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Adequate Mathematical Beam-Column Model for Active Buckling Control in a Tetrahedron Truss Structure

: Schäffner, Maximilian; Platz, Roland; Melz, Tobias


Mao, Z. ; Society for Experimental Mechanics -SEM-, Bethel:
Model Validation and Uncertainty Quantification, Vol.3 : Proceedings of the 38th IMAC, A Conference and Exposition on Structural Dynamics 2020, Houston, Texas, February 10-13, 2020
Cham: Springer Nature, 2020 (Conference proceedings of the Society for Experimental Mechanics series)
ISBN: 978-3-030-48778-2 (Print)
ISBN: 978-3-030-47638-0 (Online)
ISBN: 978-3-030-47639-7
ISBN: 978-3-030-47637-3
International Modal Analysis Conference (IMAC) <38, 2020, Houston/Tex.>
Conference and Exposition on Structural Dynamics <2020, Houston/Tex.>
Fraunhofer LBF ()
Beam-Column Model; active buckling control

Active buckling control of compressively loaded beam-columns provides a possibility to increase the maximum bearable axial load compared to passive beam-columns. Reliable mathematical beam-column models that adequately describe the lateral dynamic behavior are required for the model-based controller synthesis in order to avoid controller instability for real testing and application. This paper presents an adequate mathematical beam-column model for the active buckling control in a tetrahedron truss structure. Furthermore, it discusses model form uncertainty arising from model simplification of the global tetrahedron model to three local beam-column models. An experimental tetrahedron truss structure that comprises three passive beams and three active beam-columns with piezo-elastic supports for active buckling control is investigated. The tetrahedron is clamped at the three base nodes and free at the top node. In the two piezo-elastic supports of each active beam-column, integrated piezoelectric stack actuators compensate lateral deflections due to increasing axial compressive loads and may, thus, prevent buckling. In previous works, active buckling control was investigated for a single beam-column that was clamped rigidly in an experimental test setup. A verified and validated single beam-column model with compliant boundary conditions was used to represent the piezo-elastic supports for active buckling control. The mathematical model of the active beam-columns is calibrated with experimental data from all three nominally identical active beam-columns to account for uncertainty in manufacturing, assembly or mounting. Subsequently, they are compared with respect to the transfer functions and the first eigenfrequencies. It is shown that the boundary conditions of the single beam-column model may be calibrated to adequately describe the boundary conditions within the tetrahedron truss structure. Thus, it will be used for the model-based controller synthesis in future investigations on the active buckling control of the tetrahedron truss structure.