Multistability and localization in forced cyclic symmetric structures modelled by weakly-coupled Duffing oscillators

Many engineering structures are composed of weakly coupled sectors assembled in a cyclic and ideally symmetric configuration, which can be simplified as forced Duffing oscillators. In this paper, we study the emergence of localized states in the weakly nonlinear regime. We show that multiple spatially localized solutions may exist, and the resulting bifurcation diagram strongly resembles the snaking pattern observed in a variety of fields in physics, such as optics and fluid dynamics. Moreover, in the transition from the linear to the nonlinear behaviour isolated branches of solutions are identified. Localization is caused by the hardening effect introduced by the nonlinear stiffness, and occurs at large excitation levels. Contrary to the case of mistuning, the presented localization mechanism is triggered by the nonlinearities and arises in perfectly homogeneous systems

Shakedown in elastic contact problems with Coulomb friction

AbstractElastic systems with frictional interfaces subjected to periodic loading are sometimes predicted to ‘shake down’ in the sense that frictional slip ceases after the first few loading cycles. The similarities in behaviour between such systems and monolithic bodies with elastic–plastic constitutive behaviour have prompted various authors to speculate that Melan’s theorem might apply to them – i.e., that the existence of a state of residual stress sufficient to prevent further slip is a sufficient condition for the system to shake down.In this paper, we prove this result for ‘complete’ contact problems in the discrete formulation (i) for systems with no coupling between relative tangential displacements at the interface and the corresponding normal contact tractions and (ii) for certain two-dimensional problems in which the friction coefficient at each node is less than a certain critical value. We also present counter-examples for all systems that do not fall into these categories, thus giving a definitive statement of the conditions under which Melan’s theorem can be used to predict whether such a system will shake down

On the effect of the loading apparatus stiffness on the equilibrium and stability of soft adhesive contacts under shear loads

The interaction between contact area and frictional forces in adhesive soft contacts is receiving much attention in the scientific community due to its implications in many areas of engineering such as surface haptics and bioinspired adhesives. In this work, we consider a soft adhesive sphere that is pressed against a rigid substrate and is sheared by a tangential force where the loads are transferred to the sphere through a normal and a tangential spring, representing the loading apparatus stiffness. We derive a general linear elastic fracture mechanics solution, taking into account also the interaction between modes, by adopting a simple but effective mixed-mode model that has been recently validated against experimental results in similar problems. We discuss how the spring stiffness affects the stability of the equilibrium contact solution, i.e. the transition to separation or to sliding

Different ways of framing event attribution questions: The example of warm and wet winters in the United Kingdom similar to 2015/16

This is the final version. Available from the American Meteorological Society via the DOI in this recordAttribution analyses of extreme events estimate changes in the likelihood of their occurrence due to human climatic influences by comparing simulations with and without anthropogenic forcings. Classes of events are commonly considered that only share one or more key characteristics with the observed event. Here we test the sensitivity of attribution assessments to such event definition differences, using the warm and wet winter of 2015/16 in the United Kingdom as a case study. A large number of simulations from coupled models and an atmospheric model are employed. In the most basic case, warm and wet events are defined relative to climatological temperature and rainfall thresholds. Several other classes of events are investigated that, in addition to threshold exceedance, also account for the effect of observed sea surface temperature (SST) anomalies, the circulation flow, or modes of variability present during the reference event. Human influence is estimated to increase the likelihood of warm winters in the United Kingdom by a factor of 3 or more for events occurring under any atmospheric and oceanic conditions, but also for events with a similar circulation or oceanic state to 2015/16. The likelihood of wet winters is found to increase by at least a factor of 1.5 in the general case, but results from the atmospheric model, conditioned on observed SST anomalies, are more uncertain, indicating that decreases in the likelihood are also possible. The robustness of attribution assessments based on atmospheric models is highly dependent on the representation of SSTs without the effect of human influence.Joint BEIS/Defra Met Office Hadley Centre Climate Programm