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.
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...
SUMMARYReal-time testing with dynamic substructuring is a novel experimental technique capable of assessing the behaviour of structures subjected to dynamic loadings including earthquakes. The technique involves recreating the dynamics of the entire structure by combining an experimental test piece consisting of part of the structure with a numerical model simulating the remainder of the structure. These substructures interact in real time to emulate the behaviour of the entire structure. Time integration is the most versatile method for analysing the general case of linear and non-linear semi-discretized equations of motion. In this paper we propose for substructure testing, L-stable real-time (LSRT) compatible integrators with two and three stages derived from the Rosenbrock methods. These algorithms are unconditionally stable for uncoupled problems and entail a moderate computational cost for real-time performance. They can also effectively deal with stiff problems, i.e. complex emulated structures for which solutions can change on a time scale that is very short compared with the interval of time integration, but where the solution of interest changes on a much longer time scale. Stability conditions of the coupled substructures are analysed by means of the zero-stability approach, and the accuracy of the novel algorithms in the coupled case is assessed in both the unforced and forced conditions. LSRT algorithms are shown to be more competitive than popular Runge-Kutta methods in terms of stability, accuracy and ease of implementation. Numerical simulations and real-time substructure tests are used to demonstrate the favourable properties of the proposed algorithms.
SUMMARYIn this paper, the use of a tuned inerter damper (TID) as a vibration absorber is studied numerically and experimentally, with civil engineering applications in mind. Inerters complete the analogy between mechanical and electrical networks, as the mechanical element equivalent to a capacitor and were developed in the 2000s. Initially, inerters were used for applications in automotive engineering, where they are known as J-dampers. Recently, research has suggested that inerter-based networks could be used for civil engineering applications, offering interesting advantages over traditional tuned mass dampers. In the civil engineering context, research has been mainly theoretical, considering ideal inerters. Because the dynamics of an inerter device include nonlinearities, especially at the low frequencies associated with civil engineering applications, the performance of the TID device using an off-theshelf inerter has been experimentally tested in the work presented here. The chosen system, comprising a host structure with a TID attached to it, was tested using real-time dynamic substructuring (RTDS) or hybrid testing. The inerter was tested physically, while the remaining components of the TID device, the spring and damper, together with the host structure, were simulated numerically. Displacements and forces at the interface between numerical and physical components are updated in real time. This numerical-physical split allows the optimisation of the TID parameters, because the values of the spring and the damper can be changed without altering the experimental setup. In addition, this configuration takes into account the inerter's potentially complex dynamics by testing it experimentally, together with the characteristics of the host structure. Developing RTDS tests for physical inertial substructures, where part of the fed back interface forces are proportional to acceleration, is a challenging task because of delays arising at the interface between the experimental and the numerical substructures. Problems associated with stability issues caused by delay and causality arise, because we are dealing with neutral and advanced delayed differential equations. A new approach for the substructuring algorithm is proposed, consisting of feeding back the measured force deviation from the ideal inerter instead of the actual force at the interface. The experimental results show that with appropriate retuning of the components in the TID device, the performance in the TID incorporating the real inerter device is close to the ideal inerter device.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.