Subproject C2

Mechanical, mechatronic and adaptive technologies for the stabilization of beam-columns and truss structures

Slender beam-columns in lightweight mechanical load-bearing structures are sensitive to failure by buckling when loaded by compressive axial loads. The maximum bearable axial load of a beam-column is considerably reduced by uncertainty in the material, geometry, loading or support properties, but may be increased by active buckling control.

In this subproject C2, active buckling control of a practical beam-column system with circular cross-section, relatively low slenderness ratio and relatively high critical buckling load as well as dynamic axial loads is investigated (shown in figure 1).

Figure 1.: a) beam-column with piezo-elastic supports, b) sectional view of piezo-elastic support
Figure 1.: a) beam-column with piezo-elastic supports, b) sectional view of piezo-elastic support

The goal is to increase the maximum bearable axial load and reduce uncertainty in the buckling behavior. For the latter, probabilistic uncertainty in the maximum bearable axial loads and lateral deflections of the passive and active beam-column systems is quantified and evaluated experimentally. For the experimental results under quasi-static axial loads (shown in figure 2), the most likely maximum bearable axial load increases by 29% and the variability reduces by 70% when comparing the passive beam-column system. Overall, the results of this subproject contribute to the application of active buckling control in practical truss structures.

Figure 2.: a) absolute modal displacement versus axial load, b) normalized histogram and fitted probability density function (pdf)
Figure 2.: a) absolute modal displacement versus axial load, b) normalized histogram and fitted probability density function (pdf)

In current research, active buckling control of three-dimensional truss structures is investigated (shown in figure 3). Quasi-static and dynamic performance of the passive and active truss structures against axial load will be compared. Furthermore, the uncertainty of buckling control of the truss structures under axial dynamic load will be quantified and evaluated.

Figure 3.: a) CAD sketch of current experimental tetrahedron truss structure, b) photo of experimental test setup
Figure 3.: a) CAD sketch of current experimental tetrahedron truss structure, b) photo of experimental test setup

[1] Platz, Roland; Janssen, Enrico (2009): Mechatronische Stabilisierung knickgefährdeter Stäbe in lasttragenden Systemen des Maschinenbaus. In: Mechatronik: VDI-Verlag, S. 321–326.

[2] Hanselka, Holger; Platz, Roland (2010): Ansätze und Maßnahmen zur Beherrschung von Unsicherheit in lasttragenden Systemen des Maschinenbaus. In: VDI-Zeitschrift Konstruktion 11/12-2010, S. 55–62. Online verfügbar unter http://www.konstruktion-online.de/kon/article.php?data[article_id]=57787.

[3] Engelhardt, Roland A.; Koenen, Jan F.; Enss, Georg C.; Sichau, Adrian; Platz, Roland; Kloberdanz, Hermann et al. (2010): A Model to Categorise Uncertainty in Load-Carrying Systems. In: Peter Heisig, P. John Clarkson und Sandor Vajna (Hg.): Proceedings of the 1st International Conference on Modelling and Management of Engineering Processes (MMEP 2010). Cambridge/UK: Springer-Verlag London, S. 53–64.

[4] Enss, Georg C.; Platz, Roland; Hanselka, Holger (2010): An Approach to Control the Stability in an Active Load-Carrying Beam-Column by One Single Piezoelectric Stack Actuator. In: Proceedings of ISMA 2010 24th International Conference on Noise and Vibration Engineering. ISMA Advance Conference Programme. Leuven/Belgium, S. 535–546.

[5] Enss, Georg C.; Platz, Roland; Hanselka, Holger (2010): An Enhanced Approach to Control Stability in an Active Column Critical to Buckling. In: 21st International Conference on Adaptive Structures and Technologies 2010 (ICAST 2010), October 4 – 6. ICAST International Conference on Adaptive Structures and Technologies. University Park, Pennsylvania, USA: Curran.

[6] Ederer, Thorsten; Engelhardt, Roland A.; Enss, Georg C.; Haydn, Michael; Kloberdanz, Hermann (2011): SFB 805, AK1-Begriffe. Einordnung und Abgrenzung von Begriffen.

