A.J.: Multiple mode current flowing passive piezoelectric shunt controller. J. Sound Vib. 266, 929–942 (2003)
Porfiri M., Maurini C., Pouget J.: Identification of electromechanical modal parameters of linear piezoelectric structures. Smart Mater. Struct. 16, 323–331 (2007)
Juang J.N., Phan M.: Robust controller design for second-order dynamic systems: a virtual passive approach. J. Guid. Control Dyn. 15, 1192–1198 (1992)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Giorgio, I., Culla, A. & Del Vescovo, D. Multimode vibration control using several piezoelectric transducers shunted with a multiterminal network. Arch Appl Mech 79, 859–879 (2009). https://doi.org/10.1007/s00419-008-0258-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-008-0258-x