In this paper a novel type of frictionless mechanical inerter device is presented, where instead of gears, motion of the flywheel is achieved using living-hinges. The design is a type of pivoted ...flywheel inerter inspired in part by the Dynamic Anti-resonant Vibration Isolator (DAVI) concept, which was first developed in the 1960s. Unlike the DAVI, it will be shown that the pivoted flywheel inerter has the advantage of producing balanced forces. Furthermore the use of living-hinges eliminates the need for gears or other frictional elements in the inerter mechanism. To demonstrate the utility of the new concept, a bench-top experiment was performed using a small-scale living-hinge inerter manufactured using polypropylene hinges. By estimating the experimental system parameters, the transmissibility results from the experiment could be compared to a mathematical model. These results showed that the living-hinge inerter provided an isolation effect of at least three orders of magnitude in terms of the maximum amplitude reduction from the uncontrolled system compared to that with the inerter added. Although friction was eliminated, the living-hinges did introduce additional damping, and this was found to correspond to an increase in the equivalent damping ratio for the uncontrolled system of 1.2%. It is shown that the living-hinge inerter developed in this paper fits all of the essential conditions required to be a practical inerter device. Furthermore, as it operates without mechanical friction, or fluid flow, it represents a new paradigm in experimental inerter technology.
Linear modal analysis is a useful and effective tool for the design and analysis of structures. However, a comprehensive basis for nonlinear modal analysis remains to be developed. In the current ...work, a machine learning scheme is proposed with a view to performing nonlinear modal analysis. The scheme is focussed on defining a one-to-one mapping from a latent ‘modal’ space to the natural coordinate space, whilst also imposing orthogonality of the mode shapes. The mapping is achieved via the use of the recently-developed cycle-consistent generative adversarial network (cycle-GAN) and an assembly of neural networks targeted on maintaining the desired orthogonality. The method is tested on simulated data from structures with cubic nonlinearities and different numbers of degrees of freedom, and also on data from an experimental three-degree-of-freedom set-up with a column-bumper nonlinearity. The results reveal the method’s efficiency in separating the ‘modes’. The method also provides a nonlinear superposition function, which in most cases has very good accuracy.
•Cycle-GANs are used to define mappings between modal and physical coordinates.•An assembly of neural networks is used to enforce orthogonality of the mode shapes.•Statistical independence of modal coordinates is imposed by predefining the modal space.•Orthogonality in the frequency domain is used to pick the most efficient decomposition.•The effectiveness of the method is demonstrated on simulated and experimental systems.
The High Static Low Dynamic Stiffness (HSLDS) concept is a design strategy for a nonlinear anti-vibration mount that seeks to increase isolation by lowering the natural frequency of the mount whilst ...maintaining the same static load bearing capacity. It has previously been proposed that an HSLDS mount could be implemented by connecting linear springs in parallel with the transverse flexure of a composite bistable plate — a plate that has two stable shapes between which it may snap. Using a bistable plate in this way will lead to lightweight and efficient designs of HSLDS mounts. This paper experimentally demonstrates the feasibility of this idea. Firstly, the quasi-static force–displacement curve of a mounted bistable plate is determined experimentally. Then the dynamic response of a nonlinear mass–spring system incorporating this plate is measured. Excellent agreement is obtained when compared to theoretical predictions based on the measured force–displacement curve, and the system shows a greater isolation region and a lower peak response to base excitation than the equivalent linear system.
In this paper the backbone curves of a two-degree-of-freedom nonlinear oscillator are used to interpret its behaviour when subjected to external forcing. The backbone curves describe the loci of ...dynamic responses of a system when unforced and undamped, and are represented in the frequency–amplitude projection. In this study we provide an analytical method for relating the backbone curves, found using the second-order normal form technique, to the forced responses. This is achieved using an energy-based analysis to predict the resonant crossing points between the forced responses and the backbone curves. This approach is applied to an example system subjected to two different forcing cases: one in which the forcing is applied directly to an underlying linear mode and the other subjected to forcing in both linear modes. Additionally, a method for assessing the accuracy of the prediction of the resonant crossing points is then introduced, and these predictions are then compared to responses found using numerical continuation.
•Population-based SHM allows knowledge transfer between structures of a population.•Collecting manifolds of potential structural states, a fibre bundle is defined.•The normal-condition cross section ...is of particular interest in the SHM discipline.•A graph representation of structures in combination with graph neural networks is used to construct the section.•Method is demonstrated successfully on a population of simulated structures.
