Abstract
This paper presents a study on the application of a shunt damping circuit for vibration control in electro-mechanically coupled structures. The effectiveness of this design is demonstrated through experimentation with a cantilever beam featuring a magnet at its tip, moving in a wire coil that is connected to the shunt damping circuit. The study showcases the reduction of beam vibrations under both frequency response and free vibration conditions. Results show that the shunt damping circuit significantly reduces the first peak in frequency response during harmonic excitation. Additionally, the settling time of free vibrations is reduced by adjusting the electrical resistance. The paper uses analytical expressions for achieving critical damping for the free response, along with experimental validation. The study also offers a detailed description of the design process of the negative impedance converter used in the electrical circuit. This includes an examination of the influence of the transducer mass and moment of inertia on the converter's design. Finally, this paper offers valuable insights into the design of shunt damping circuits for vibration control in electro-mechanically coupled structures. The experimental results and analytical expressions provided in the study can help guide the realization of such circuits in various applications.
Similar content being viewed by others
References
Hagood NW, von Flotow A (1991) Damping of structural vibrations with piezoelectric materials and passive electrical networks. J Sound Vib 146:243–268. https://doi.org/10.1016/0022-460X(91)90762-9
Uchino K, Ishii T (1988) Mechanical damper using piezoelectric ceramics. Nippon Seramikkusu Kyokai Gakujutsu Ronbunshi/J Ceram Soc Jpn 96:863–867. https://doi.org/10.2109/jcersj.96.863
Forward RL (1979) Electronic damping of vibrations in optical structures. Appl Opt 18:690. https://doi.org/10.1364/ao.18.000690
Wu S (1996) Piezoelectric shunts with a parallel R-L circuit for structural damping and vibration control. In: Proceedings smart structures and materials: passive damping and isolation, pp 259–269
He H, Tan X, He J et al (2020) A novel ring-shaped vibration damper based on piezoelectric shunt damping: theoretical analysis and experiments. J Sound Vib 468:115125. https://doi.org/10.1016/j.jsv.2019.115125
Darleux R, Lossouarn B, Deü JF (2018) Passive self-tuning inductor for piezoelectric shunt damping considering temperature variations. J Sound Vib 432:105–118. https://doi.org/10.1016/j.jsv.2018.06.017
Lesieutre GA (1998) Vibration damping and control using shunted piezoelectric materials. Shock Vib Digest 30:187–195
Rocha TL, Calçada M, Silva YAR (2013) Enhancement of low-frequency sound insulation using piezoelectric resonators. J Braz Soc Mech Sci Eng 35:357–367. https://doi.org/10.1007/s40430-013-0034-x
Bahador A, Du C, Jin Y (2022) Piezoelectric active damper for surface roughness improvement in hard turning processes. J Braz Soc Mech Sci Eng 44:156. https://doi.org/10.1007/s40430-022-03464-4
Ahmadian M, DeGuilio AP (2001) Recent advances in the use of piezoceramics for vibration suppression. Schock Vib Digest 33:15–22
Berardengo M, Manzoni S, Conti AM (2017) Multi-mode passive piezoelectric shunt damping by means of matrix inequalities. J Sound Vib 405:287–305. https://doi.org/10.1016/j.jsv.2017.06.002
Gripp JAB, Rade DA (2018) Vibration and noise control using shunted piezoelectric transducers: a review. Mech Syst Signal Process 112:359–383. https://doi.org/10.1016/j.ymssp.2018.04.041
Han X, Neubauer M, Wallaschek J (2013) Improved piezoelectric switch shunt damping technique using negative capacitance. J Sound Vib 332:7–16. https://doi.org/10.1016/j.jsv.2012.08.001
Berardengo M, Høgsberg J, Manzoni S et al (2020) LRLC-shunted piezoelectric vibration absorber. J Sound Vib. https://doi.org/10.1016/j.jsv.2020.115268
Ducarne J, Thomas O, Deü JF (2012) Placement and dimension optimization of shunted piezoelectric patches for vibration reduction. J Sound Vib 331:3286–3303. https://doi.org/10.1016/j.jsv.2012.03.002
