Fast Bayesian identification of a class of elastic weakly nonlinear systems using backbone curves

This paper introduces a method for the identification of the parameters of nonlinear structures using a probabilistic Bayesian framework, employing a Markov chain Monte Carlo algorithm. This approach uses analytical models to describe the unforced, undamped dynamic responses of structures in the frequency–amplitude domain, known as the backbone curves. The analytical models describing these backbone curves are then fitted to measured responses, found using the resonant-decay method. To investigate the proposed identification method, a nonlinear two-degree-of-freedom example structure is simulated numerically and analytical expressions describing the backbone curves are found. These expressions are then used, in conjunction with the backbone curve data found through simulated experiment, to estimate the system parameters. It is shown that the use of these computationally-cheap analytical expressions allows for an extremely efficient method for modelling the dynamic behaviour, providing an identification procedure that is both fast and accurate. Furthermore, for the example structure, it is shown that the estimated parameters may be used to accurately predict the existence of dynamic behaviours that are well-away from the backbone curve data provided; specifically the existence of an isola is predicted

Substructurability:The effect of interface location on a real-time dynamic substructuring test

A full-scale experimental test for large and complex structures is not always achievable. This can be due to many reasons, the most prominent one being the size limitations of the test. Real-time dynamic substructuring is a hybrid testing method where part of the system is modelled numerically and the rest of the system is kept as the physical test specimen. The numerical–physical parts are connected via actuators and sensors and the interface is controlled by advanced algorithms to ensure that the tested structure replicates the emulated system with sufficient accuracy. The main challenge in such a test is to overcome the dynamic effects of the actuator and associated controller, that inevitably introduce delay into the substructured system which, in turn, can destabilize the experiment. To date, most research concentrates on developing control strategies for stable recreation of the full system when the interface location is given a priori. Therefore, substructurability is mostly studied in terms of control. Here, we consider the interface location as a parameter and study its effect on the stability of the system in the presence of delay due to actuator dynamics and define substructurability as the system’s tolerance to delay in terms of the different interface locations. It is shown that the interface location has a major effect on the tolerable delays in an experiment and, therefore, careful selection of it is necessary

Connecting nonlinear normal modes to the forced response of a geometric nonlinear structure with closely spaced modes

This paper numerically and experimentally investigates the relationship between the nonlinear normal modes and the forced response of a clamped-clamped cross beam structure. The system possesses closely-spaced linear modes such that the applied force distribution across the structure plays a central role in the appropriation of the nonlinear normal modes. Numerical simulations show that the quadrature conditions of the forced response does not necessarily match the peak response nor the nonlinear normal modes of the underlying conservative system, but instead are dependent upon the applied excitation. Experimental investigations performed with a single-point excitation and control based continuation further demonstrate the necessity for appropriate forcing in order to extract the NNMs of such systems.</p

Emulator-Based Control for Actuator-Based Hardware-in-the-Loop Testing, Control Engineering Practice

Abstract Hardware-in-the-loop (HWiL) is a form of component testing where hardware components a linked with software models. In order to test mechanical components an additional transfer system is required to link the software and hardware subsystems. The transfer system typically comprises of sensors and actuators and the dynamic effects of these components need to be eliminated to give accurate results. In this paper an emulator-based control strategy is presented for actuator based HWiL. Emulator-based control can solve the twin problems of stability and fidelity caused by the unwanted transfer system (actuator) dynamics. Significantly EBC can emulate the inverse of a transfer system which is not causally invertible, allowing a wider range of more complex transfer systems to be controlled. A robustness analysis is given and experimental results presented