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For slender beam-columns loaded by axial compressive forces, active buckling control provides a possibility to increase the maximum bearable axial load above that of a purely passive structure. In this paper, the potential of active buckling control of an imperfect beam-column with circular cross-section using piezo-elastic supports is investigated numerically. Imperfections are given by an initial deformation of the beam-column caused by a constant imperfection force. With the piezo-elastic supports, active bending moments in arbitrary directions orthogonal to the beam-column's longitudinal axis can be applied at both beam- column's ends. The imperfect beam-column is loaded by a gradually increasing axial compressive force resulting in a lateral deformation of the beam-column. First, a finite element model of the imperfect structure for numerical simulation of the active buckling control is presented. Second, an integral linear-quadratic regulator (LQR) that compensates the deformation via the piezo-elastic supports is derived for a reduced modal model of the ideal beam-column. With the proposed active buckling control it is possible to stabilize the imperfect beam-column in arbitrary lateral direction for axial loads above the theoretical critical buckling load and the maximum bearable load of the passive structure.

In this paper, active buckling control of an imperfect slender beam-column with circular cross-section by piezo-elastic supports and Linear Parameter-Varying (LPV) control is investigated experimentally. The beam-column is loaded by a time-varying axial compressive load resulting in a lateral deflection of the beam-column due to imperfections. A finite element model of the beam-column under axial load is designed as an LPV system. A reduced and augmented modal model is used to design a quadratically stable gain scheduled LPV control. The control is implemented in an experimental test setup and the maximum bearable loads of the beam-column are obtained. Two cases are tested: with and without LPV control or, respectively, active and passive configuration. With the proposed active LPV buckling control it is possible to compensate the influence of beam-column imperfections and to compensate uncertainty in mounting and loading that in passive configuration without LPV control may lead to early buckling. Eventually, the maximum bearable axial compressive load is increased above the theoretical critical buckling load.

Buckling of slender beam-columns subject to axial compressive loads represents a critical design constraint for light-weight structures. Active buckling control provides a possibility to stabilize slender beam-columns by active lateral forces or bending moments. In this paper, the potential of active buckling control of an axially loaded beam-column with circular solid cross-section by piezo-elastic supports is investigated experimentally. In the piezo-elastic supports, lateral forces of piezoelectric stack actuators are transformed into bending moments acting in arbitrary directions at the beam-column ends. A mathematical model of the axially loaded beam-column is derived to design an integral linear quadratic regulator (LQR) that stabilizes the system. The effectiveness of the stabilization concept is investigated in an experimental test setup and compared with the uncontrolled system. With the proposed active buckling control it is possible to stabilize the beam-column in arbitrary lateral direction for axial loads up to the theoretical critical buckling load of the system.

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.

Beams in lightweight truss structures are subject to axial and lateral loads that may lead to undesired structural vibration or failure by buckling. The axial and lateral forces may be transferred via the truss supports that offer possibilities for state control of single beams and larger structures. In earlier own studies, the concept of a piezo-elastic support for active buckling control and resonant shunt damping has been investigated. An elastic spring element is used to allow a rotation in the beam's bearing in any plane perpendicular to the beam's longitudinal axis. The rotation is laterally transferred to an axial displacement of piezoelectric stack transducers that are either used to generate active lateral forces for active buckling control or to attenuate vibrations with a resonant shunt. In this paper, the model verification and validation of the elastic properties of the piezo-elastic support for passive and active structural control of beams with circular cross-section is presented. The rotational and lateral spring element stiffness is investigated numerically and experimentally and the existing models are updated in the verification process. The model is validated by comparing the numerical results and experimental ability for vibration attenuation.

Buckling of slender load-bearing beam-columns is a crucial failure scenario in light-weight structures as it may result in the collapse of the entire structure. If axial load and load capacity are unknown, stability becomes uncertain. To compensate this uncertainty, the authors successfully developed and evaluated an approach for active buckling control for a slender beam-column, clamped at the base and pinned at the upper end. Active lateral forces are applied with two piezoelectric stack actuators in opposing directions near the beam-column' clamped base to prevent buckling. A Linear Quadratic Regulator is designed and implemented on the experimental demonstrator and statistical tests are conducted to prove effectivity of the active approach. The load capacity of the beam-column could be increased by 40% and scatter of buckling occurrences for increasing axial loads is reduced. Weibull analysis is used to evaluate the increase of the load capacity and its related uncertainty compensation.

Uncertainty in usage of load-carrying systems mainly results from not fully knownloads and strength. This article discusses basic approaches to control uncertainty in usage ofload-carrying systems by passive and active means. An active low damped column system critical to buckling is presented in which a slender column can be stabilised actively by piezo stackactuators at one of its ends only. Uncertainty may be controlled in the active column systemby temporarily enhancing the bearable axial load theoretically up to three times compared to the passive column system in case of critical loading. However, in the implementation of theseapproaches, system-speci c uncertainty may also occur. In numerical examinations it is shown, that small deviations in measured axial loading may increase the active force signi cantly to achieve stabilisation. The increase of applied active force might affect lifetime of the piezo stackactuators and thus the stabilising capability of the active column system.

Buckling of load-carrying beam-columns is a severe failure scenario in light-weight structures. The authors present an approach to actively stabilize a slender beam-column under static axial load to prevent it from buckling in its first buckling mode. For that, controlled active counteracting forces are applied by two piezoelectric stack actuators near the column’s fixed base, achieving a 40% higher axial critical load and leaving most of the column’s surface free from actuation devices. However, uncertain actuator properties due to tolerances in characteristic maximum free stroke and blocking force capability have an influence on the active stabilization. This uncertainty and its effect on active buckling control is investigated by numerical simulation, based on experimental tests to determine the actual maximum free stroke and blocking force for several piezoelectric stack actuators. The simulation shows that the success of active buckling control depends on the actuator’s variation in its maximum free stroke and blocking force capability.

Buckling of axially loaded beam-columns represents a critical design constraint for light-weight structures. Besides passive solutions to increase the critical buckling load, active buckling control provides a possibility to stabilize slender elements in structures. So far, buckling control by active forces or bending moments has been mostly investigated for beam-columns with rectangular cross-section and with a preferred direction of buckling. The proposed approach investigates active buckling control of a beam-column with circular solid cross-section which is fixed at its base and pinned at its upper end. Three controlled active lateral forces are applied near the fixed base with angles of 120° to each other to stabilize the beam-column and allow higher critical axial loads. The beam-column is subject to supercritical static axial loads and lateral disturbance forces with varying directions and offsets. Two independent modal state space systems are derived for the bending planes in the lateral y- and z-directions of the circular cross-section. These are used to design two linear-quadratic regulators (LQR) that determine the necessary control forces which are transformed into the directions of the active lateral forces. The system behavior is simulated with a finite element model using one-dimensional beam elements with six degrees of freedom at each node. With the implemented control, it is possible to actively stabilize a beam-column with circular cross-section in arbitrary buckling direction for axial loads significantly above the critical axial buckling load.

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.