Quantification and evaluation of uncertainty in active buckling control of a beam-column subject to dynamic axial loads
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 ma...
| Summary: | 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. So far, studies on active buckling control have investigated academic beam-column systems with rectangular cross-sections, high slenderness ratios and small critical buckling loads as well as (quasi-)static axial loads. In this thesis, 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, as opposed to the academic beam-column systems is investigated. 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.
This thesis opens with a review of the background in static and dynamic passive buckling and the previous research on active buckling control. The concept for active buckling control uses innovative piezo-elastic supports with integrated piezoelectric stack actuators. A mathematical linear parameter-varying (LPV) model of the axially loaded beam-column system with electrical components accounts for the axial load-dependency of the lateral dynamic behavior. The model is calibrated with experimental data and then used to design an LPV controller, in particular a gain-scheduled H_∞ controller, which guarantees stability and robust performance for the entire operation range of axial loads. Passive buckling and active buckling control are investigated in an experimental test setup with slowly increasing quasi-static and step-shaped dynamic axial loads. Probabilistic uncertainty in the maximum bearable quasi-static axial loads and the lateral deflections for dynamic axial loads due to component variations in a representative sample of beam-column systems is investigated experimentally. The experimental results are quantified and evaluated by three-parameter WEIBULL distributions and compared for the passive and active beam-column systems with respect to their most likely values and variability.
The proposed gain-scheduled H_∞ buckling control stabilizes the beam-column system in arbitrary lateral direction. For quasi-static axial loads, the most likely maximum bearable axial loads increase by 29% and the variability reduces by 70% when comparing the passive and active beam-column system. For dynamic axial loads, the most likely lateral deflections reduce by up to 87% and the variability reduces by up to 90%. Overall, the results of this thesis contribute to the application of active buckling control in practical truss structures. |
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