Dj Wagg

An adaptive polynomial based forward prediction algorithm for multi-actuator real-time dynamic substructuring

Real-time dynamic substructuring is a novel experimental technique used to test the dynamic behaviour of complex structures. The technique involves creating a hybrid model of the entire structure by combining an experimental test piece—the substructure—with a set of numerical models. In this paper we describe a multi-actuator substructured system of a coupled three mass–spring–damper system and use this to demonstrate the nature of delay errors which can first lead to a loss of accuracy and then to instability of the substructuring algorithm. Synchronization theory and delay compensation are used to show how the delay errors, present in the transfer systems, can be minimized by online forward prediction. This new algorithm uses a more generic approach than the single step algorithms applied to substructuring thus far, giving considerable advantages in terms of flexibility and accuracy. The basic algorithm is then extended by closing the control loop resulting in an error driven adaptive feedback controller which can operate with no prior knowledge of the plant dynamics. The adaptive algorithm is then used to perform a real substructuring test using experimentally measured forces to deliver a stable substructuring algorithm.

Real-time dynamic substructuring in a coupled oscillator-pendulum system

Real-time dynamic substructuring is a powerful testing method, which brings together analytical, numerical and experimental tools for the study of complex structures. It consists of replacing one part of the structure with a numerical model, which is connected to the remainder of the physical structure (the substructure) by a transfer system. In order to provide reliable results, this hybrid system must remain stable during the whole test. A primary mechanism for destabilization of these type of systems is the delays which are naturally present in the transfer system. In this paper, we apply the dynamic substructuring technique to a nonlinear system consisting of a pendulum attached to a mechanical oscillator. The oscillator is modelled numerically and the transfer system is an actuator. The system dynamics is governed by two coupled second-order neutral delay differential equations. We carry out local and global stability analyses of the system and identify the delay dependent stability boundaries for this type of system. We then perform a series of hybrid experimental tests for a pendulum–oscillator system. The results give excellent qualitative and quantitative agreement when compared to the analytical stability results.

