SUMMARYThis paper proposes the use of a novel type of passive vibration control system to reduce vibrations in civil engineering structures subject to base excitation. The new system is based on the inerter, a device that was initially developed for high‐performance suspensions in Formula 1 racing cars. The principal advantage of the inerter is that a high level of vibration isolation can be achieved with low amounts of added mass. This feature makes it an attractive potential alternative to traditional tuned mass dampers (TMDs). In this paper, the inerter system is modelled inside a multi‐storey building and is located on braces between adjacent storeys. Numerical results show that an excellent level of vibration reduction is achieved, potentially offering improvement over TMDs. The inerter‐based system is compared to a TMD system by using a range of base excitation inputs, including an earthquake signal, to demonstrate how the performance could potentially be improved by using an inerter instead of a TMD. Copyright © 2013 John Wiley & Sons, Ltd.

ReuseUnless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version -refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher's website. TakedownIf you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. 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.Synchronisation theory and delay compensation are used to show how the delay errors, present in the transfer systems, can be minimised 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.

SUMMARYReal-time dynamic substructuring is an experimental technique for testing the dynamic behaviour of complex structures. It involves creating a hybrid model of the entire structure by combining an experimental test piece-the substructure-with a numerical model describing the remainder of the system. The technique is useful when it is impractical to experimentally test the entire structure or complete numerical modelling is insu cient.In this paper, we focus on the in uence of delay in the system, which is generally due to the inherent dynamics of the transfer systems (actuators) used for structural testing. This naturally gives rise to a delay di erential equation (DDE) model of the substructured system. With the case of a substructured system consisting of a single mass-spring oscillator we demonstrate how a DDE model can be used to understand the in uence of the response delay of the actuator. Speciÿcally, we describe a number of methods for identifying the critical time delay above which the system becomes unstable.Because of the low damping in many large structures a typical situation is that a substructuring test would operate in an unstable region if additional techniques were not implemented in practice. We demonstrate with an adaptive delay compensation technique that the substructured mass-spring oscillator system can be stabilized successfully in an experiment. The approach of DDE modelling also allows us to determine the dependence of the critical delay on the parameters of the delay compensation scheme. Using this approach we develop an over-compensation scheme that will help ensure stable experimental testing from initiation to steady state operation. This technique is particularly suited to sti structures or those with very low natural damping as regularly encountered in structural engineering.

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.

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.

SUMMARYReal-time substructuring is a method of dynamically testing a structure without experimentally testing a physical model of the entire system. Instead the structure can be split into two linked parts, the region of particular interest, which is tested experimentally, and the remainder which is tested numerically. A transfer system, such as a hydraulic actuator or a shaking table, is used to impose the displacements at the interface between the two parts on the experimental substructure. The corresponding force imposed by the substructure on the transfer system is fed back to the numerical model. Control of the transfer system is critical to the accuracy of the substructuring process. A study of two controllers used in conjunction with the University of Bristol shaking table is presented here. A proof-of-concept one degree-of-freedom mass-spring-damper system is substructured such that a portion of the mass forms the experimental substructure and the remainder of the mass plus the spring and the damper is modelled numerically. Firstly a linear controller is designed and tested. Following this an adaptive substructuring strategy is considered, based on the minimal control synthesis algorithm. The deleterious e ect of oilcolumn resonance common to shaking tables is examined and reduced through the use of ÿlters. The controlled response of the experimental specimen is compared for the two control strategies.

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We present a continuation method that enables one to track or continue branches of periodic orbits directly in an experiment when a parameter is changed. A control-based setup in combination with Newton iterations ensures that the periodic orbit can be continued even when it is unstable. This is demonstrated with the continuation of initially stable rotations of a vertically forced pendulum experiment through a fold bifurcation to find the unstable part of the branch. Characterizing a nonlinear dynamical system typically requires the systematic investigation of stable and unstable steady-states and periodic orbits in the relevant parameter region of the system. When a mathematical model is available this task can be tackled efficiently by performing a bifurcation analysis with the method of numerical continuation. It allows one to find and follow (or continue) solutions when varying a parameter -a technique that can also be used to map out stability boundaries (bifurcations) in multiple parameters. Several software packages are available for this task; see the review papers [1,2] as an entry point to the literature.In physical experiments the use of continuation methods has proved much more difficult. One approach is a combination of system identification and feedback control as applied by [3,4] to equilibria. In principle, it is also applicable to periodic orbits [5] but, as is reported in [6], these methods do not generally work well when applied to real physical experiments. An alternative is extended time-delayed feedback (ETDF) [7,8], where the system is subject to a feedback loop with a delay that is given by the period of the periodic orbit one wishes to stabilize. This approach avoids system identification and, thus, is easier to implement in real experiments [9]; see also the recent collection of reviews [10]. An important prototype problem for experimental continuation is the continuation of a stable periodic orbit through a fold (saddle-node bifurcation). As one varies a system parameter the stable periodic orbit gradually loses stability and then becomes unstable as it 'turns around' at the fold point. One problem is that ETDF and its modifications such as described in [8] do not converge uniformly near a fold of periodic orbits, meaning that they can generally not be used for tracking through a fold point; for a treatment of the autonomous case see [11].We present and demonstrate here a continuation method that can be used directly in an experiment to continue periodic orbits irrespective of their stability. Our method does not require a mathematical model nor the setting of specific initial conditions. Instead it relies on standard feedback control. The feedback reference signal is updated by a Newton iteration that converges to a state where the control becomes zero. The general ideas behind this method are described and tested extensively in simulations in [12]. The implementation of feedback control requires one to measure some output of the experiment with sufficient accuracy and to provide inp...