The use of both shunted piezoelectric elements and periodic arrays have been investigated independently as well as used in conjunction to modify the vibration of a system. Piezoelectric patches bonded to a cantilever beam which is shunted with an active circuit, specifically a negative capacitance shunt, can control broadband flexural vibrations of a structure. Also, periodic arrays integrated into a structure allow for modification of propagating waves through the mechanical ‘‘stop-bands’’. The performance of a combined shunted periodic piezoelectric patch array will be analyzed in this study by investigating the velocity amplitude of the beam upstream and downstream of the array section and the number of control elements in the array. The negative capacitance shunts caused a global spatial average velocity reduction of 5 dB at the modal peaks from 500 to 5000 Hz. The reduction is shown to be greater in the downstream section of the beam. Also, by increasing the number of patches in the array, the attenuation of the resonances increased non-linearly. The results show that a negative capacitance periodic control array is an effective global vibration reduction system and has the ability to localize energy near the forcing of a structure.
Baz, A.2001. ‘‘Active Control of Periodic Structures,’’ Journal of Vibration and Acoustics, Transactions of the ASME , 123:472-479.
2.
Beck, B., Cunefare, K.A. and Collet, M.2008. ‘‘Experimental Assessment of Negative Impedance Shunts for Vibration Suppression on a Beam,’’ In: Proceedings of SPIE - Smart Structures and Materials, 9-13 March, San Diego, CA, Vol. 6928.
3.
Beck, B., Cunefare, K.A. and Ruzzene, M.2008. ‘‘Broadband Vibration Suppression Assessment of Negative Impedance Shunts,’’ In: Proceedings of SMASIS08, 28-30 October, Ellicott City, MA, Vol. 6928.
4.
Beck, B., Cunefare, K.A. and Ruzzene, M.2010. ‘‘Periodic Piezoelectric Sensor-Actuator Array for Vibration Suppression on a Beam,’’ In: Proceedings of SPIE - Smart Structures and Materials, 9-12 March, San Diego, CA, Vol. 7643.
5.
Beck, B., Cunefare, K.A., Ruzzene, M. and Collet, M.2009. ‘‘Experimental Implementation of Negative Impedance Shunts on Periodic Structures,’’ In: Proceedings of SMASIS09, 20-24 September, Oxnard, CA, pp. 567-576.
6.
Behrens, S., Fleming, A.J. and Reza Moheimani, S.O.2001. ‘‘New Method for Multiple-Mode Shunt Damping of Structural Vibration Using a Single Piezoelectric Transducer,’’ In: Proceedings of SPIE - Smart Structures and Materials 2001: Damping and Isolation, 5-7 March, Newport Beach, CA, Vol. 4331.
7.
Brioullin, L.2003. Wave Propagation in Periodic Structures, Dover, New York.
8.
Casadei, F., Beck, B., Ruzzene, M. and Cunefare, K.2009. ‘‘Vibration Control of Plates Featuring Periodic Arrays of Hybrid Shunted Piezoelectric Patches,’’ In: Proceedings of SPIE - Smart Structures and Materials, 11-15 March, San Diego, CA, Vol. 7288.
9.
Collet, M., Cunefare, K.A. and Ichchou, M.N.2009. ‘‘Wave Motion Optimization in Periodically Distributed Shunted Piezoelectric Beam Structures,’’ Journal of Intelligent Material Systems and Structures, 20:787-808.
10.
Cook, R.D., Malkus, D.S., Plesha, M.E. and Witt, R.J.1989. Concepts and Applications of Finite Element Analysis, Wiley, New York, NY.
11.
Cunefare, K.A.2006. ‘‘Negative Capacitance Shunts for Vibration Suppression: Wave Based Tuning and Reactive Input Power,’’ In: Proceedings of ACTIVE 2006, 18-20 September, Adelaide, Australia, Vol. 6525.
12.
Fleming, A.J., Behrens, S. and Mohaeimani, S.O.R.2002. ‘‘Optimization and Implementation of Multimode Piezoelectric Shunt Damping Systems’’ IEEE/ASME , Transactions on Mechatronics, 7:87-94.