Adaptive Structures: Engineering Applications

List of Contributors. Preface. 1 Adaptive Structures for Structural Health Monitoring (Daniel J. Inman and Benjamin L. Grisso). 1.1 Introduction. 1.2 Structural Health Monitoring. 1.3 Impedance-Based Health Monitoring. 1.4 Local Computing. 1.5 Power Analysis. 1.6 Experimental Validation. 1.7 Harvesting, Storage and Power Management. 1.8 Autonomous Self-healing. 1.9 The Way Forward: Autonomic Structural Systems for Threat Mitigation. 1.10 Summary. Acknowledgements. References. 2 Distributed Sensing for Active Control (Suk-Min Moon, Leslie P. Fowler and Robert L. Clark). 2.1 Introduction. 2.2 Description of Experimental Test Bed. 2.3 Disturbance Estimation. 2.4 Sensor Selection. 2.5 Conclusions. Acknowledgments. References. 3 Global Vibration Control Through Local Feedback (Stephen J. Elliott). 3.1 Introduction. 3.2 Centralised Control of Vibration. 3.3 Decentralised Control of Vibration. 3.4 Control of Vibration on Structures with Distributed Excitation. 3.5 Local Control in the Inner Ear. 3.6 Conclusions. Acknowledgements. References. 4 Lightweight Shape-Adaptable Airfoils: A New Challenge for an Old Dream (L.F. Campanile). 4.1 Introduction. 4.2 Otto Lilienthal and the Flying Machine as a Shape-Adaptable Structural System. 4.3 Sir George Cayley and the Task Separation Principle. 4.4 Being Lightweight: A Crucial Requirement. 4.5 Coupling Mechanism and Structure: Compliant Systems as the Basis of Lightweight Shape-Adaptable Systems. 4.6 Extending Coupling to the Actuator System: Compliant Active Systems. 4.7 A Powerful Distributed Actuator: Aerodynamics. 4.8 The Common Denominator: Mechanical Coupling. 4.9 Concluding Remarks. Acknowledgements. References. 5 Adaptive Aeroelastic Structures (Jonathan E. Cooper). 5.1 Introduction. 5.2 Adaptive Internal Structures. 5.3 Adaptive Stiffness Attachments. 5.4 Conclusions. 5.5 The Way Forward. Acknowledgements. References. 6 Adaptive Aerospace Structures with Smart Technologies - A Retrospective and Future View (Christian Boller). 6.1 Introduction. 6.2 The Past Two Decades. 6.3 Added Value to the System. 6.4 Potential for the Future. 6.5 A Reflective Summary with Conclusions. References. 7 A Summary of Several Studies with Unsymmetric Laminates (Michael W. Hyer, Marie-Laure Dano, Marc R. Schultz, Sontipee Aimmanee and Adel B. Jilani). 7.1 Introduction and Background. 7.2 Room-Temperature Shapes of Square [02/902]T Cross-Ply Laminates. 7.3 Room-Temperature Shapes of More General Unsymmetric Laminates. 7.4 Moments Required to Change Shapes of Unsymmetric Laminates. 7.5 Use of Shape Memory Alloy for Actuation. 7.6 Use of Piezoceramic Actuation. 7.7 Consideration of Small Piezoceramic Actuators. 7.8 Conclusions. References. 8 Negative Stiffness and Negative Poissons Ratio in Materials which Undergo a Phase Transformation (T.M. Jaglinski and R.S. Lakes). 8.1 Introduction. 8.2 Experimental Methods. 8.3 Composites. 8.4 Polycrystals. 8.5 Discussion. References. 9 Recent Advances in Self-Healing Materials Systems (M.W. Keller, B.J. Blaiszik, S.R. White and N.R. Sottos). 9.1 Introduction. 9.2 Faster Healing Systems - Fatigue Loading. 9.3 Smaller Size Scales. 9.4 Alternative Materials Systems - Elastomers. 9.5 Microvascular Autonomic Composites. 9.6 Conclusions. References. 10 Adaptive Structures - Some Biological Paradigms (Julian F.V. Vincent). 10.1 Introduction. 10.2 Deployment. 10.3 Turgor-Driven Mechanisms. 10.4 Dead Plant Tissues. 10.5 Morphing and Adapting in Animals. 10.6 Sensing in Arthropods - Campaniform and Slit Sensilla. 10.7 Developing an Interface Between Biology and Engineering. 10.8 Envoi. Acknowledgements. References. Index.

Applying the method of normal forms to second-order nonlinear vibration problems

Vibration problems are naturally formulated with second-order equations of motion. When the vibration problem is nonlinear in nature, using normal form analysis currently requires that the second-order equations of motion be put into first-order form. In this paper, we demonstrate that normal form analysis can be carried out on the second-order equations of motion. In addition, for forced, damped, nonlinear vibration problems, we show that the invariance properties of the first- and second-order transforms differ. As a result, using the second-order approach leads to a simplified formulation for forced, damped, nonlinear vibration problems.

Dynamic snap-through for morphing of bi-stable composite plates

Composite laminate plates designed to have two statically stable configurations have been the focus of recent research, with a particular emphasis on morphing applications. In this article, we consider how external vibration energy can be used to assist with the actuation between stable states. This is of interest in the case when surface bonded macro-fiber composites (MFC) actuators are employed as the actuation system. Typically, these type of actuators have been found to require considerably high voltage inputs to achieve significant levels of actuation authority. Therefore, assisting the actuation process will allow lower voltages and/or stiffer plates to be actuated. Two bi-stable plates with different thickness, [04 - 904]T and [02 - 902]T, are tested. The results show a significant reduction in the force required to change state for the case where dynamic excitation provided by an MFC actuator is used to assist the process. This strategy demonstrates the potential of dynamically assisting actuation as a mechanism for morphing of bi-stable composites.

