The non-local nature of structure functions

Kolmogorov's two-thirds, ((Δv) 2) ∼ e 2/ 3r 2/ 3, and five-thirds, E ∼ e 2/ 3k -5/ 3, laws are formally equivalent in the limit of vanishing viscosity, v → 0. However, for most Reynolds numbers encountered in laboratory scale experiments, or numerical simulations, it is invariably easier to observe the five-thirds law. By creating artificial fields of isotropic turbulence composed of a random sea of Gaussian eddies whose size and energy distribution can be controlled, we show why this is the case. The energy of eddies of scale, s, is shown to vary as s 2/ 3, in accordance with Kolmogorov's 1941 law, and we vary the range of scales, γ = s max/s min, in any one realisation from γ = 25 to γ = 800. This is equivalent to varying the Reynolds number in an experiment from R λ = 60 to R λ = 600. While there is some evidence of a five-thirds law for g > 50 (R λ > 100), the two-thirds law only starts to become apparent when g approaches 200 (R λ ∼ 240). The reason for this discrepancy is that the second-order structure function is a poor filter, mixing information about energy and enstrophy, and from scales larger and smaller than r. In particular, in the inertial range, ((Δv) 2) takes the form of a mixed power-law, a 1+a 2r 2+a 3r 2/ 3, where a 2r 2 tracks the variation in enstrophy and a 3r 2/ 3 the variation in energy. These findings are shown to be consistent with experimental data where the polution of the r 2/ 3 law by the enstrophy contribution, a 2r 2, is clearly evident. We show that higherorder structure functions (of even order) suffer from a similar deficiency.

Moderate speed impact damage to 2D-braided glass-carbon composites

Hybrid glass-carbon 2D braided composites with varying carbon contents are impacted using a gas gun by impactors of masses 12.5 and 44.5. g, at impact energies up to 50. J. The damage area detected by ultrasound C-scan is found to increase roughly linearly with impact energy, and is larger for the lighter impactor at the same impact energy. The area of whitening of the glass tows on the distal side corresponds with the measured C-scan damage area. X-ray imaging shows more intense damage, at the same impact energy, for a higher-mass impactor. Braids with more glass content have a modest increase in density, decrease in modulus, and reduction in the C-scan area and dent depth at the impact site, particularly at the higher impact energies. Impact damage is found to reduce significantly the compressive strength, giving up to a 26% reduction at the maximum impact energy. © 2012 Elsevier Ltd.

On the functions of products

Understanding the performance and manner of functioning of existing products is at the base of new product development activities. In engineering design the term function is generally used to refer to the technical actions performed by a product. However, products accomplish a wider range of goals. This research explores the opportunity to describe and model, through the concept of function, product actions across four dimensions including technical, aesthetic, social and economic. The research demonstrates that non-technical functions can be represented through active verbs and nouns and modelled using a method known as the Function Analysis Diagram (FAD). The research argues that when technical, aesthetic, social and economic perspectives on product development are considered as different types of function, stakeholders have a common language to communicate which can benefit design collaboration.

Real Time Concrete Damage Visual Assessment for First Responders

First responders are in danger when they perform tasks in damaged buildings after earthquakes. Structural collapse due to the failure of critical load bearing structural members (e.g. columns) during a post-earthquake event such as an aftershock can make first responders victims, considering they are unable to assess the impact of the damage inflicted in load bearing members. The writers here propose a method that can provide first responders with a crude but quick estimate of the damage inflicted in load bearing members. Under the proposed method, critical structural members (reinforced concrete columns in this study) are identified from digital visual data and the damage superimposed on these structural members is detected with the help of Visual Pattern Recognition techniques. The correlation of the two (e.g. the position, orientation and size of a crack on the surface of a column) is used to query a case-based reasoning knowledge base, which contains apriori classified states of columns according to the damage inflicted on them. When query results indicate the column's damage state is severe, the method assumes that a structural collapse is likely and first responders are warned to evacuate.

700V smart trench IGBT with monolithic over-voltage and over-current protecting functions

An advanced 700V Smart Trench IGBT with monolithically integrated over-voltage and over-current protecting circuits is presented in this paper. The proposed Smart IGBT comprises a sense IGBT, a low voltage lateral n-channel MOSFET (M 1), an avalanche diode (D av), and poly-crystalline Zener diodes (ZD) and resistor (R poly). Mix-mode transient simulations with MEDICI have proven the functionalities of the protecting circuits when the device is operating under abnormal conditions, such as Unclamped Inductive Switching (UIS) and Short Circuit (SC) condition. A Trench IGBT process is used to fabricate this device with total 11 masks including one metal mask only. The characterizations of the fabricated device exhibit the clamping capability of the avalanche diode and voltage pull-down ability of the MOSFET. © 2012 IEEE.

Characterization of impact induced damage modes in single lap joints of woven GFRP composites

Single lap joints of woven GFRP composites have been investigated for impact induced damage modes using C-scan, X-ray micro tomography, imaging and finite element (FE) modelling. This has allowed for damage modes to be observed in 3D from macro to micro level-resulting in much better understanding of damage mechanisms and realistic FE modelling.

A flexural crack model for damage detection in reinforced concrete structures

The use of changes in vibration data for damage detection of reinforced concrete structures faces many challenges that obstruct its transition from a research topic to field applications. Among these is the lack of appropriate damage models that can be deployed in the damage detection methods. In this paper, a model of a simply supported reinforced concrete beam with multiple cracks is developed to examine its use for damage detection and structural health monitoring. The cracks are simulated by a model that accounts for crack formation, propagation and closure. The beam model is studied under different dynamic excitations, including sine sweep and single excitation frequency, for various damage levels. The changes in resonant frequency with increasing loads are examined along with the nonlinear vibration characteristics. The model demonstrates that the resonant frequency reduces by about 10% at the application of 30% of the ultimate load and then drops gradually by about 25% at 70% of the ultimate load. The model also illustrates some nonlinearity in the dynamic response of damaged beams. The appearance of super-harmonics shows that the nonlinearity is higher when the damage level is about 35% and then decreases with increasing damage. The restoring force-displacement relationship predicted the reduction in the overall stiffness of the damaged beam. The model quantitatively predicts the experimental vibration behaviour of damaged RC beams and also shows the damage dependency of nonlinear vibration behaviour. © 2011 Published under licence by IOP Publishing Ltd.

Lyapunov functions for stable cascades and applications to global stabilization

This paper generalizes recent Lyapunov constructions for a cascade of two nonlinear systems, one of which is stable rather than asymptotically stable. A new cross-term construction in the Lyapunov function allows us to replace earlier growth conditions by a necessary boundedness condition. This method is instrumental in the global stabilization of feedforward systems, and new stabilization results are derived from the generalized construction.