[en] This work presents a new approach to design an electrical network which, when coupled to a structure through an array of piezoelectric transducers, provides multimodal vibration mitigation. The characteristics of the network are specified in terms of modal properties. On the one hand, the electrical resonance frequencies are chosen to be close to those of the targeted set of structural modes. On the other hand, the electrical mode shapes are selected to maximize the electromechanical coupling between the mechanical and electrical modes while guaranteeing the passivity of the network. The effectiveness of this modal-based synthesis is demonstrated using a free–free beam and a fully clamped plate.
Hagood, N., von Flotow, A., Damping of structural vibrations with piezoelectric materials and passive electrical networks. J. Sound Vib. 146:2 (1991), 243–268, 10.1016/0022-460X(91)90762-9 URL https://linkinghub.elsevier.com/retrieve/pii/0022460X91907629.
Wu, S.-Y., Piezoelectric shunts with a parallel R-L circuit for structural damping and vibration control. Johnson, C.D., (eds.) Spie, Vol. 2720, 1996, 259–269, 10.1117/12.239093 URL http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=1017503.
Gripp, J., Rade, D., Vibration and noise control using shunted piezoelectric transducers: A review. Mech. Syst. Signal Process. 112 (2018), 359–383, 10.1016/j.ymssp.2018.04.041 URL https://linkinghub.elsevier.com/retrieve/pii/S0888327018302437.
Moheimani, S.O.R., Fleming, A.J., Piezoelectric Transducers for Vibration Control and Damping Advances in Industrial Control, 2006, Springer-Verlag, London, 10.1007/1-84628-332-9 URL http://link.springer.com/10.1007/1-84628-332-9.
Berardengo, M., Manzoni, S., Conti, A.M., Multi-mode passive piezoelectric shunt damping by means of matrix inequalities. J. Sound Vib. 405 (2017), 287–305, 10.1016/j.jsv.2017.06.002.
Gardonio, P., Zientek, M., Dal Bo, L., Panel with self-tuning shunted piezoelectric patches for broadband flexural vibration control. Mech. Syst. Signal Process., 134, 2019, 106299, 10.1016/j.ymssp.2019.106299 URL https://linkinghub.elsevier.com/retrieve/pii/S0888327019305205.
Raze, G., Paknejad, A., Zhao, G., Collette, C., Kerschen, G., Multimodal vibration damping using a simplified current blocking shunt circuit. J. Intell. Mater. Syst. Struct. 31:14 (2020), 1731–1747, 10.1177/1045389X20930103 URL http://journals.sagepub.com/doi/10.1177/1045389X20930103.
Dell'Isola, F., Vidoli, S., Continuum modelling of piezoelectromechanical truss beams: an application to vibration damping. Arch. Appl. Mech. 68:1 (1998), 1–19, 10.1007/s004190050142 URL http://link.springer.com/10.1007/s004190050142.
Alessandroni, S., Dell'Isola, F., Porfiri, M., A revival of electric analogs for vibrating mechanical systems aimed to their efficient control by PZT actuators. Int. J. Solids Struct. 39:20 (2002), 5295–5324, 10.1016/S0020-7683(02)00402-X URL https://linkinghub.elsevier.com/retrieve/pii/S002076830200402X.
Maurini, C., Dell'Isola, F., Del Vescovo, D., Comparison of piezoelectronic networks acting as distributed vibration absorbers. Mech. Syst. Signal Process. 18:5 (2004), 1243–1271, 10.1016/S0888-3270(03)00082-7 URL https://linkinghub.elsevier.com/retrieve/pii/S0888327003000827.
Porfiri, M., Dell'Isola, F., Frattale Mascioli, F.M., Circuit analog of a beam and its application to multimodal vibration damping, using piezoelectric transducers. Int. J. Circuit Theory Appl. 32:4 (2004), 167–198, 10.1002/cta.273 URL http://doi.wiley.com/10.1002/cta.273.
Lossouarn, B., Aucejo, M., Deü, J.-F., Multimodal coupling of periodic lattices and application to rod vibration damping with a piezoelectric network. Smart Mater. Struct., 24(4), 2015, 045018, 10.1088/0964-1726/24/4/045018 URL http://dx.doi.org/10.1088/0964-1726/24/4/045018https://iopscience.iop.org/article/10.1088/0964-1726/24/4/045018.
Lossouarn, B., Deü, J.F., Aucejo, M., Multimodal vibration damping of a beam with a periodic array of piezoelectric patches connected to a passive electrical network. Smart Mater. Struct., 24(11), 2015, 115037, 10.1088/0964-1726/24/11/115037 URL https://iopscience.iop.org/article/10.1088/0964-1726/24/11/115037.
