This work deals with the reduction of structural vibrations by means of synchronized switch damping techniques on piezoelectric elements. Piezoelectric patches are attached to the vibrating structure and connected to an electrical circuit that includes a switch. The latter allows to continuously switch the piezoelectric elements from an open-circuit state to a specific electric impedance, synchronously with the mechanical oscillations. The present study focuses on two goals: (i) the quantification of the added damping, (ii) the optimization of the electric circuit parameters, carried out on a one degree of freedom model. The free and forced responses of one mode of the mechanical structure are studied in detail. The precise time response of the system is obtained with semi-analytical models for the two cases where the electrical impedance is a simple resistance (synchronized switch damping on short circuit) or a resistance in series with an inductance (synchronized switch damping on inductor). The damping added by the device is estimated. In all cases, the main result of the study is that the piezoelectric coupling factor is the only parameter to optimize and has to be maximized in order to maximize the added damping. An optimal value of the electric circuit quality factor is obtained when using an inductance, for free and forced response.
ANSI/IEEE Std 176-1987.1988. IEEE Standard on Piezoelectricity. The Institute of Electrical and Electronics Engineers, Inc. New York, USA.
2.
Caruso, G.2001. ‘‘A Critical Analysis of Electric Shunt Circuits Employed in Piezoelectric Passive Vibration Damping, ’’ Smart Materials and Structures, 10:1051-1068.
3.
Clark, W.W.2000. ‘‘Vibration Control with State-switching Piezoelectric Material,’’ Journal of Intelligent Material Systems and Strutures, 11:263-271.
4.
Corr, L.R. and Clark, W.W.2003. ‘‘A Novel Semi-active Multimodal Vibration Control Law for a Piezoceramic Actuator,’’ Journal of Vibration and Acoustics, 125:214-222.
5.
Davis, C.L. and Lesieutre, G.A.1998. ‘‘Actively Tuned Solid State Piezoelectric Vibration Absorber,’’ In: Proceedings of SPIE: Smart Structures and Materials 1998: Passive Damping and Isolation, Vol. 3327, San Diego, CA, USA, pp. 169-182.
6.
Dell’Isola, F., Maurini, C. and Porfiri, M.2004. ‘‘Passive Damping of Beam Vibrations Through Distributed Electric Networks and Piezoelectric Transducers: Prototype Design and Experimental Validation,’’Smart Materials and Structures, 13:299-308.
7.
Ducarne, J.2009. ‘‘Modélisation et Optimisation de Dispositifs Nonlinéaires d’amortissement de Structures par Systèmes Piézoélectriques Commutés’’ , PhD Thesis, Conservatoire National des Arts et Metiers, (in French).
8.
Ducarne, J., Thomas, O. and Deü, J.-F.2007. ‘‘Optimisation de Dispositif Passif d’atténuation de Vibration par Shunt Piézoélectrique,’’ In: Actes du 8ème Colloque National en Calcul de Structures, Vol. 2, Giens , France, pp. 519-524.
9.
Ducarne, J., Thomas, O. and Deü, J.-F.2008. ‘‘Vibration Reduction by Switch Shunting of Piezoelectric Elements: Nonlinear Energy Transfers Between Modes and Optimization,’’ In: Proceedings of the 19th International Conference on Adaptative Structures and Technologies, Ascona, Switzerland, October.
10.
Ducarne, J., Thomas, O. and Deü, J.-F.2010. ‘‘Performance and Optimization of Piezoelectric Shunts for Vibration Reduction,’’Journal of Sound and Vibration, (accepted).
11.
Guyomar, D. and Badel, A.2006. ‘‘Nonlinear Semi-passive Multimodal Vibration Damping: An Efficient Probabilistic Approach,’’ Journal of Sound and Vibration, 294:249-268.
12.
Guyomar, D., Richard, T. and Richard, C.2008. ‘‘Sound Wave Transmission Reduction Through a Plate Using Piezoelectric Synchronized Switch Damping Technique , ’’ Journal of Intelligent Material Systems and Structures, 19:791-803.
13.
Hagood, N.W. and Von Flotow, A.1991. ‘‘Damping of Structural Vibrations with Piezoelectric Materials and Passive Electrical Networks,’’Journal of Sound and Vibration, 146:243-268.
14.