Billon K, Montcoudiol N, Aubry A et al (2020) Vibration isolation and damping using a piezoelectric flextensional suspension with a negative capacitance shunt. Mech Syst Signal Process. https://doi.org/10.1016/j.ymssp.2020.106696
Gardonio P, Zientek M, Dal Bo L (2019) Panel with self-tuning shunted piezoelectric patches for broadband flexural vibration control. Mech Syst Signal Process. https://doi.org/10.1016/j.ymssp.2019.106299
Ma H, Yan B (2021) Nonlinear damping and mass effects of electromagnetic shunt damping for enhanced nonlinear vibration isolation. Mech Syst Signal Process 146:107010. https://doi.org/10.1016/j.ymssp.2020.107010
Yan B, Ma H, Zhang L et al (2020) A bistable vibration isolator with nonlinear electromagnetic shunt damping. Mech Syst Signal Process 136:106504. https://doi.org/10.1016/j.ymssp.2019.106504
Yan B, Ma H, Yu N et al (2020) Theoretical modeling and experimental analysis of nonlinear electromagnetic shunt damping. J Sound Vib 471:115184. https://doi.org/10.1016/j.jsv.2020.115184
Yan B, Ma H, Zhang L et al (2020) Electromagnetic shunt damping for shock isolation of nonlinear vibration isolators. J Sound Vib 479:115370. https://doi.org/10.1016/j.jsv.2020.115370
Auleley M, Thomas O, Giraud-Audine C, Mahé H (2021) Enhancement of a dynamic vibration absorber by means of an electromagnetic shunt. J Intell Mater Syst Struct 32:331–354. https://doi.org/10.1177/1045389X20957097
Wang X, Wu H, Yang B (2020) Micro-vibration suppressing using electromagnetic absorber and magnetostrictive isolator combined platform. Mech Syst Signal Process 139:106606. https://doi.org/10.1016/j.ymssp.2019.106606
Wan S, Li X, Su W et al (2020) Active chatter suppression for milling process with sliding mode control and electromagnetic actuator. Mech Syst Signal Process 136:106528. https://doi.org/10.1016/j.ymssp.2019.106528
Gruzman M, Santos IF (2016) Vibration control of a flexible structure with electromagnetic actuators. J Braz Soc Mech Sci Eng 38:1131–1142. https://doi.org/10.1007/s40430-015-0438-x
Foong FM, Thein CK, Yurchenko D (2019) On mechanical damping of cantilever beam-based electromagnetic resonators. Mech Syst Signal Process 119:120–137. https://doi.org/10.1016/j.ymssp.2018.09.023
Foong FM, Thein CK, Yurchenko D (2020) Important considerations in optimising the structural aspect of a SDOF electromagnetic vibration energy harvester. J Sound Vib. https://doi.org/10.1016/j.jsv.2020.115470
Saravia CM (2020) On the electromechanical coupling in electromagnetic vibration energy harvesters. Mech Syst Signal Process 136:106027. https://doi.org/10.1016/j.ymssp.2019.03.026
Griffiths DJ (2013) Introduction to electrodynamics, 4th edn. Cambridge University Press
Diez-Jimenez E, Rizzo R, Gómez-García M-J, Corral-Abad E (2019) Review of passive electromagnetic devices for vibration damping and isolation. Shock Vib 2019:1250707. https://doi.org/10.1155/2019/1250707
Cheng TH, Oh IK (2009) Coil-based electromagnetic damper and actuator for vibration suppression of cantilever beams. J Intell Mater Syst Struct 20:2237–2247. https://doi.org/10.1177/1045389X09352819
Tadesse Y, Zhang S, Priya S (2009) Multimodal energy harvesting system: piezoelectric and electromagnetic. J Intell Mater Syst Struct 20:625–632. https://doi.org/10.1177/1045389X08099965
Antoniou A (1969) Realization of gyrators using operational amplifiers, and their used in RC-active-network synthesis. In: Proceedings of the institution of electrical engineers, pp 1838–1850
Li JY, Zhu S (2018) Versatile behaviors of electromagnetic shunt damper with a negative impedance converter. IEEE/ASME Trans Mechatron 23:1415–1424. https://doi.org/10.1109/TMECH.2018.2813307
Stabile A, Aglietti GS, Richardson G, Smet G (2017) A 2-collinear-DoF strut with embedded negative-resistance electromagnetic shunt dampers for spacecraft micro-vibration. Smart Mater Struct. https://doi.org/10.1088/1361-665X/aa61e3