Lossouarn, B., Deü, J.-F., Aucejo, M., Cunefare, K.A., Multimodal vibration damping of a plate by piezoelectric coupling to its analogous electrical network. Smart Mater. Struct., 25(11), 2016, 115042, 10.1088/0964-1726/25/11/115042 URL https://iopscience.iop.org/article/10.1088/0964-1726/25/11/115042.
Darleux, R., Lossouarn, B., Deü, J.-f., Broadband vibration damping of non-periodic plates by piezoelectric coupling to their electrical analogues. Smart Mater. Struct., 29(5), 2020, 054001, 10.1088/1361-665X/ab7948 URL https://iopscience.iop.org/article/10.1088/1361-665X/ab7948.
Giorgio, I., Galantucci, L., Della Corte, A., Del Vescovo, D., Piezo-electromechanical smart materials with distributed arrays of piezoelectric transducers: Current and upcoming applications. Int. J. Appl. Electromagn. Mech. 47:4 (2015), 1051–1084, 10.3233/JAE-140148 URL https://www.medra.org/servlet/aliasResolver?alias=iospress&doi=10.3233/JAE-140148.
Darleux, R., Development of Analogous Piezoelectric Networks for the Vibration Damping of Complex Structures. (Ph.D. thesis), 2020, HESAM Université URL https://tel.archives-ouvertes.fr/tel-02902755.
Bao, B., Guyomar, D., Lallart, M., Vibration reduction for smart periodic structures via periodic piezoelectric arrays with nonlinear interleaved-switched electronic networks. Mech. Syst. Signal Process. 82 (2017), 230–259, 10.1016/j.ymssp.2016.05.021 URL https://linkinghub.elsevier.com/retrieve/pii/S0888327016301066.
Thomes, R.L., Beli, D., De Marqui, C., Space–time wave localization in electromechanical metamaterial beams with programmable defects. Mech. Syst. Signal Process., 167(PB), 2022, 108550, 10.1016/j.ymssp.2021.108550 arXiv:2108.13742. URL https://linkinghub.elsevier.com/retrieve/pii/S088832702100889X.
Giorgio, I., Culla, A., Del Vescovo, D., Multimode vibration control using several piezoelectric transducers shunted with a multiterminal network. Arch. Appl. Mech. 79:9 (2009), 859–879, 10.1007/s00419-008-0258-x URL http://link.springer.com/10.1007/s00419-008-0258-x.
Yamada, K., Matsuhisa, H., Utsuno, H., Sawada, K., Optimum tuning of series and parallel LR circuits for passive vibration suppression using piezoelectric elements. J. Sound Vib. 329:24 (2010), 5036–5057, 10.1016/j.jsv.2010.06.021 URL http://dx.doi.org/10.1016/j.jsv.2010.06.021https://linkinghub.elsevier.com/retrieve/pii/S0022460X10004116.
Thomas, O., Deü, J.-F., Ducarne, J., Vibrations of an elastic structure with shunted piezoelectric patches: efficient finite element formulation and electromechanical coupling coefficients. Internat. J. Numer. Methods Engrg. 80:2 (2009), 235–268, 10.1002/nme.2632 URL http://doi.wiley.com/10.1002/nme.2632.
Géradin, M., Rixen, D.J., Mechanical Vibrations: Theory and Application to Structural Dynamics. 2014, John Wiley & Sons.
Lossouarn, B., Kerschen, G., Deü, J.-F., An analogue twin for piezoelectric vibration damping of multiple nonlinear resonances. J. Sound Vib., 511(May), 2021, 116323, 10.1016/j.jsv.2021.116323 URL https://linkinghub.elsevier.com/retrieve/pii/S0022460X21003825.
Grainger, J.J., Stevenson, W.D. Jr., Power System Analysis. 1994, McGraw-Hill Education.
Gannett, J., Chua, L., Frequency Domain Passivity Conditions for Linear Time-Invariant Lumped Networks: Tech. Rep. Technical Report No. UCB/ERL M78/21., 1978, EECS Department, University of California, Berkeley, Berkeley URL https://www2.eecs.berkeley.edu/Pubs/TechRpts/1978/28925.html.
Piefort, V., Finite Element Modelling of Piezoelectric Active Structures. (Ph.D. thesis), 2001, Université Libre de Bruxelles URL https://difusion.ulb.ac.be/vufind/Record/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/211645/Holdings.
Raze, G., Jadoul, A., Guichaux, S., Broun, V., Kerschen, G., A digital nonlinear piezoelectric tuned vibration absorber. Smart Mater. Struct., 29(1), 2020, 015007, 10.1088/1361-665X/ab5176 URL https://iopscience.iop.org/article/10.1088/1361-665X/ab5176.
Raze, G., Dietrich, J., Lossouarn, B., Kerschen, G., Supplementary material from “Modal-based synthesis of passive electrical networks for multimodal piezoelectric damping”. 2020, 10.6084/m9.figshare.13283873.v2.
