Jürgen Schöftner, Gerda Buchberger,
"An Electromechanically-Coupled Bernoulli-Euler Beam-Theory Taking into Account the Finite Conductivity of the Electrodes for Sensing and Actuation"
: Proceedings of the 2012 World Congress on Advances in Civil, Environmental, and Material Research (ACEM´12): CD-ROM. ed. / Chang-Koon Choi, Seite(n) 1051-1065, 8-2012, ISBN: 978-89-89693-34-5-98530
An Electromechanically-Coupled Bernoulli-Euler Beam-Theory Taking into Account the Finite Conductivity of the Electrodes for Sensing and Actuation
Sprache des Titels:
Proceedings of the 2012 World Congress on Advances in Civil, Environmental, and Material Research (ACEM´12): CD-ROM. ed. / Chang-Koon Choi
In this contribution an extended Bernoulli-Euler theory for a laminated beam is developed which takes into account elastic and piezoelectric material properties and resistive electrodes. The motivation of this study is to provide a deeper knowledge of the coupling mechanism of the mechanical and the electrical domain. This knowledge can be used to derive new strategies for active and passive vibration control and also for structural health monitoring of mechatronic systems. If the electrodes of a single piezoelectric layer are connected by an electrical resistance, the developed theory can be used for passive applications. Otherwise, if the voltage at a certain location of the electrode is controlled by a power supply, the presented theory also holds for actuated slender beams. The resulting coupled governing equations for the bending vibrations of the beam are (1) the well-known Bernoulli-Euler equation of a purely elastic beam, extended by a voltage term (forth order in space, second order in time), and (2) a diffusion equation for the voltage distribution (second order in space, first order in time) excited by the axial strain of the structure. In order to verify the derived extended beam theory, a slender beam is investigated and analytical results of the theory are compared to three-dimensional finite element results performed with ANSYS. Eigenfrequencies are compared for a clamped-free beam and different types of electrodes and electrical impedances (short and open circuits with either highly conductive or highly resistive electrodes). The frequency responses of the tip-displacement, the voltage distribution and the electrical field in the axial and in the thickness direction between analytical and FE results are in good agreement in the low and high frequency domain.