Thermodynamic formalism for transient dynamics on the real line

We develop a new thermodynamic formalism to investigate the transient behaviour of maps on the real line which are skew-periodic Z -extensions of expanding interval maps. Our main focus lies in the dimensional analysis of the recurrent and transient sets as well as in determining the full dimension spectrum with respect to α-escaping sets. Our results provide a one-dimensional model for the phenomenon of a dimension gap occurring for limit sets of Kleinian groups. In particular, we show that a dimension gap occurs if and only if we have non-zero drift and we are able to precisely quantify its width as an application of our new formalism.

Seismic velocity recovery in the subsurface: transient damage and groundwater drainage following the 2015 Gorkha earthquake, Nepal

Shallow earthquakes frequently disturb the hydrological and mechanical state of the subsurface, with consequences for hazard and water management. Transient post-seismic hydrological behaviour has been widely reported, suggesting that the recovery of material properties (relaxation) following ground shaking may impact groundwater fluctuations. However, the monitoring of seismic velocity variations associated with earthquake damage and hydrological variations are often done assuming that both effects are independent. In a field site prone to highly variable hydrological conditions, we disentangle the different forcing of the relative seismic velocity variations $\delta v$ retrieved from a small dense seismic array in Nepal in the aftermath of the 2015 Mw 7.8 Gorkha earthquake. We successfully model transient damage effects by introducing a universal relaxation function that contains a unique maximum relaxation timescale for the main shock and the aftershocks, independent of the ground shaking levels. Next, we remove the modeled velocity from the raw data and test whether the corresponding residuals agree with a background hydrological behaviour we inferred from a previously calibrated groundwater model. The fitting of the $\delta v$ data with this model is improved when we introduce transient hydrological properties in the phase immediately following the main shock. This transient behaviour, interpreted as an enhanced permeability in the shallow subsurface, lasts for $\sim$ 6 months and is shorter than the damage relaxation ($\sim$ 1 year). Thus, we demonstrate the capability of seismic interferometry to deconvolve transient hydrological properties after earthquakes from non-linear mechanical recovery.

THE TRANSIENT EFFECTS OF FLOOD WATER ON A WARSHIP IN CALM WATER IMMEDIATELY FOLLOWING DAMAGE

The safety of a ship which is damaged below the waterline will depend on the way water floods into the internal compartments. The water will cause the ship to take on an angle of heel and trim which will further affect the flooding into the compartments. The ship’s equilibrium position in calm water can be predicted using hydrostatic theory, however at present it is difficult to predict the transient behaviour between the initial upright position of the ship and its final equilibrium. In some cases, the transient motion may cause a capsize prior to a possible equilibrium position being reached. This paper describes an investigation of this phenomenon using a model of a warship with simplified, typical internal geometry. With the model initially stationary, a rapid damage event was generated, and the global motions measured, along with the water levels in some of the internal compartments, as functions of time. Immediately after the damage occurred the model rolled to starboard (towards the damage). It then rolled to port (away from the damage) before eventually returning to starboard and settling at its equilibrium value. In all the tests conducted the equilibrium heel angle was less than that reached during the initial roll to starboard. This implies that the roll damping, and the way in which the water floods into the model immediately following the damage, could both have a very important influence on the likelihood of survival.

Experimental investigation of the dynamics of a slider-crank mechanism with local linear force input

Conventional implementation of slider-crank mechanisms result in high loads transmitted through the mechanical structure, inhibiting the design of compact and oil-free machines. Therefore, this research proposes to step away from the conventional, i.e. rotative, actuation and to investigate local linear actuation on the slider-component directly, while maintaining the kinematic link of the slider-crank configuration. In this work the local linear actuating principle is evaluated experimentally where the goal is to obtain a continuous movement of the slider mechanism where Top Dead Centre & Bottom Dead Centre are reached and to minimise the loads transmitted through the mechanical structure. The non-isochronous transient behaviour of a slider-crank mechanism loaded with a spring-damper element is detailed as well as the optimal working conditions at steady state to achieve a reduced loading of the kinematic structure. By matching the operating frequency and resonance frequency of the system, a reduction of the loads transmitted through the system by 63% of the nominal spring load can be achieved. Further experimental (and multibody mechanical) investigation on the influence of flywheel exposes a clear trade-off between the sensitivity of the system and the transmission of the actuation force through the kinematic link.

Towards an Understanding of the Effect of Adding a Foam Core on the Blast Performance of Glass Fibre Reinforced Epoxy Laminate Panels

This paper presents insights into the blast response of sandwich panels with lightweight foam cores and asymmetric (different thicknesses) glass fibre epoxy face sheets. Viscously damped elastic vibrations were observed in the laminates (no core), while the transient response of the sandwich panels was more complex, especially after the peak displacement was observed. The post-peak residual oscillations in the sandwich panels were larger and did not decay as significantly with time when compared to the equivalent mass laminate panel test. Delamination was the predominant mode of failure on the thinner facesheet side of the sandwich panel, whereas cracking and matrix failure were more prominent on the thicker side (which was exposed to the blast). The type of constituent materials used and testing conditions, including the clamping method, influenced the resulting failure modes observed. A probable sequence of damage in the sandwich panels was proposed, based on the transient displacement measurements, a post-test failure analysis, and consideration of the stress wave propagation through the multilayered, multimaterial structure. This work demonstrates the need for detailed understanding of the transient behaviour of multilayered structures with significant elastic energy capacity and a wide range of possible damage mechanisms. The work should prove valuable to structural engineers and designers considering the deployment of foam-core sandwich panels or fibre reinforced polymer laminates in applications when air-blast loading may pose a credible threat.

Dynamic Modelling and Experimental Validation of a Domestic Refrigeration Cycle

Performance analysis and design optimization of refrigerators are primarily carried out by time-consuming experiments. The current study presents an alternative method of analysing refrigerators through modelling of the cooling cycle using a software called Dymola, based on an object-oriented programming language, called Modelica. The main components of a domestic refrigerator (compressor, condenser, evaporator, cabinet and capillary tube-suction-line heat exchanger) are first modelled and validated individually. The full dynamic refrigeration cycle model is created afterwards. Both the simulations and the experiments have been conducted using R600a as the refrigerant with on-and off-modes of the reciprocating, single speed compressor. To represent the dynamic cyclic behaviour of the refrigerator, an algorithm block is also included. The algorithm controls the operation using two set-point temperatures of the cabinet. Experiments have been carried out on a single door refrigerator having an interior volume of 343 litres for the validation of the one-dimensional dynamic model. Results show that the cabinet air, evaporation temperature, condensation temperature, power and energy values deviate from experimental values by less than 2°C and 2% respectively. The dynamic modelling is found to be in good agreement with the experiments in the on mode of the compressor and a promising and rapid tool to represent the transient behaviour of the refrigerator.