[7] Eifler, Tobias; Enss, Georg C.; Haydn, Michael; Mosch, Lucia; Platz, Roland; Hanselka, Holger (2011): Approach for a Consistent Description of Uncertainty in Process Chains of Load Carrying Mechanical Systems. In: AMM 104, S. 133–144. DOI: 10.4028/www.scientific.net/AMM.104.133.

[8] Enss, Georg C.; Eifler, Tobias; Haydn, Michael; Mosch, Lucia; Platz, Roland; Hanselka, Holger (Hg.) (2011): Prozessmodell zur systematischen Beschreibung und Verkettung von Unsicherheit. Aachen/Germany (Posterbeitrag).

[9] Enss, Georg C.; Platz, Roland; Hanselka, Holger (2011): A survey on uncertainty in the control of an active column critical to buckling. In: Proceedings of International Conference on Structural Engineering Dynamics ICEDyn 2011. Instituto Superior Técnico, Technical University of Lisbon. Tavira/Portugal, S. 1–8.

[10] Enss, Georg C.; Platz, Roland; Hanselka, Holger (2011): Parameter study on an actively stabilised beam column. In: Proceedings of SMART’11. 5th ECCOMAS Thematic Conference on Smart Structures and Materials. ECCOMAS European Community on Computational Methods in Applied Sciences. Saarbruecken/Germany, S. 17–25.

[11] Koenen, Jan F.; Enss, Georg C.; Ondoua, Serge; Platz, Roland; Hanselka, Holger (2011): Evaluation and Control of Uncertainty in Using an Active Column System. In: AMM 104, S. 187–195. DOI: 10.4028/www.scientific.net/AMM.104.187.

[12] Enss, Georg C.; Platz, Roland; Hanselka, Holger (2012): Mathematical modelling of postbuckling in a slender beam column for active stabilisation control with respect to uncertainty. In: Proceedings of SPIE Vol. 8341 Active and Passive Smart Structures and Integrated Systems VI. SPIE international society for optics and photonics. San Diego, CA/USA, S. 834119.

[13] Enss, Georg C.; Platz, Roland; Hanselka, Holger (2012): Uncertainty in loading and control of an active column critical to buckling. In: Shock and Vibration 19 (5), S. 929–937. DOI: 10.3233/SAV-2012-0700.

[14] Enss, Georg C.; Platz, Roland; Hanselka, Holger (2013): Uncertainty in Passive and Active Stabilisation of Critically Loaded Columns. Fundamentals. In: Christian Boller und Hartmut Janocha (Hg.): New Trends in Smart Technologies: Fraunhofer Verlag Stuttgart, S. 61–67. Online verfügbar unter http://publica.fraunhofer.de/documents/N-256458.html.

[15] Enss, Georg C.; Platz, Roland; Hanselka, Holger (2013): Uncertainty in Passive and Active Stabilisation of Crtitcally Loaded Columns. In: Christian Boller und Hartmut Janocha (Hg.): New Trends in Smart Technologies: Fraunhofer Verlag Stuttgart, S. 61–67.

[16] Enss, Georg C.; Götz, Benedict; Kohler, Michael; Krzyzak, Adam; Platz, Roland (2014): Nonparametric estimation of a maximum of quantiles. In: Electronic Journal of Statistics 8 (2), S. 3176–3192. DOI: 10.1214/14-EJS970.

[17] Enss, Georg C.; Platz, Roland (2014): Statistical Approach for Active Buckling Control With Uncertainty. In: H. Sezer Atamturktur, Babak Moaveni, Costas Papadimitriou und Tyler Schoenherr (Hg.): Model Validation and Uncertainty Quantification, Volume 3. Proceedings of the 32nd IMAC, a Conference and Exposition on Structural Dynamics, 2014. [held in Orlando, Florida, February 3-6, 2014]. Cham: Springer International Publishing (Conference Proceedings of the Society for Experimental Mechanics Series), S. 291–297.

[18] Platz, Roland; Enss, Georg C.; Ondoua, Serge; Melz, Tobias (2014): Active stabilization of a slender beam-column under static axial loading and estimated uncertainty in actuator properties. In: Proceedings of the Second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) and the Sixth International Symposium on Uncertainty Modeling and Analysis (ISUMA). ASCE American Society of Civil Engineers. Liverpool, UK, S. 235–244.

