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Smart Structures and Systems Volume 18, Number 2, August 2016 , pages 355-374 DOI: https://doi.org/10.12989/sss.2016.18.2.355 |
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Transverse dynamics of slender piezoelectric bimorphs with resistive-inductive electrodes [Open access article] |
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Juergen Schoeftner, Gerda Buchberger and Ayech Benjeddou
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| Abstract | ||
| This paper presents and compares a one-dimensional (1D) bending theory for piezoelectric thin beam-type structures with resistive-inductive electrodes to ANSYS three-dimensional (3D) finite element (FE) analysis. In particular, the lateral deflections and vibrations of slender piezoelectric beams are considered. The peculiarity of the piezoelectric beam model is the modeling of electrodes in such a manner that is does not fulfill the equipotential area condition. The case of ideal, perfectly conductive electrodes is a special case of our 1D model. Two-coupled partial differential equations are obtained for the lateral deflection and for the voltage distribution along the electrodes: the first one is an extended Bernoulli-Euler beam equation (second-order in time, forth order in space) and the second one the so-called Telegrapher\'s equation (second-order in time and space). Analytical results of our theory are validated by 3D electromechanically coupled FE simulations with ANSYS. A clamped-hinged beam is considered with various types of electrodes for the piezoelectric layers, which can be either resistive and/or inductive. A natural frequency analysis as well as quasi-static and dynamic simulations are performed. A good agreement between the extended beam theory and the FE results is found. Finally, the practical relevance of this type of electrodes is shown. It is found that the damping capability of properly tuned resistive or resistive-inductive electrodes exceeds the damping performance of beams, where the electrodes are simply linked to an optimized impedance. | ||
| Key Words | ||
| piezoelectric effect; conductive electrodes; linear piezoelectric beam and bar modeling; passive vibration control; bending vibration; finite element analysis | ||
| Address | ||
| Juergen Schoeftner: Johannes Kepler University, Institute of Technical Mechanics, Altenbergerstrasse 69, 4040 Linz, Austria Gerda Buchberger: Johannes Kepler University, Institute of Biomedical Mechatronics, Altenbergerstrasse 69, 4040 Linz, Austria Ayech Benjeddou: SUPMECA, 3 rue Fernand Hainaut, 93407 Saint Ouen CEDEX, France | ||