Stabile A, Aglietti GS, Richardson G, Smet G (2017) Design and verification of a negative resistance electromagnetic shunt damper for spacecraft micro-vibration. J Sound Vib 386:38–49. https://doi.org/10.1016/j.jsv.2016.09.024
Zhou S, Jean-Mistral C, Chesné S (2019) Electromagnetic shunt damping with negative impedances: optimization and analysis. J Sound Vib 445:188–203. https://doi.org/10.1016/j.jsv.2019.01.014
Tang X, Liu Y, Cui W, Zuo L (2016) Analytical solutions to H2 and H∞ optimizations of resonant shunted electromagnetic tuned mass damper and vibration energy harvester. J Vib Acoust. https://doi.org/10.1115/1.4031823
Inoue T, Ishida Y, Sumi M (2008) Vibration suppression using electromagnetic resonant shunt damper. J Vib Acoust. https://doi.org/10.1115/1.2889916
Zhu S, Shen W, Qian X (2013) Dynamic analogy between an electromagnetic shunt damper and a tuned mass damper. Smart Mater Struct. https://doi.org/10.1088/0964-1726/22/11/115018
Yan B, Wang K, Hu Z et al (2017) Shunt damping vibration control technology: a review. Appl Sci (Switzerland). https://doi.org/10.3390/app7050494
Kuhnert WM, Cammarano A, Silveira M, Gonçalves PJP (2020) Synthesis of viscoelastic behavior through electromechanical coupling. J Vib Eng Technol. https://doi.org/10.1007/s42417-020-00235-0
Minnemann Kuhnert W, Cammarano A, Silveira M, Paupitz Gonçalves PJ (2020) Optimum design of electromechanical vibration isolators. JVC/J Vib Control. https://doi.org/10.1177/1077546320925362
Brennan MJ, Carrella A, Waters TP, Lopes V Jr (2008) On the dynamic behaviour of a mass supported by a parallel combination of a spring and an elastically connected damper. J Sound Vib 309:823–837. https://doi.org/10.1016/j.jsv.2007.07.074
Fahy F (1985) Sound and structural vibration, radiation, transmission and response. Academic Press Inc, New York
Fahy F, Gardonio P, Hambric S (2006) Sound and structural vibration. Academic Press, New York
Banerjee JR (1997) Dynamic stiffness formulation for structural elements: a general approach. Comput Struct 63:101–103. https://doi.org/10.1016/S0045-7949(96)00326-4
Gonçalves PJPPJP, Brennan MJMJ, Peplow A, Tang B (2019) Calculation of the natural frequencies and mode shapes of a Euler-Bernoulli beam which has any combination of linear boundary conditions. J Vib Control 25:2473–2479. https://doi.org/10.1177/1077546319857336
Gardonio P, Brennan MJ (2004) Chapter 9 in Advanced applications in acoustics, noise and vibration. Spon Press Publisher.
Crandall S (1982) Dynamics of mechanical and electromechanical systems. Krieger Pub Co
Blevins RD (2001) Formulas for natural frequency and mode shape. Krieger Pub Co
de Haro SL, Paupitz Gonçalves PJ, Wagg D (2018) On the dynamic behavior of the Zener model with nonlinear stiffness for harmonic vibration isolation. Mech Syst Signal Process 112:343–358. https://doi.org/10.1016/j.ymssp.2018.04.037
Brennan M, Tang B (2022) Virtual experiments in mechanical vibrations. Wiley
Acknowledgements
The authors would like to acknowledge the financial support of Fapesp (Fundação de Amparo à Pesquisa do Estado de São Paulo) Grant Number: 16/17083-4 and 18/15894-0 and CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) Grant Number: 406594/2021-0.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript.
Additional information
Technical Editor: Pedro Manuel Calas Lopes Pacheco.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Information
Below is the link to the electronic supplementary material.
Supplementary file1 (MP4 194 KB)
Supplementary file2 (MP4 20 KB)
Supplementary file3 (MP4 45 KB)
Supplementary file4 (MP4 40 KB)
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Minnemann Kuhnert, W., Silva, T.M., De Marqui Junior, C. et al. Application of a shunt damping circuit in a structure with an electromagnetically coupled beam: free vibration and frequency response. J Braz. Soc. Mech. Sci. Eng. 46, 307 (2024). https://doi.org/10.1007/s40430-024-04884-0
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s40430-024-04884-0