Lallart, M., Badel, A. and Guyomar, D.2008. ‘‘Nonlinear Semi-active Damping Using Constant or Adaptive Voltage Sources: A Stability Analysis, ’’ Journal of Intelligent Material Systems and Structures, 19:1131-1142.
15.
Lallart, M., Lefeuvre, E., Richard, C. and Guyomar, D.2008. ‘‘Self-powered Circuit for Broadband, Multimodal Piezoelectric Vibration Control,’’ Sensors and Actuators A, 143:377-382.
16.
Lefeuvre, E., Badel, A., Petit, L., Richard, C. and Guyomar, D.2006. ‘‘Semi-passive Piezoelectric Structural Damping by Synchronized Switching on Voltage Sources,’’ Journal of Intelligent Material Systems and Structures, 17:653-660.
17.
Makihara, K., Onoda, J. and Minesugi, K.2005. ‘‘Lowenergy-consumption Hybrid Vibration Suppression Based on an Energy-recycling Approach,’’ AIAA Journal, 43:1706-1715.
18.
Makihara, K., Onoda, J. and Minesugi, K.2008. ‘‘Performance of Simple and Sophisticated Control in Energy-recycling Semi-active Vibration Suppression, ’’ Journal of Vibration and Control, 14:417-436.
19.
Niederberger, D. and Morari, M.2005. ‘‘An Autonomous Shunt Circuit for Vibration Damping,’’ Smart Materials and Structures, 15:359-364.
20.
Onoda, J., Makihara, K. and Minesugi, K.2003. ‘‘Energy-recycling Semi-active Method for Vibration Suppression with Piezoelectric Transducers, ’’ AIAA Journal, 41:711-719.
21.
Petit, L., Lefeuvre, E., Richard, C. and Guyomar, D.2004. ‘‘A Broadband Semi Passive Piezoelectric Technique for Structural Damping’’, In: Proceedings of SPIE Smart Structures and Materials Conference: Passive Damping and Isolation , Vol. 5386, pp. 414-425.
22.
Richard, C., Guyomar, D., Audigier, D. and Ching, G.1999. ‘‘Semipassive Damping Using Continuous Switching of a Piezoelectric Device’’, In: Proceedings of SPIE Smart Structures and Materials Conference: Passive Damping and Isolation , Vol. 3672, pp. 104-111.
23.
Richard, C., Guyomar, D., Audigier, D. and Bassaler, H.2000. ‘‘Enhanced Semi-passive Damping Using Continuous Switching of a Piezoelectric Device on an Inductor’’ , In: Proceedings of SPIE Smart Structures and Materials Conference: Passive Damping and Isolation, Vol. 3989, pp. 288-299.
24.
Richard, C., Guyomar, D. and Lefeuvre, E.2007. ‘‘Self-powered Electronic Breaker with Automatic Switching by Detecting Maxima or Minima of Potential Difference Between its Power Electrodes’’, Technical Report, Organisation Mondiale de la Propriété Intellectuelle 2007. Patent # PCT/FR2005/003000, Publication number: WO/2007/063194.
25.
Sénéchal, A., Thomas, O., Deü, J.-F. and Jean, P.2009. ‘‘Atténuation de Vibrations de Structures Complexes par Élément Piéeoélectrique. Application à une aube de Turbomachine,’’ In: Actes du 9ème Colloque National en Calcul de Structures , Giens, France. May (in French).
26.
Senechal, A., Thomas, O., Deü, J.-F. and Jean, P.2010. ‘‘Optimization of Shunted Piezoelectric Patches for Complex Structure Vibration Reduction - Application to a Turbojet Fan Blade,’’ In: Proceedings of the 4th European Congress on Computational Mechanics, Paris , France.
27.
The MathWorks, Inc. Available at: http://www.mathworks.com . MATLAB Function Reference.
28.
Thomas, O., Deü, J.-F. and Ducarne, J.2009. ‘‘Dynamics of an Elastic Structure with Piezoelectric Patches: Finite-element Formulation and Electromechanical Coupling Coefficients,’’International Journal of Numerical Methods in Engineering , 80:235-268.
29.
Wang, K.W., Lai, J.S. and Yu, W.K.1996. ‘‘An Energy-based Parametric Control Approach for Structural Vibration Suppression via Semi-active Piezoelectric Networks ,’’ Journal of Vibration and Acoustics , 118:505-509.