[19] Schaeffner, Maximilian; Enss, Georg C.; Platz, Roland (2014): Influence of uncertain support boundary conditions on the buckling load of an axially loaded beam-column. In: Proceedings of ISMA2014 including USD2014 International Conference on Uncertainty in Structural Dynamics. ISMA Advance Conference Programme. Leuven, Belgium, S. 4675–4686.

[20] Schaeffner, Maximilian; Enss, Georg C.; Platz, Roland (2014): Mathematical modeling and numerical simulation of an actively stabilized beam-column with circular cross-section. In: Proceedings of SPIE Vol. 9057 Active and Passive Smart Structures and Integrated Systems. SPIE international society for optics and photonics. San Diego, CA/USA, 90572H.

[21] Enss, Georg C.; Platz, Roland; Melz, Tobias (2015): Evaluation of uncertainty in experimental active buckling control of a slender beam-column using Weibull analysis. In: Proceedings of International Conference on Structural Engineering Dynamics ICEDyn. Lagos, Portugal, June 22-24. Instituto Superior Técnico, Technical University of Lisbon, S. 8.

[22] Götz, Benedict; Schaeffner, Maximilian; Platz, Roland; Melz, Tobias (2015): Model verification and validation of a piezo-elastic support for passive and active structural control of beams with circular cross-section. In: Applied Mechanics and Materials, Trans Tech Publications 807, S. 67–77.

[23] Schaeffner, Maximilian; Platz, Roland; Melz, Tobias (2015): Active buckling control of an axially loaded beam-column with circular cross-section by active supports with integrated piezoelectric actuators. In: Proceedings of SMART2015. 7th ECCOMAS Thematic Conference on Smart Structures and Materials. ECCOMAS European Community on Computational Methods in Applied Sciences. Ponta Delgada, Azores.

[24] Enss, Georg C.; Kohler, Michael; Krzyzak, Adam; Platz, Roland (2016): Nonparametric Quantile Estimation Based on Surrogate Models. In: IEEE Transaction on Information Theory 62 (10), S. 5727–5739.

[25] Enss, Georg C.; Platz, Roland (2016): Evaluation of uncertainty in experimental active buckling control of a slender beam-column using Weibull analysis. In: Mechanical Systems and Signal Processing 79, S. 123–131. DOI: 10.1016/j.ymssp.2016.02.066.

[26] Enß, Georg Christoph (2016): Beherrschung von Unsicherheit am Beispiel eines aktiv gegen Knicken stabilisierten Systems. Dissertation Technische Universität Darmstadt, [Online-Edition: http://tuprints.ulb.tu-darmstadt.de/id/eprint/5176].

[27] Götz, Benedict; Schaeffner, Maximilian; Platz, Roland; Melz, Tobias (2016): Lateral vibration attenuation of a beam with circular cross-section by a support with integrated piezoelectric transducers shunted to negative capacitances. In: Smart Materials and Structures 25 (9), S. 95045. DOI: 10.1088/0964-1726/25/9/095045.

[28] Schaeffner, Maximilian; Götz, Benedict; Platz, Roland (2016): Active buckling control of a beam-column with circular cross-section using piezo-elastic supports and integral LQR control. In: Smart Materials and Structures 25 (6), S. 65008. DOI: 10.1088/0964-1726/25/6/065008.

[29] Schaeffner, Maximilian; Platz, Roland (2016): Active buckling control of an imperfect beam-column with circular cross-section using piezo-elastic supports and integral LQR control. In: Journal of Physics: Conference Series 744 (1), S. 12165. Online verfügbar unter http://stacks.iop.org/1742-6596/744/i=1/a=012165.

[30] Schaeffner, Maximilian; Platz, Roland (2017): Linear Parameter-Varying (LPV) Buckling Control of an Imperfect Beam-Column Subject to Time-Varying Axial Loads Model Validation and Uncertainty Quantification. In: Springer International Publishing, In: 35th IMAC, A Conference and Exposition on Structural Dynamics 2017, Garden Grove, USA, 29.01. – 02.02.2017, S. 103-112.