One of the requirements of the population-based approach to Structural Health Monitoring (SHM) proposed in the earlier papers in this sequence, is that structures be represented by points in an abstract space. Furthermore, these spaces should be metric spaces in a loose sense; i.e.there should be some measure of distance applicable to pairs of points; similar structures should then be ‘close’ in the metric. However, this geometrical construction is not enough for the framing of problems in data-based SHM, as it leaves undefined the notion of feature spaces. Interpreting the feature values on a structure-by-structure basis as a type of field over the space of structures, it seems sensible to borrow an idea from modern theoretical physics, and define feature assignments as sections in a vector bundle over the structure space. With this idea in place, one can interpret the effect of environmental and operational variations as gauge degrees of freedom, as in modern gauge field theories. One can then regard data normalisation procedures like cointegration as gauge-fixing operations. This paper will discuss the various geometrical structures required for an abstract theory of feature spaces in SHM, and will draw analogies with how these structures have shown their power in modern physics.
Having motivated a number of problems in Population-Based SHM (PBSHM) in geometrical terms, it remains to show how these problems might be solved. In the second part of the paper, the problem of determining the normal condition cross section of a feature bundle is addressed. The solution is provided by the application of Graph Neural Networks (GNN), a versatile non-Euclidean machine learning algorithm which is not restricted to inputs and outputs from vector spaces. In particular, the algorithm is well suited to operating directly on the sort of graph structures which are an important part of the proposed framework for PBSHM. The solution of the normal section problem is demonstrated for a heterogeneous population of truss structures for which the feature of interest is the first natural frequency. The GNN approach is shown to not only solve the normal section problem, but also to accommodate varying temperatures across the population; it thus provides a means of data normalisation.
In this paper, we describe a direct normal form decomposition for systems of coupled nonlinear oscillators. We demonstrate how the order of the system can be reduced during this type of normal form ...transformation process. Two specific examples are considered to demonstrate particular challenges that can occur in this type of analysis. The first is a 2 d.f. system with both quadratic and cubic nonlinearities, where there is no internal resonance, but the nonlinear terms are not necessarily
ε
1
-order small. To obtain an accurate solution, the direct normal form expansion is extended to
ε
2
-order to capture the nonlinear dynamic behaviour, while simultaneously reducing the order of the system from 2 to 1 d.f. The second example is a thin plate with nonlinearities that are
ε
1
-order small, but with an internal resonance in the set of ordinary differential equations used to model the low-frequency vibration response of the system. In this case, we show how a direct normal form transformation can be applied to further reduce the order of the system while simultaneously obtaining the normal form, which is used as a model for the internal resonance. The results are verified by comparison with numerically computed results using a continuation software.
The high static low dynamic stiffness (HSLDS) concept is a design strategy for an anti-vibration mount that seeks to increase isolation by lowering the natural frequency of the mount, whilst ...maintaining the same static load bearing capacity. Previous studies have successfully analysed many features of the response by modelling the concept as a Duffing oscillator. This study extends the previous findings by characterising the HSLDS model in terms of two simple parameters. A fifth-order polynomial model allows us to explore the effects of these parameters. We analyse the steady-state response, showing that simple changes to the shape of the force displacement curve can have large effects on the amplitude and frequency of peak response, and can even lead to unbounded response at certain levels of excitation. Harmonics of the fundamental response are also analysed, and it is shown that they are unlikely to pose significant design limitations. Predictions compare well to simulation results.
Digital twins seek to replicate a physical structure in a digital domain. For a digital twin to have close correspondence to its physical twin, data are required. However, it is not always possible, ...or cost-effective, to collect a complete set of data for a structure in all configurations of interest. It is nonetheless useful to repurpose data to help validate predictions for different configurations and scenarios. This statement is true in drilling applications, where, for example, the length of the drill string is altered throughout operation. This paper demonstrates how transfer learning, in the form of three domain-adaptation methods, — transfer component analysis (TCA), maximum independence domain adaptation (MIDA) and geodesic flow kernel (GFK) — can be used to construct a digital twin for localising torsional friction in deviated wells under structural changes (e.g., when the drill column gets longer). The method uses a physics-based torsional model to train a machine-learning classifier that can localise torsional friction for a given drill string length and diameter, where friction localisation labels are known (source). As the length or diameter of the drill string are altered in the field, transfer learning is utilised to map the classifier from the labelled (source) scenario onto these unlabelled (target) scenarios. As a result, transfer learning improves the performance of the classifier when applied to the target data, and increases the domain of validity for the classifier. The performance of the classifier, and therefore its suitability to new drill-string configurations, is estimated by utilising two different distance metrics between the source and a proposed target dataset.
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