Abstract
Structural vibration may occur in mechanical systems leading to fatigue, reduced durability or undesirable noise. In this context, shunting piezoelectric transducers to resonant shunts can be an appropriate measure for attenuating vibrations. The achieved vibration attenuation significantly depends on the tuning of the shunt parameters. Uncertainty in design and application of resonant shunted piezoelectric transducers may result in a detuned attenuation system and loss of attenuation performance. Therefore, we propose an approach based on robust optimization using the Bounded Real Lemma to contain the loss of vibration attenuation due to uncertainty. It is shown for resonant shunts, that for increasing electromechanical coupling coefficients the worst-case maximal vibration amplitudes for non-robust and robust optimization of shunt parameters converge. Furthermore by adding a negative capacitance to the resonant shunt, the worst-case maximal amplitude remains almost constant for all considered coupling coefficients for non-robust and robust optimization of the shunt parameters.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Beck, B.S.: Negative capacitance shunting of piezoelectric patches for vibration control of continuous systems. PhD thesis, Georgia Institute of Technology (2012)
Niederberger, D.: Smart damping materials using shunt control. PhD thesis, Swiss Federal Institute of Technology Zürich (2005)
Moheimani, S.O.R., Fleming, A.J.: Piezoelectric Transducers for Vibration Control and Damping. Springer, London (2006)
Hagood, N.W., von Flotow, A.H.: Damping of structural vibrations with piezoelectric materials and passive electrical networks. J. Sound Vib. 146(2), 243–268 (1991)
Neubauer, M., Oleskiewicz, R., Popp, K., Krzyzynski, T.: Optimization of damping and absorbing performance of shunted piezo elements utilizing negative capacitance. J. Sound Vib. 298, 84–107 (2006)
Soltani, P., Kerschen, G., Tondreau, G., Deraemaeker, A.: Piezoelectric vibration damping using resonant shunt circuits: an exact solution. Smart Mater. Struct. 23, 1–11 (2014)
Zambolini-Vicente, B.G.G.L., Silva, V.A.C., de Lima, A.M.G.: Robust design of shunt circuits for passive control of vibrations of composite structures. In: Proceedings of the 2nd International Symposium on Uncertainty Quantification and Stochastic Modeling (2014)
Mokrani, B., Burday, I., Tian, Z., Preumont, A.: Adaptive inductor for vibration damping in presence of uncertainty. In: Proceedings of SMART2015 7th ECCOMAS Thematic Conference on Smart Structures and Materials, Ponta Delgada, Azores, June 3–6 2015
Götz, B., Platz, R., Melz, T.: Consistent approach to describe and evaluate uncertainty in vibration attenuation using resonant piezoelectric shunting and tuned mass dampers. In: Proceedings of the 2nd International Symposium on Uncertainty Quantification and Stochastic Modeling Uncertainties 2014, Rouen/France, June 23–27 2014, pp. 51–64. INSA-Rouen
de Marneffe, B.: Active and passive vibration isolation and damping via shunted transducers. PhD thesis, Université Libre de Bruxelles (2007)
Scherer, C.: The Riccati inequality and state-space H ∞ -optimal control. PhD thesis, Bayerische Julius Maximilians-Universität Würzburg (1990)
Nemirovksi, A., Ben-Tal, A., El Ghaoui, L.: Robust Optimization. Princeton University Press, Princeton (2009)
Correa, R., Ramirez, H.C.: A global algorithm for nonlinear semidefinite programming. SIAM J. Optim. 15(1), 303–318 (2005)
Sturm, J.F.: Using sedumi 1.02, a matlab toolbox for optimization over symmetric cones. Optim. Methods Softw. 11–12, 625–653 (1999)
Acknowledgements
The authors like to thank the German Research Foundation DFG for funding this research within the SFB 805.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 The Society for Experimental Mechanics, Inc.
About this paper
Cite this paper
Kuttich, A., Götz, B., Ulbrich, S. (2017). Robust Optimization of Shunted Piezoelectric Transducers for Vibration Attenuation Considering Different Values of Electromechanical Coupling. In: Barthorpe, R., Platz, R., Lopez, I., Moaveni, B., Papadimitriou, C. (eds) Model Validation and Uncertainty Quantification, Volume 3. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-54858-6_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-54858-6_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-54857-9
Online ISBN: 978-3-319-54858-6
eBook Packages: EngineeringEngineering (R0)