[31] Li, Sushan; Götz, Benedict; Schaeffner, Maximilian; Platz, Roland (2017): Approach to prove the efficiency of the Monte Carlo method combined with the elementary effect method to quantify uncertainty of a beam structure with piezo-elastic supports. In: 2nd ECCOMAS – International Conference on Uncertainty Quantification in Computational Sciences and Engineering, Rhodes Island, Greece, 15–17 June 2017.

[32] Schaeffner, Maximilian; Platz, Roland (2018): Gain-scheduled H∞ buckling control of a circular beam-column subject to time-varying axial loads. In: Smart Materials and Structures 27 (6), DOI: 10.1088/1361-665X/aab63a.

[33] Gally, Tristan; Kuttich, Anja; Pfetsch, Marc E.; Schaeffner, Maximilian; Ulbrich, Stefan (2018): Optimal Placement of Active Bars for Buckling Control in Truss Structures under Bar Failures. 885, In: Applied Mechanics and Materials, Trans Tech Publications, S. 119-130, ISSN 1660-9336, [Online-Edition: https://www.scientific.net/AMM.885.119].

[34] Hoppe, Florian; Knoll, Maximilian; Götz, Benedict; Schaeffner, Maximilian; Groche, Peter (2018): Reducing Uncertainty in Shunt Damping by Model-Predictive Product Stiffness Control in a Single Point Incremental Forming Process. In: AMM 885, S. 35–47. DOI: 10.4028/www.scientific.net/AMM.885.35.

[35] Schäffner, Maximilian Frederic (2019): Quantification and evaluation of uncertainty in active buckling control of a beam-column subject to dynamic axial loads. Dissertation Technische Universität Darmstadt, [Online-Edition: https://tuprints.ulb.tu-darmstadt.de/8652].

[36] Feldmann, Robert; Gehb, Christopher M.; Schaeffner, Maximilian; Melz, Tobias (2020): Recursive Gaussian Processes for Discrepancy Modeling. In: Proceedings of ISMA2020 including USD2020 International Conference on Uncertainty in Structural Dynamics. ISMA. Leuven, Belgium.

[37] Lenz, Jonathan; Rexer, Manuel; Al-Baradoni, Nassr; Gehb, Christopher M.; Feldmann, Robert; Schaeffner, Maximilian (2020): Topology Selection for a Load-Carrying Truss Structure using an Info-Gap Approach. Proceedings of the 38th IMAC, A Conference and Exposition on Structural Dynamics 2020.

[38] Lenz, Jonathan; Schäffner, Maximilian; Platz, Roland; Melz, Tobias (2020): Selection of an adequate model of a piezo-elastic support for structural control in a beam truss structure. In: M. Zhu (Hg.): Model Validation and Uncertainty Quantification, Volume 3. Proceedings of the 38th IMAC. Springer, Cham, S. 41-49.

[39] Feldmann, Robert; Schaeffner, Maximilian; Gehb, Christopher M.; Platz, Roland; Melz, Tobias (2020): Analyzing Propagation of Model Form Uncertainty for Different Suspension Strut Models. In: M. Zhu (Hg.): Model Validation and Uncertainty Quantification, Volume 3. Proceedings of the 38th IMAC. Springer, Cham, S. 255-263.

[40] Feldmann, Robert; Gehb, Christopher M.; Schäffner, Maximilian; Matei, Alexander; Lenz, Jonathan; Kersting, Sebastian; Weber Moritz (2020): A Detailed Assessment of Model Form Uncertainty in a Load-Carrying Truss Structure. In: M. Zhu (Hg.): Model Validation and Uncertainty Quantification, Volume 3. Proceedings of the 38th IMAC. Springer, Cham, S. 303-314.

[41] Schaeffner, Maximilian; Platz, Roland; Melz, Tobias (2020): Adequate mathematical beam-column model for active buckling control in a tetrahedron truss structure. In: M. Zhu (Hg.): Model Validation and Uncertainty Quantification, Volume 3. Proceedings of the 38th IMAC. Springer, Cham, S. 323-332.

Subproject Managers

Photo Name Contact
H
Prof. Dr.-Ing. Holger Hanselka
Prof. Dr.-Ing. Tobias Melz
+49 6151 16-23657
Dr.-Ing. Roland Platz