Vibration Control and Structural Damping of a Rotating Beam by Using Piezoelectric Actuators
In this paper, the application of piezoelectric vibration control in flexible multibody systems is studied and verified. Exemplarily, beam-type structures are considered that are subject to inertial and external forces. The equations of motion for three-d
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Vibration Control and Structural Damping of a Rotating Beam by Using Piezoelectric Actuators Christian Zehetner and Georg Zenz
Abstract In this paper, the application of piezoelectric vibration control in flexible multibody systems is studied and verified. Exemplarily, beam-type structures are considered that are subject to inertial and external forces. The equations of motion for three-dimensional flexible and torsional vibrations are presented considering the influence of piezoelectric actuation strains. In the framework of Bernoulli-Euler beam theory the shape control solution is derived, i.e. the distribution of actuation strains such that the flexible displacements are completely compensated. For the experimental verification, a laboratory model has been developed, in which the theoretical distribution of actuation strains is discretized by piezoelectric patches. A suitable control algorithm is implemented within a dSpace environment. Finally, the results are validated by numerical computations utilizing ABAQUS and HOTINT, and verified by experimental evaluation.
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Introduction
Recently, the interest in vibration compensation by means of distributed actuation has increased rapidly. On the one hand, structures become more and more light-weighted, on the other hand there are considerable advances in the development of materials suitable for such kinds of actuators and sensors. This paper concentrates on the application of piezoelectric transducers in order to control flexible vibrations in beams, which are important components of many multibody systems. Piezoelectric transducers can be used for sensing and actuation, utilizing either the direct or the converse piezoelectric effect, respectively [1]. An efficient possibility for realisation is to apply piezoelectric patches on the surfaces of beams.
C. Zehetner (*) • G. Zenz Austrian Center of Competence in Mechatronics (ACCM), Altenbergerstr. 69, 4040 Linz, Austria e-mail: [email protected]; [email protected] H. Gattringer and J. Gerstmayr (eds.), Multibody System Dynamics, Robotics and Control, DOI 10.1007/978-3-7091-1289-2_15, # Springer-Verlag Wien 2013
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C. Zehetner and G. Zenz
Depending on the type of the piezoelectric material, and on the position of the patch on the beam, such transducers can be used for sensing and actuation of bending and torsional modes. Vibration compensation by piezoelectric materials has been extensively treated in the literature. The exact compensation of flexible displacements by distributed actuation has been denoted as shape control, for a review see Irschik [2]. An exact solution in the framework of Bernoulli-Euler beam theory for the complete compensation of plane bending vibrations under influence of rigidbody motions has been presented by Zehetner and Irschik [3]. Torsional vibration control has been investigated by Zehetner and Krommer [4], where it has been shown how piezoelectric transducers can be used for torsional sensing and actuation. A comparison of some specific piezoelectric mate
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