Algorithm for the layout of a piezoelectric element in an elastic medium providing the maximal piezoelectric effect within a specified frequency range

References

• N.W. Hagood and A. Von Flotow, Damping of structural vibrations with piezoelectric materials and passive electrical networks, J. Sound Vib. 146 (2) (1991), pp. 243–268. doi:10.1016/0022-460X(91)90762-9.
   Web of Science ®Google Scholar
• J.J. Hollkamp, Multimodal passive vibration suppression with piezoelectric materials and resonant shunts, J. Intell. Mater. Syst. Struct. 5 (1994), pp. 49–56. doi:10.1177/1045389X9400500106.
   Web of Science ®Google Scholar
• S.Y. Wu, Method for multiple mode shunt damping of structural vibration using a single PZT transducer, Smart Struct. Mater. Smart Struct. Int. Sys. Proc. SPIE. 3327 (1998), pp. 159–168.
   Google Scholar
• S.Y. Wu, Multiple PZT transducers implemented with multiple-mode piezoelectric shunting for passive vibration damping, Smart Struct. Mater. Passive Damp. Iso. Proc. SPIE. 672 (1999), pp. 112–122.
   Google Scholar
• S.Y. Wu and A.S. Bicos, Structural vibration damping experiments using improved piezoelectric shunts, Smart Struct. Mater. Passive Damp. Iso. Proc. SPIE. 3045 (1997), pp. 40–50.
   Google Scholar
• S. Behrens and S.O.R. Moheimani, Current flowing multiple mode piezoelectric shunt dampener, Proceedings of SPIE 4697, Smart Structures and Materials 2002: Damping and Isolation, San Diego, CA, 2002.
   Google Scholar
• S. Behrens, S.O.R. Moheimani, and A.J. Fleming, Multiple mode passive piezoelectric shunt dampener, Proc. IFAC Mechatronics 35 (2002), pp. 161–166.
   Google Scholar
• A.J. Fleming and S.O.R. Moheimani, Adaptive piezoelectric shunt damping, Smart Mater. Struct. 1 (2003), pp. 36–48. doi:10.1088/0964-1726/12/1/305.
   Google Scholar
• S. Behrens and S.O.R. Moheimani, Optimal resistive elements for multiple mode shunt damping of a piezoelectric laminate beam, 39th IEEE Conference on Decision and Control, 4 (2000), pp. 4018–4023, Sydney, NSW, Australia, 2000.
   Google Scholar
• T.H. Cheng and I.K. Oh, A current-flowing electromagnetic shunt damper for multi-mode vibration control of cantilever beams, Smart Mater Struct. 18 (2009), pp. 095036.
   Web of Science ®Google Scholar
• S. Vidoli and F. dell’Isola, Vibration control in plates by uniformly distributed PZT actuators interconnected via electric networks, Eur. J. Mech./A Solids 20 (2001), pp. 435–456. doi:10.1016/S0997-7538(01)01144-5.
   Web of Science ®Google Scholar
• M. Porfri, F. dell’Isola, and F.M.F. Mascioli, Circuit analog of a beam and its application to multimodal vibration damping, using piezoelectric transducers, Int. J. Circ. Theor. Appl. 32 (2004), pp. 167–198. doi:10.1002/cta.273.
   Web of Science ®Google Scholar
• F. dell’Isola, E.G. Henneke, and M. Porfiri, Piezoelectromechanical structures: New trends towards the multimodal passive vibration control, Smart Struct. Mater. Passive Damp. Iso. Proc. SPIE. 5052 (2003), pp. 392–402.
   Google Scholar
• C. Maurini, F. dell’Isola, and D.D. Vescovo, Comparison of piezoelectronic networks acting as distributed vibration absorbers, Mech. Sys. Signal Proc. 18 (5) (2004), pp. 1243–1271. doi:10.1016/S0888-3270(03)00082-7.
   Web of Science ®Google Scholar
• I. Giorgio, A. Culla, and D. Del Vescovo, Multimode vibration control using several piezoelectric transducers shunted with a multiterminal network, Arch. Appl. Mech. 79 (2009), pp. 859–879.
