Mathematical modelling of postbuckling in a slender beam column for active stabilisation control with respect to uncertainty

Georg C. Enss; Roland Platz; Holger Hanselka

doi:10.1117/12.913766

27 March 2012 Mathematical modelling of postbuckling in a slender beam column for active stabilisation control with respect to uncertainty

Georg C. Enss, Roland Platz, Holger Hanselka

Author Affiliations +

Proceedings Volume 8341, Active and Passive Smart Structures and Integrated Systems 2012; 834119 (2012) https://doi.org/10.1117/12.913766
Event: SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring, 2012, San Diego, California, United States

Abstract

Buckling is an important design constraint in light-weight structures as it may result in the collapse of an entire structure. When a mechanical beam column is loaded above its critical buckling load, it may buckle. In addition, if the actual loading is not fully known, stability becomes highly uncertain. To control uncertainty in buckling, an approach is presented to actively stabilise a slender flat column sensitive to buckling. For this purpose, actively controlled forces applied by piezoelectric actuators located close to the column's clamped base stabilise the column against buckling at critical loading. In order to design a controller to stabilise the column, a mathematical model of the postcritically loaded system is needed. Simulating postbuckling behaviour is important to study the effect of axial loads above the critical axial buckling load within active buckling control. Within this postbuckling model, different kinds of uncertainty may occur: i) error in estimation of model parameters such as mass, damping and stiffness, ii) non-linearities e. g. in the assumption of curvature of the column's deflection shapes and many more. In this paper, numerical simulations based on the mathematical model for the postcritically axially loaded column are compared to a mathematical model based on experiments of the actively stabilised postcritically loaded real column system using closed loop identification. The motivation to develop an experimentally validated mathematical model is to develop of a model based stabilising control algorithm for a real postcritically axially loaded beam column.

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Georg C. Enss, Roland Platz, and Holger Hanselka "Mathematical modelling of postbuckling in a slender beam column for active stabilisation control with respect to uncertainty", Proc. SPIE 8341, Active and Passive Smart Structures and Integrated Systems 2012, 834119 (27 March 2012); https://doi.org/10.1117/12.913766

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