Alicia Gonzalez-Buelga

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.

An electromagnetic inerter-based vibration suppression device

This paper describes how an inerter-based device for structural vibration suppression can be realized using an electromagnetic transducer such as a linear motor. When the motor shaft moves, a difference of voltage is generated across the transducer coil. The voltage difference is proportional to the relative velocity between its two terminals. The electromagnetic transducer will exert a force proportional to current following the Lorentz principle if the circuit is closed around the transducer coil. If an electronic circuit consisting of a capacitor, an inductance and a resistance with the appropriate configuration is connected, the resulting force reflected back into the mechanical domain is equivalent to that achieved by a mechanical inerter-based device. The proposed configuration is easy to implement and very versatile, provided a high quality conversion system with negligible losses. With the use of electromagnetic devices, a new generation of vibration absorbers can be realized, for example in the electrical domain it would be relatively uncomplicated to synthesize multi-frequency or real time tunable vibration absorbers by adding electrical components in parallel. In addition by using resistance emulators in the electrical circuits, part of the absorbed vibration energy can be converted into usable power. Here an electromagnetic tuned inerter damper (E-TID) is tested experimentally using real time dynamic substructuring. A voltage compensation unit was developed in order to compensate for coil losses. This voltage compensation unit requires power, which is acquired through harvesting from the vibration energy using a resistance emulator. A power balance analysis was developed in order to ensure the device can be self sufficient. Promising experimental results, using this approach, have been obtained and are presented in this paper. The ultimate goal of this research is the development of autonomous electromagnetic vibration absorbers, able to harvest energy, convert it into usable power, and use it for vibration control and health monitoring.

Modelling real-time dynamic substructuring using partial delay differential equations

Real-time dynamic substructuring is a new component testing method for simulating the dynamics of complex engineering systems. The physical component is tested within a computer-generated ‘virtual’ environment using real-time control techniques. Delays in communication which occur between the component and the virtual environment can potentially destabilize the simulation. In this paper, the mechanism for this instability is examined using a beam-oscillator system as a case study. We will show how the stability and the amplitude response of the system change with the time delay. Numerical simulations of the reduced system as well as a full-delayed beam equation are performed. A series of experimental tests is carried out on a beam-oscillator system. Comparison of the theoretical, numerical and experimental results is presented and these agree remarkably well.

Bandwidth of a Nonlinear Harvester with Optimized Electrical Load

Many researchers have investigated the possibility of amplifying ambient vibrations and converting the associated kinetic energy into usable electric energy. The vast majority of vibration harvesting devices use mechanical oscillators to boost the amplitude of vibration; however, this can result in a rather narrow band of excitation over which the harvesting device is effective. One approach proposed to overcome this limitation is to substitute the conventional linear oscillator with an oscillator featuring a non-linear compliance characteristic: these mechanisms produce broader frequency responses. The design and optimization of nonlinear energy harvesting devices is however not trivial and there is no consensus among the publish works that the benefits of non-linear oscillators can be realized in the energy harvesting context. This work attempts to further develop understanding of nonlinear energy harvesters by investigating the optimum resistive load. The definition of an optimal load for the nonlinear device is first considered, given due consideration to bandwidth and stability of the operating point, and comparisons with linear devices is shown. Finally, the issue of multiple solutions in the frequency response is addressed.

Stability Switches in a Neutral Delay Differential Equation with Application to Real-Time Dynamic Substructuring

In this paper delay differential equations approach is used to model a real-time dynamic substructuring experiment. Real-time dynamic substructuring involves dividing the structure under testing into two or more parts. One part is physically constructed in the lab- oratory and the remaining parts are being replaced by their numerical models. The numerical and physical parts are connected via an actuator. One of the main difficulties of this testing technique is the presence of delay in a closed loop system. We apply real-time dynamic sub- structuring to a nonlinear system consisting of a pendulum attached to a mass-spring-damper. We will show how a delay can have (de)stabilising effect on the behaviour of the whole system. Theoretical results agree very well with experimental data.

