Abstract
In many applications, nonlinear beams undergoing bending, axial and shear deformation are important structural elements. In the present paper, a shear deformable beam finite element is presented for such applications. Since displacements and displacement gradients are chosen as the nodal degrees of freedom, an equivalent displacement and rotation interpolation is retrieved. The definition of strain energy is based on Reissner’s nonlinear rod theory with special strain measures for axial strain, shear strain and bending strain. Furthermore, a thickness deformation is introduced by adding an according term to the virtual work of internal forces. This underlying formulation is extended for piezo-electric actuation. The obtained beam finite elements are applied to a two-link robot with two flexible arms with tip masses. Distributed and concentrated masses cause flexural vibrations, which are compensated by means of piezo-electric actuators attached to the arms. A numerical example of a highly flexible robot with piezo-electric actuation and feedforward control is presented to show the applicability of the finite element.
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Acknowledgements
K. Nachbagauer acknowledges support from the Austrian Science Funds FWF via the project I337-N18, C. Zehetner and J. Gerstmayr from the K2-Comet Austrian Center of Competence in Mechatronics ACCM.
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Nachbagauer, K., Zehetner, C., Gerstmayr, J. (2012). Nonlinear Finite Element Modelling of Moving Beam Vibrations Controlled by Distributed Actuators. In: Irschik, H., Krommer, M., Belyaev, A. (eds) Advanced Dynamics and Model-Based Control of Structures and Machines. Springer, Vienna. https://doi.org/10.1007/978-3-7091-0797-3_20
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DOI: https://doi.org/10.1007/978-3-7091-0797-3_20
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