CHATTER, STICKING AND CHAOTIC IMPACTING MOTION IN A TWO-DEGREE OF FREEDOM IMPACT OSCILLATOR

We consider the dynamics of a two-degree of freedom impact oscillator subject to a motion limiting constraint. These systems exhibit a range of periodic and nonperiodic impact motions. For a particular set of parameters, we consider the bifurcations which occur between differing regimes of impacting motion and in particular those which occur due to a grazing bifurcation. Unexpected resonant behavior is also observed, due to the complexity of the dynamics. We consider both periodic and chaotic chatter motions and the regions of sticking which exist. Finally we consider the types of chaotic motion that occur within the parameter range. We discuss the possibility in relating successive low velocity impacts, especially with respect to possible low dimensional mappings for such a system.

The use of normal forms for analysing nonlinear mechanical vibrations

A historical introduction is given of the theory of normal forms for simplifying nonlinear dynamical systems close to resonances or bifurcation points. The specific focus is on mechanical vibration problems, described by finite degree-of-freedom second-order-in-time differential equations. A recent variant of the normal form method, that respects the specific structure of such models, is recalled. It is shown how this method can be placed within the context of the general theory of normal forms provided the damping and forcing terms are treated as unfolding parameters. The approach is contrasted to the alternative theory of nonlinear normal modes (NNMs) which is argued to be problematic in the presence of damping. The efficacy of the normal form method is illustrated on a model of the vibration of a taut cable, which is geometrically nonlinear. It is shown how the method is able to accurately predict NNM shapes and their bifurcations.

Out-of-unison resonance in weakly nonlinear coupled oscillators

Resonance is an important phenomenon in vibrating systems and, in systems of nonlinear coupled oscillators, resonant interactions can occur between constituent parts of the system. In this paper, out-of-unison resonance is defined as a solution in which components of the response are 90° out-of-phase, in contrast to the in-unison responses that are normally considered. A well-known physical example of this is whirling, which can occur in a taut cable. Here, we use a normal form technique to obtain time-independent functions known as backbone curves. Considering a model of a cable, this approach is used to identify out-of-unison resonance and it is demonstrated that this corresponds to whirling. We then show how out-of-unison resonance can occur in other two degree-of-freedom nonlinear oscillators. Specifically, an in-line oscillator consisting of two masses connected by nonlinear springs—a type of system where out-of-unison resonance has not previously been identified—is shown to have specific parameter regions where out-of-unison resonance can occur. Finally, we demonstrate how the backbone curve analysis can be used to predict the responses of forced systems.

Use of control to maintain period-1 motions during wind-up or wind-down operations of an impacting driven beam

We consider the dynamical response of a thin beam held fixed at one end while excited by an external driving force. A motion limiting constraint, or stop, causes the beam to impact. During wind-up or wind-down operations, in which the driving frequency is continuously altered, the system can undergo complicated motions close to the value of frequency at which impacts may first occur, the grazing bifurcation. In this region, the beam may experience several impacts within a long period-repeating solution or even chaotic behavior which, in practical terms, may be undesirable to the long-term integrity of the system. The first task is to identify the zones in the space of parameters (forcing amplitude or, alternatively, the gap between the beam and the stop) in which period-1 motions can be guaranteed. In this paper, in the areas in which complicated or chaotic motion occurs, a control strategy is proposed which stabilises unstable period-1 motions. As a consequence, numerical simulations indicate that, for any choice of parameter in the range, simple period-1 motions can be maintained, limiting the number of impacts (together with their velocity).

Optimum resistive loads for vibration-based electromagnetic energy harvesters with a stiffening nonlinearity

The exploitation of nonlinear behavior in vibration-based energy harvesters has received much attention over the last decade. One key motivation is that the presence of nonlinearities can potentially increase the bandwidth over which the excitation is amplified and therefore the efficiency of the device. In the literature, references to resonating energy harvesters featuring nonlinear oscillators are common. In the majority of the reported studies, the harvester powers purely resistive loads. Given the complex behavior of nonlinear energy harvesters, it is difficult to identify the optimum load for this kind of device. In this paper the aim is to find the optimal load for a nonlinear energy harvester in the case of purely resistive loads. This work considers the analysis of a nonlinear energy harvester with hardening compliance and electromagnetic transduction under the assumption of negligible inductance. It also introduces a methodology based on numerical continuation which can be used to find the optimum load for a fixed sinusoidal excitation.