   Web of Science ®Google Scholar
• F.A.C. Viana and V. Steffen Jr., Multimodal vibration damping through piezoelectric patches and optimal resonant shunt circuits, J. Of the Braz. Soc. Of Mech. Sci. & Eng. XXVIII (3) (2006), pp. 293–310. doi:10.1590/S1678-58782006000300007.
   Google Scholar
• F. Casadei, M. Ruzzene, L. Dozio, and K.A. Cunefare, Broadband vibration control through periodic arrays of resonant shunts: Experimental investigation on plates, Smart Mater Struct. 19 (2010), pp. 015002
   Google Scholar
• B. Lossouarn, J.-F. Deü, and M. Aucejo, Multimodal vibration damping of a beam with a periodic array of piezoelectric patches connected to a passive electrical network, Smart Mater Struct. 24 (2015), pp. 115037.
   Web of Science ®Google Scholar
• F. Botta, D. Dini, S. Gentili, C. Schwingshackl, L. Di Mare, and G. Cerri, Optimal placement of piezoelectric plates to control multimode vibrations of a beam, Adv. Acoust. Vib. 2013 (2013), pp. 905160.
   Google Scholar
• F. Botta, A. Scorza, and A. Rossi, Optimal piezoelectric potential distribution for controlling multimode vibrations, Appl. Sci. 8 (2018), pp. 551. doi:10.3390/app8040551.
   Google Scholar
• Q. Huang, S. Chen, H. Pu, and N. Zhang, Optimal piezoelectric actuators and sensors configuration for vibration suppression of aircraft framework using particle swarm algorithm, Math. Prob. Eng. 2017 (2017), pp. 7213125. doi:10.1155/2017/7213125.
   Google Scholar
• E.F. Crawley and J. de Luis, Use of piezoelectric actuators as elements of intelligent structures, Aiaa J. 25 (10) (1987), pp. 1373–1385. doi:10.2514/3.9792.
   Google Scholar
• F. Bachmann, A. Bergamini, and P. Ermanni, Optimal piezoelectric positioning a strain-energy based finite element approach, J. Int. Mat. Syst. Struct. 23 (14) (2012), pp. 1575–1591. doi:10.1177/1045389X12447985.
   Web of Science ®Google Scholar
• K. Ramesh and S. Narayanan, The optimal location of piezoelectric actuators and sensors for vibration control of plates, Smart Mater. Struct. 16 (2007), pp. 2680–2691. doi:10.1088/0964-1726/16/6/073.
   Google Scholar
• M. Hasanlu, A. Bagheri, and F. Najafi, Optimal placement of piezoelectric S/A for active vibration control of engineering structures by using controller design, J. Eng. Tech. 5 (2016), pp. 22–44.
   Google Scholar
• V. Gupta, M. Sharma, and N. Thakur, Optimization criteria for optimal placement of piezoelectric sensors and actuators on a smart structure: A technical review, J. Int. Mat. Syst. Struct. 21 (8) (2010), pp. 1227–1243. doi:10.1177/1045389X10381659.
   Google Scholar
• J. Ducarne, O. Thomas, and J.-F. Deu, Placement and dimension optimization of shunted piezoelectric patches for vibration reduction, J. Sound Vib. 331 (2013), pp. 3286–3303. doi:10.1016/j.jsv.2012.03.002.
   Web of Science ®Google Scholar
• A. Belloli and P. Ermanni, Optimum placement of piezoelectric ceramic modules for vibration suppression of highly constrained structures, Smart Mater. Struct. 16 (2007), pp. 1662–1671.
   Web of Science ®Google Scholar
• H. Ning, Optimal number and placements of piezoelectric patch actuators in structural active vibration control, Eng. Comput. 21 (2004), pp. 651–665. doi:10.1108/02644400410545218.
   Google Scholar
• A.M. Sadri, J.R. Wright, and R.J. Wynne, Modeling and optimal placement of piezoelectric actuators in isotropic plates using genetic algorithms, Smart Mater. Struct. 9 (1999), pp. 490–498. doi:10.1088/0964-1726/8/4/306.
   Google Scholar
• S.S. Rao and P.T. Shii, Optimal placement of actuators in actively controlled structures using genetic algorithms, AIAA J. 29 (6) (1991), pp. 942–943. doi:10.2514/3.10683.