Strategies for Coupled Vibration Suppression and Energy Harvesting

The use of tuned-mass-dampers (TMD) as structural vibration suppressors has been discussed widely over several decades and many parameter selection strategies exist for minimising the displacement of the host structure. Normally these strategies work best when the resonant frequency of the TMD is closely tuned to that of the structural mode that is being targeted. This can be an issue for structures with significant live loads such as slender bridges with heavy traffic. For this type of structure nonlinear or semi-active retunable TMDs have been proposed. In this paper we consider replacing the damper in the TMD with an electrical generator device. In its simplest form this device could be a motor/generator with a resistive load such that the velocity- force relationship is approximately proportional hence mimicking a viscous damper. Here we consider using a voice-coil linear actuator connected to an impedance emulator, which is capable of harvesting, rather than dissipating, some of the vibrational energy. We discuss how this harvested power can then be used to modify the resistive loading in real-time and hence allow a wider bandwidth of operation. The work present both numerical and experimental results and shows some viable strategies for the control and the design of the device.

Vibration absorber and harvester for energy efficient structures

Most work has been conducted on vibration absorbers, such as tuned mass dampers, where significant energy is extracted from a structure. We investigate the concept of recovering some of this energy electrically. We present experimental results from a vibration absorber/harvester. Our results suggest that sufficient energy might be harvested such the device can be self tuning and self powered to optimize vibration suppression.Copyright

Optimum Load for Energy Harvesting with Non-linear Oscillators

A viable way to increase the band-width of a vibration-based energy harvester is exploiting the frequency response of non-linear oscillators. In the literature there are several works on resonating energy harvesters featuring non-linear oscillators. In the majority of these works, the harvester powers purely resistive loads. Given the complex behaviour of non-linear energy harvesters, it is difficult to identify the optimum load for these kind of devices. The aim of this work is to find the optimal load for a non-linear energy harvester in the case of purely resistive loads. The work, following the analysis of a non-linear energy harvesting with hardening compliance, introduces a methodology based on numerical continuation which can be used to find the optimum load once the characteristics of device as well as the excitation is known.

A Comparison of Runge Kutta and Novel L-Stable Methods for Real-Time Integration Methods for Dynamic Substructuring

In this paper we compare the performance of Runge-Kutta and novel L-stable real-time (LSRT) integration algorithms for real-time dynamic substructuring testing. Substructuring is a hybrid numerical-experimental testing method which can be used to test critical components in a system experimentally while the remainder of the system is numerically modelled. The physical substructure and the numerical model must interact in real time in order to replicate the behavior of the whole (or emulated) system. The systems chosen for our study are mass-spring-dampers, which have well known dynamics and therefore we can benchmark the performance of the hybrid testing techniques and in particular the numerical integration part of the algorithm. The coupling between the numerical part and experimental part is provided by an electrically driven actuator and a load cell. The real-time control algorithm provides bi-directional coupling and delay compensation which couples together the two parts of the overall system. In this paper we consider the behavior of novel L-stable real-time (LSRT) integration algorithms, which are based on Rosenbrocks method. The new algorithms have considerable advantages over 4th order Runge-Kutta in that they are unconditionally stable, real-time compatible and less computationally intensive. They also offer the possibility of damping out unwanted high frequencies and integrating stiff problems. The paper presents comparisons between 4th order Runge-Kutta and the LSRT integration algorithms using three experimental configurations which demonstrate these properties.Copyright

Modelling Autoparametric Resonance in a Coupled Pendulum Oscillator System Using Hybrid Testing

Hybrid testing is a novel form of system modelling which consists of a model which is part numerical, part experimental. This form of testing has applications in the automotive, aerospace and construction industry where it is being developed as an advanced form of component testing. In this paper we present results from a hybrid numerical-experimental system of a coupled pendulum oscillator system. This system is a good test case example for developing the science of hybrid testing because it has clearly defined linear and nonlinear parts. We show how such a system can be modeled by coupling an experimental pendulum with a numerical oscillator. We include discussion on delay effects, control techniques, accuracy and stability of the system.Copyright