Chapter24 Sensitivity Analysis of Beams Controlled by Shunted Piezoelectric Transducers G. Matten, M. Collet, S. Cogan, and E. Sadoulet-Reboul Abstract This paper aims at quantifying the robustness of a cantilever beam behavior, controlled with a shunted piezoelectric patch, with respect to uncertainties in the system parameters. Vibration control based on piezoelectric transducers has proven to be particularly efficient, in particular the use of thin piezoelectric patches shunted by negative capacitance circuits allowing broadband applications. However, the optimal tuning of the control can lead to instability and the influence of a variation in the physical properties or in geometry is not well known. Through multiphysical finite element simulations, a sensitivity analysis of the beam coupled with a piezoelectric transducer is performed. The effects of a variability in the material characteristics, the geometry of the system and the parameters of the shunt circuit on the stability and the damping performances are investigated. Keywords Vibration control • Sensitivity • Robust design • Negative capacitance controller • Morris 24.1 Introduction Appearing in the late 1970s, vibroacoustic control has been extensively studied [1–3]. In this context, a technique based on shunted piezoelectric transducers has been proven to be efficient. It consists in adding thin piezoelectric patches on a structure and connecting electrical shunts between the two electrodes of the transducers. With the piezoelectric effect, they are both sensors and actuators and the shunt behaves as a feedback controller. One particular shunt is a negative capacitance circuit. It is designed to counteract the capacitive effect of the transducer in order to realize a broadband resistive dissipator. The experiments performed so far have shown that the tuning of such a shunt is delicate. Indeed, the damping of the structure is very sensitive to the variation of the shunt capacitance. This paper intends to better understand the sensitivity of such systems to variations or uncertainties in the system characteristics. The goal is to determine which parameters are critical for the efficiency and for the stability of the controlled beam so as to propose a more robust design. 24.2 The System The system studied here is a steel fixed-free cantilever beam with a PZT-5A piezoelectric transducer fixed on it with epoxy glue (see Fig. 24.1). The control of this system with a negative capacitance shunt has been achieved in [4]. A three dimensional finite element model is presented here to study the sensitivity of the damping efficiency towards the material properties (density, Young modulus and Poisson ratio), the geometric properties (position and dimensions of the transducer and dimensions of the beam) and the shunt properties (resistance Rand capacitance C). G.Matten ( ) • S. Cogan • E. Sadoulet-Reboul Applied Mechanics Department, FEMTO-ST Institute - 24, rue de l’Épitaphe, 25000 Besançon, France e-mail: gael.matten@femto-st.fr; scott.cogan@univ-fcomte.fr; emeline.sadoulet-reboul@univ-fcomte.fr M. Collet Laboratoire de Tribologie et Dynamique des Systèmes, École Centrale de Lyon - 36, Avenue Guy de Collongues, 69130 Ecully, France e-mail: manuel.collet@ec-lyon.fr H.S. Atamturktur et al. (eds.), Model Validation and Uncertainty Quantification, Volume 3: Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics, 2014, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-04552-8__24, © The Society for Experimental Mechanics, Inc. 2014 243
RkJQdWJsaXNoZXIy MTMzNzEzMQ==