   Google Scholar
• D. Chhabra, G. Bhushan, and P. Chandna, Optimal placement of piezoelectric actuators on plate structures for active vibration control via modified control matrix and singular value decomposition approach using modified heuristic genetic algorithm, Mech. Adv. Mater. Struct. 23 (3) (2016), pp. 272–280. doi:10.1080/15376494.2014.949932.
   Web of Science ®Google Scholar
• I. Bruant, L. Gallimard, and S. Nikoukar, Optimization of piezoelectric sensors location and number using a genetic algorithm, Mech. Adv. Mater. Struct. 18 (7) (2011), pp. 469–475. doi:10.1080/15376494.2011.604600.
   Web of Science ®Google Scholar
• J.M. Hale and A.H. Daraji, Optimal placement of sensors and actuators for active vibration reduction of a flexible structure using a genetic algorithm based on modified H infinity, J. Phys. 382 (2012), pp. 012036.
   Google Scholar
• S.T. Quek, S.Y. Wang, and K.K. Ang, Vibration control of composite plates via optimal placement of piezoelectric patches, J. Intell. Mater. Syst. Struct. 14 (4–5) (2003), pp. 229–245. doi:10.1177/1045389X03034686.
   Web of Science ®Google Scholar
• K.R. Kumar and S. Narayanan, The optimal location of piezoelectric sensor and actuators for vibration control of plates, J. Smart Mater. Struct. 16 (2007), pp. 2680–2691. doi:10.1088/0964-1726/16/6/073.
   Web of Science ®Google Scholar
• K. Morris and S. Yang, Comparison of actuator placement criteria for control of structures, J. Sound Vib. 353 (2015), pp. 1–18. doi:10.1016/j.jsv.2015.05.002.
   Web of Science ®Google Scholar
• N.V. Sevodina, N.A. Yurlova, and D.A. Oshmarin, The optimal placement of the piezoelectric element in a structure based on the solution of the problem of natural vibrations, Solid State Phenom. 243 (2015), pp. 67–74. doi:10.4028/www.scientific.net/SSP.243.67.
   Google Scholar
• Q. Wang and C. Wang, A controllability index for optimal design of piezoelectric actuators in vibration control of beam structures, J. Sound Vib. 242 (3) (2001), pp. 507–518. doi:10.1006/jsvi.2000.3357.
   Web of Science ®Google Scholar
• Z. Liu, D. Wang, H. Hu, and M. Yu, Measures of modal controllability and observability in vibration control of flexible structures, J. Guid. Contr. Dyn. 17 (6) (1994), pp. 1377–1380. doi:10.2514/3.21363.
   Web of Science ®Google Scholar
• D.A. Oshmarin, M.A. Iurlov, N.V. Sevodina, and N.A. Iurlova, Passive multimodal damping of vibrations in structures with piezoelectric elements and external electric circuits, 8th ECCOMAS Thematic Conference on Smart Structures and Materials (SMART 2017) and 6th International Conference on Smart Materials and Nanotechnology in Engineering. pp. 1125–1136, , Madrid, Spain, 2017.
   Google Scholar
• N.A. Iurlova, V.P. Matveenko, D.A. Oshmarin, N.V. Sevodina, and M.A. Yurlov, Layout optimization of piezoelectric elements with external electric circuits in smart constructions based on solution of the natural vibrations problem, VIIth ECCOMAS Congress 2016, Crete, Greece, 2016.
   Google Scholar
• Ansys 17.2 Documentation, SAS IP, Inc, Canonsburg, 2016.
   Google Scholar
• V.P. Matveenko, N.A. Iurlova, D.A. Oshmarin, N.V. Sevodina, and M.A. Iurlov, An approach to determination of shunt circuits parameters for damping vibrations, Int. J. Smart and Nano Mater. 9 (2) (2018), pp. 135–149. doi:10.1080/19475411.2018.1461144.
   Web of Science ®Google Scholar
• V.P. Matveenko, D.A. Oshmarin, N.V. Sevodina, and N.A. Yurlova, Natural vibration problem for electroviscoelstic body with external electric circuits and finite-element relations for its numerical implementation, Comp. Cont. Mech. 9 (2016), pp. 476–485.
   Google Scholar