Identification of mass–spring–damper model of walking humans

Interaction of walking people with vibrating structures is known to be an important yet challenging phenomenon to simulate. Despite of its considerable effects on the structural response, no properly formulated and experimentally verified model currently exists to simulate this interaction in the vertical direction. This work uses a single-degree-of-freedom mass–spring–damper model of a walking human to simulate its interaction with a vibrating structure. Extensive frequency response function measurements were performed on a test structure that was occupied by more than a hundred test subjects walking in various group sizes and at different times in 23 tests. The identified modal properties of the occupied structure were used in three different identification procedures to estimate the parameters of the walking human model. A discrete model of human–structure system was used to simulate interaction of each walking person with the structure. The analysis identified the range of 2.75–3.00 Hz for the natural frequency and 27.5%–30% for the damping ratio of the model of a walking human, having constant mass of 70 kg. The extent of the experimental data and the measurement details, diversity of loading scenarios and consistency of the results of the different identification procedures, provided high level of confidence on the suggested parameters for the single-degree-of-freedom walking human model.UK Engineering and Physical Sciences Research Council (EPSRC

Oscillations and secondary bifurcations in nonlinear magnetoconvection

Complicated bifurcation structures that appear in nonlinear systems governed by partial differential equations (PDEs) can be explained by studying appropriate low-order amplitude equations. We demonstrate the power of this approach by considering compressible magnetoconvection. Numerical experiments reveal a transition from a regime with a subcritical Hopf bifurcation from the static solution, to one where finite-amplitude oscillations persist although there is no Hopf bifurcation from the static solution. This transition is associated with a codimension-two bifurcation with a pair of zero eigenvalues. We show that the bifurcation pattern found for the PDEs is indeed predicted by the second-order normal form equation (with cubic nonlinearities) for a Takens-Bogdanov bifurcation with Z2 symmetry. We then extend this equation by adding quintic nonlinearities and analyse the resulting system. Its predictions provide a qualitatively accurate description of solutions of the full PDEs over a wider range of parameter values. Replacing the reflecting (Z2) lateral boundary conditions with periodic [O(2)] boundaries allows stable travelling wave and modulated wave solutions to appear; they could be described by a third-order system

Minimal Information Data-Modelling (MID) and an easily implementable low-cost SHM system for use on a short-span bridge

Structural Health Monitoring (SHM) is a technique that involves gathering information to ensure that a structure is safe and behaving as expected. Within SHM, vibration-based monitoring is generally seen as one of the more cost-effective types of monitoring. However, vibration-based monitoring has mostly been undertaken on long-span bridges using data collected with a dense network of sensors. Historically, the logistical difficulty of collecting data on short- and medium-span bridges has meant that the usefulness of vibration-based methods on these bridges is largely unknown. Therefore, this study proposes Minimal Information Data-modelling (MID). MID is an approach that utilises low-cost, easily implementable sensors that are potentially feasible for operators to purchase and operate across a network. This approach will be investigated to determine whether MID is a feasible approach for monitoring short- and medium- span bridges. The results from MID were assessed to determine whether they could detect a suitably small shift in frequency, which is indicative of damage. It was determined that the data models could reliably detect frequency shifts as low as 0.01 Hz. This magnitude of frequency shift is similar to the level of frequency shift reported for a range of bridge damage cases found by others and validated with FE models. The accuracy achieved by the data models indicates that MID could potentially be used as a damage detection method. The cost of the equipment used to collect the data was approximately £370, demonstrating that it is feasible to use MID to monitor bridges across an entire network

A Multidisciplinary Computational Framework for Topology Optimisation of Offshore Helidecks

Maintaining offshore steel structures is challenging and not environmentally friendly due to the frequent visits for inspection and repairs. Some offshore lighthouses are equipped with carbon steel helidecks fixed onto their lantern galleries in the 1970s to provide easy and safe access to maintenance staff and inspectors. Even though the helidecks supporting structures have maintained their integrity and are still functional in the offshore harsh environmental conditions, their inspection and maintenance remains a challenge due to the need of frequent visits which requires flying to the location of the lighthouse to bring the maintenance staff and equipment. We have developed a multidisciplinary computational framework to design new generation of aluminium helidecks for offshore lighthouses. We calculated the wind speed at the location of the Bishop Rock lighthouse based on the meteorological data, and the load distribution on the helideck due to such a wind condition, using computational fluid dynamic analysis. Then, we used the calculated wind load with other mechanical loads in the events of normal and emergency landings of a helicopter on this structure to find the best design configuration for this helideck. We generated a design space for different configurations of a beam structure and carried out, static, transient and buckling analysis to assess each case using finite element method. The selection criterion was set to find the structure with the minimum volume fraction and compliance while keeping the stress below the allowable stress. We found the structure with eight vertical and circumferential sections featuring two rows of diagonal bracing with one at the base and the other one at the third section from the base of the helideck was the optimum design for the considered loading in this work. This framework can be adopted for the design and optimisation of other offshore structures by other researchers and designers

Analysis of the shearing instability in nonlinear convection and magnetoconvection

Numerical experiments on two-dimensional convection with or without a vertical magnetic field reveal a bewildering variety of periodic and aperiodic oscillations. Steady rolls can develop a shearing instability, in which rolls turning over in one direction grow at the expense of rolls turning over in the other, resulting in a net shear across the layer. As the temperature difference across the fluid is increased, two-dimensional pulsating waves occur, in which the direction of shear alternates. We analyse the nonlinear dynamics of this behaviour by first constructing appropriate low-order sets of ordinary differential equations, which show the same behaviour, and then analysing the global bifurcations that lead to these oscillations by constructing one-dimensional return maps. We compare the behaviour of the partial differential equations, the models and the maps in systematic two-parameter studies of both the magnetic and the non-magnetic cases, emphasising how the symmetries of periodic solutions change as a result of global bifurcations. Much of the interesting behaviour is associated with a discontinuous change in the leading direction of a fixed point at a global bifurcation; this change occurs when the magnetic field is introduced