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Irschik H.,Johannes Kepler University | Gerstmayr J.,Linz Center of Mechatronics
Mathematical and Computer Modelling of Dynamical Systems | Year: 2011

This article deals with the non-linear modelling of beams that are bent, sheared and stretched by external forces and moments. In the following, we restrict to planedeformations and static conditions. Our task is to present a continuum mechanicsbased interpretation of the celebrated large displacement finite deformation structural mechanics theory, which was presented by Eric Reissner [On one-dimensional finitestrain beam theory: the plane problem, J. Appl. Math. Phys. 23 (1972), pp. 795-804]. The latter formulation was restricted to the notions of structural mechanics and thus did not use the notions of stress and strain, which are fundamental for continuum mechanics. Thus, the common continuum mechanics-based constitutive modelling at the stress-strain level cannot be utilized in connection with Reissner's original theory. Instead, Reissner suggested that constitutive relations between certain generalized strains (bending, shear and axial force strains) and generalized static entities (bending moments, shear and normal forces) should be evaluated from physical experiments. This means that the beam to be studied must be first built up, and the experiments must be performed for the real beam as a whole. Although such physical experiments are indeed to be performed in practice for safety reasons in sensible cases, for example, bridge decks or aircraft wings, it is nevertheless felt to be a drawback that the results of simple standardized stress-strain experiments concerning the constitutive behaviour of the materials, from which the beam is built up, cannot be used. Moreover, relying only on physical experiments on the whole beam means that computations (virtual experiments) can be made only after the beam has been built up. To overcome this problem, we subsequently present a continuum mechanics-based interpretation of Reissner's structural mechanics modelling, by attaching a proper continuum mechanics-based meaning to both the generalized static entities and the generalized strains in Reissner's theory [E. Reissner, On one-dimensional finite-strain beam theory: the plane problem, J. Appl. Math. Phys. 23 (1972), pp. 795-804]. Consequently, these generalized static entities can be related to the generalized strains on the basis of a constitutive modelling on the stress-strain level. We show this in some detail in this contribution for a hyperelastic material proposed by Simo and Hughes [Computational Inelasticity, Springer, New York, 1998]. An illustrative numerical example is given which shows the results of large bending and axial deformation behaviour for different constitutive relations. This article represents an extended version of a preliminary work published in [H. Irschik and J. Gerstmayr, A hyperelastic Reissner-type model for non-linear shear deformable beams, Proceedings of the Mathmod 09 Vienna, I. Troch and F. Breitenecker, eds., 2009, pp. 1-7]. © 2011 Taylor & Francis.

Zehetner C.,Linz Center of Mechatronics | Krommer M.,Johannes Kepler University
Structural Control and Health Monitoring | Year: 2012

This paper is concerned with active control of torsional vibrations in laminated rods by piezoelectric shear sensors and actuators. A piezoelectric layer can be used as a sensor by utilizing the direct piezoelectric effect, measuring either the charge on short-circuited electrodes or the voltage on open electrodes. On the other hand, the converse piezoelectric effect enables actuation by applying an electric potential difference to the electrodes of a piezoelectric layer. The sensor and actuator equations are formulated in the framework of an extended Saint-Venant torsion theory considering additional cross-sectional warping due to piezoelectric eigenstrains. A solution of the shape control problem for torsional vibrations is presented, i.e. the necessary distribution of actuation strains in order to completely compensate vibrations caused by external excitations. For the case, in which the external excitations are not known exactly, a feedback control solution is presented using one piezoelectric layer as a sensor and a second one as an actuator. For the examples of a rectangular and a circular cross-section, the theoretical results are validated by three-dimensional finite element computations, showing a very good coincidence. Copyright © 2011 John Wiley & Sons, Ltd.

Vetyukov Y.,Linz Center of Mechatronics
Acta Mechanica | Year: 2012

A multi-stage approach for the mathematical modeling in the field of nonlinear problems of mechanics of thin-walled structures is the subject of the present paper. A combination of the asymptotic, direct, and numerical methods for consistent and efficient analysis of problems of structural mechanics is presented on the example of plane problem of finite vibrations of a thin curved strip with material inhomogeneity. The method of asymptotic splitting allows for a consistent dimensional reduction of the original two-dimensional continuous problem as the thickness is small: the leading-order solution of the full system of equations of the theory of elasticity results in a one-dimensional formulation of the reduced theory and a problem in the cross-section. The direct approach to a material line extends the results to the geometrically nonlinear range. The appropriate finite element formulation allows for practical applications of the theory; with the numerical solution of the reduced problem, we restore the distributions of stresses, strains, and displacements over the thickness. Numerically and analytically investigated convergence of the solutions of various problems in the original (two-dimensional) and reduced (one-dimensional) models as the thickness tends to zero justifies the analytical conclusion that the curvature and variation of the material properties over the thickness do not require special treatment for classical Kirchhoff's rods. Further terms of the asymptotic expansion lead to a model with shear and extension, in which curvature appears in a nontrivial way. © Springer-Verlag 2011.

Grabner H.,Linz Center of Mechatronics | Amrhein W.,Johannes Kepler University | Silber S.,Johannes Kepler University | Gruber W.,Johannes Kepler University
IEEE/ASME Transactions on Mechatronics | Year: 2010

The demands on bearingless drive configurations concerning performance as well as costs are high. The proposed bearingless brushless dc motor consists of five concentrated coils in a symmetrical arrangement, which generate radial forces and motor torque simultaneously in interaction with a permanent-magnet-excited disk-shaped rotor. Additionally, tilting deflection and the axial position of the rotor are stabilized passively by means of magnetic reluctance forces. Thus, system costs can be reduced significantly compared to a conventional bearingless motor setup, which actively stabilizes all 6 DOF. Due to the nonlinearity of the plant, the use of linear control design methods alone is not suitable for achieving a high operation performance. This paper introduces a novel radial position and motor torque control algorithm for a bearingless brushless dc motor based on the theory of feedback linearization. Thereby, the combined model of translatory and rotatory dynamics can be split into independent linear systems by means of a nonlinear change of system coordinates and a static-state feedback. Experimental results demonstrate the effectiveness of the proposed approach. © 2009 IEEE.

Potsch A.,Linz Center of Mechatronics
2016 15th ACM/IEEE International Conference on Information Processing in Sensor Networks, IPSN 2016 - Proceedings | Year: 2016

At least since the terms Internet of Things, Factories of the Future or Industrial Internet gave distinction to the modern world of communication, there is a special need for efficient test- and debug tools targeting research and development of embedded wireless sensor and actuator networks (WSAN) in industrial automation technology and other non-consumer application areas in adverse environments. Those networks usually have tighter requirements on dependability, synchronization, and real-time capability as compared applications in environmental monitoring or home automation. For WSAN research and development, testbeds are a valuable tool as they enable controlled and repeatable operation under conditions close to reality. The contribution of this Ph.D. dissertation is to design, implement and set up a test environment for embedded industrial wireless sensor actuator networks, with special focus on energy constrained network nodes. This testbed should offer an previously unattained level of insight in timing characteristics of the network and the energy behavior of a single node. It allows to make statements about limitations of the deployed WSAN technology, or to compare different WSAN solutions in an automated manner. The uniqueness of this testbed setup is due to a scalable, affordable and maintainable organization both in software as well as the structure of the used hardware components. © 2016 IEEE.

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