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Nonlinear normal modes (NNMs) are widely used as a tool for developing mathematical models of nonlinear structures and understanding their dynamics. NNMs can be identified experimentally through a phase quadrature condition between the system response and the applied excitation. This paper demonstrates that this commonly used quadrature condition can give results that are significantly different from the true NNM, in particular, when the excitation applied to the system is limited to one input force, as is frequently used in practice. The system studied is a clamped–clamped cross-beam with two closely spaced modes. This paper shows that the regions where the quadrature condition is (in)accurate can be qualitatively captured by analysing transfer of energy between the modes of the system, leading to a discussion of the appropriate number of input forces and their locations across the structure.

Abstract. Offshore wind turbine (OWT) support structures need to be designed against fatigue failure under cyclic aerodynamic and wave loading. The fatigue failure can be accelerated in a corrosive sea environment. Traditionally, a stress–life approach called the S–N (stress–number of cycles) curve method has been used for the design of structures against fatigue failure. There are a number of limitations in the S–N approach related to welded structures which can be addressed by the fracture mechanics approach. In this paper the limitations of the S–N approach related to OWT support structure are addressed and a fatigue design framework based on fracture mechanics is developed. The application of the framework to a monopile OWT support structure is demonstrated and optimisation of in-service inspection of the structure is studied. It was found that both the design of the weld joint and non-destructive testing (NDT) techniques can be optimised to reduce in-service inspection frequency. Furthermore, probabilistic fracture mechanics as a form of risk-based design is outlined and its application to the monopile support structure is studied. The probabilistic model showed a better capability to account for NDT reliability over a range of possible crack sizes as well as to provide a risk associated with the chosen inspection time which can be used in inspection cost–benefit analysis. There are a number of areas for future research, including a better estimate of fatigue stress with a time-history analysis, the application of the framework to other types of support structures such as jackets and tripods, and integration of risk-based optimisation with a cost–benefit analysis.

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. 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. 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.

Abstract To provide an eco-friendly disposal way of increasingly accumulated waste tyres and reduce the environmental impact caused by the production of industrial fibres, this study explores the feasibility of using recycled tyre materials as substitutes for natural fine aggregates and manufactured fibres in cementitious mortar. The effects of crumb rubber (CR) replacement ratio (5%–15% by volume of fine aggregates), recycled tyre steel (RTS) fibre content (0.5–1.5 vol%) and recycled tyre polymer (RTP) fibre content (0.5–1.0 vol%) on the engineering properties of fibre reinforced cementitious composite (FRRC) were experimentally investigated. Results indicate that the pre-treated CR using NaOH solution is feasible to combine with a high dosage of recycled fibres without considerably weakening the workability, bulk density, ultrasonic pulse velocity and compressive strength of FRRC. The incorporation of CR, RTS fibre and RTP fibre together can reduce the drying shrinkage by up to 41.6% and enhance the flexural strength by at most 174% as compared to the plain mortar. The production cost, embodied carbon and embodied energy of FRRC are decreased by 13.3%–68.2% when replacing the manufactured fibres with recycled tyre fibres. The optimal content of CR and RTS fibre and RTP fibre is 5%–10%, 1.0 vol% and 0.5 vol%, respectively, considering the engineering properties, cost and environmental impact.

Wind turbine foundations are typically cast in place, leaving the concrete to mature under environmental conditions that vary in time and space. As a result, there is uncertainty around the concrete’s initial performance, and this can encourage both costly over-design and inaccurate prognoses of structural health. Here, we demonstrate the field application of a dense, wireless thermocouple network to monitor the strength development of an onshore, reinforced-concrete wind turbine foundation. Up-to-date methods in fly ash concrete strength and maturity modelling are used to estimate the distribution and evolution of foundation strength over 29 days of curing. Strength estimates are verified by core samples, extracted from the foundation base. In addition, an artificial neural network, trained using temperature data, is exploited to demonstrate that distributed concrete strengths can be estimated for foundations using only sparse thermocouple data. Our techniques provide a practical alternative to computational models, and could assist site operators in making more informed decisions about foundation design, construction, operation and maintenance.

The vibro-acoustic response of complex structures with uncertain properties is a problem of great concern for modern industries. In recent years, much research has been devoted to the prediction of this response in the mid-frequency range where, because neither Finite element analysis nor statistical energy analysis are appropriate, a hybrid deterministic-statistical approach becomes a suitable solution. Despite its potential, the existence of systems with active components that are too complex to be modelled numerically can limit the application of the method. However, it may still be possible to measure the dynamical response of these structures experimentally. This paper is hence concerned with the possibility of integrating experimental data into a hybrid deterministic-statistical method. To explain the new methodology, two similar case studies, consisting of a deterministic source structure that is coupled to a statistical plate receiver using passive isolators, are used. For each case, the vibratory excitation, characterised using in-situ blocked force measurements, the source structure mobility, and the isolators stiffness are experimentally determined and inserted in the proposed hybrid model of the system. The paper explains the techniques used for obtaining the considered experimental data and the theoretical model proposed for describing the systems. To validate the proposed approach, the predicted vibration response of the receiver plate is compared to the one obtained by experimentally randomising the plate in both case studies. The results show that a good agreement is obtained, both for the ensemble average response of the receiver structure and for the ensemble variance of this response. Moreover, the upper con dence bounds predicted by the hybrid method enclose well the ensemble of experimental results. The cause of some narrow-band differences observed between the predicted response and the experimental measurements is finally discussed. It is therefore concluded that the capabilities of the hybrid deterministic-statistical method can be clearly enhanced through the incorporation of experimental data prescribing active sub-systems.