13.
Fleming, A.J. and Moheimani, S.O.R.2002. ‘‘Adaptive Piezoelectric Shunt Damping,’’ In: Proceedings of SPIE - Smart Structures and Materials 2002: Modeling, Signal Processing, and Control, 18-21 March 2002, San Diego, CA, Vol. 4693.
14.
Fleming, A.J. and Moheimani, S.O.R.2003. ‘‘Adaptive Piezoelectric Shunt Damping, ’’ Smart Materials and Structures, 12:36-48.
15.
Fleming, A.J. and Moheimani, S.O.R.2004. ‘‘Optimal Impedance Design for Piezoelectric Vibration Control,’’ In: Proceedings of 43rd IEEE Conference on Decision and Control, 14-17 December, Atlantis, Paradise Island, Bahamas, Vol. 3.
16.
Forward, R.L.1979. ‘‘Electronic Damping of Vibrations in Optical Structures,’’ Applied Optics, 18:690-697.
17.
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.
18.
Hofer, M., Finger, N., Kovacs, G., Schëberl, J., Zaglmayr, S., Langer, U. and Lerch, R.2006. ‘‘Finite-Element Simulation of Wave Propagation in Periodic Piezoelectric SAW Structures,’’ IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 53:1192-1201.
19.
Hollkamp, J.J.1994. ‘‘Multimodal Passive Vibration Suppression with Piezoelectric Materials and Resonant Shunts,’’ Journal of Intelligent Material Systems and Structures, 5:49-57.
20.
Horowitz, P. and Hill, W.1996. The Art of Electronics, Cambridge University Press, New York, NY.
21.
Mead, D.J.1986. ‘‘A New Method of Analyzing Wave Propagation in Periodic Structures; Applications to Periodic Timoshenko Beams and Stiffened Plates,’’ Journal of Sound and Vibration, 114:9-27.
22.
Mead, D.J. and Yaman, Y.1991. ‘‘The Response of Infinite Periodic Beams to Point Harmonic Forces: A Flexural Wave Analysis,’’ Journal of Sound and Vibration, 144:507-529.
23.
Neubauer, M., Oleskiewicz, R. and Popp, K.2005. ‘‘Comparison of Damping Performance of Tuned Mass Dampers and Shunted Piezo Elements,’’Proceedings in Applied Mathematics and Mechanics, 5:117-118.
24.
Park, C.H.2005. Multi-mode Vibration Damping Device and Method Using Negative Capacitance Shunt Circuits. US Patent No. 6870303.
25.
Park, C.H. and Baz, A.2005. ‘‘Vibration Control of Beams with Negative Capacitive Shunting of Interdigital Electrode Piezoceramics, ’’ Journal of Vibration and Control, 11:331-346.
26.
Park, J. and Palumbo, D.L.2004. ‘‘A New Approach to Identify Optimal Properties of Shunting Elements for Maximum Damping of Structural Vibration Using Piezoelectric Patches,’’ In: Proceedings of ACTIVE 2004, 20-24 September, Williamsburg, VA, CD proceedings published by the Institute of Noise Control Engineers .
27.
Quaegebeur, N., Micheau, P. and Berry, A.2009. ‘‘Decentralized Harmonic Control of Sound Radiation and Transmission by a Plate Using a Virtual Impedance Approach, ’’ Journal of the Acoustical Society of America, 125:2978-2986.
28.
Ruzzene, M. and Baz, A.2000. ‘‘Control of Wave Propagation in Periodic Composite Rods Using Shape Memory Alloys,’’ Journal of Vibration and Acoustics, Transactions of the ASME, 122:151-159.
29.
Spadoni, A., Ruzzene, M. and Cunefare, K.2009. ‘‘Vibration and Wave Propagation Control of Plates with Periodic Arrays of Shunted Piezoelectric Patches, ’’ Journal of Intelligent Material Systems and Structures, 20:979-990.
30.
Wu, S.-Y.1998. ‘‘Method for Multiple Mode Piezoelectric Shunting with Single PZT Transducer for Vibration Control,’’ Journal of Intelligent Material Systems and Structures, 9:991-998.
