Semi-analytical solution for nonlinear vibration of laminated FGM plates with geometric imperfections

This paper investigates the nonlinear vibration of imperfect shear deformable laminated rectangular plates comprising a homogeneous substrate and two layers of functionally graded materials (FGMs). A theoretical formulation based on Reddy's higher-order shear deformation plate theory is presented in terms of deflection, mid-plane rotations, and the stress function. A semi-analytical method, which makes use of the one-dimensional differential quadrature method, the Galerkin technique, and an iteration process, is used to obtain the vibration frequencies for plates with various boundary conditions. Material properties are assumed to be temperature-dependent. Special attention is given to the effects of sine type imperfection, localized imperfection, and global imperfection on linear and nonlinear vibration behavior. Numerical results are presented in both dimensionless tabular and graphical forms for laminated plates with graded silicon nitride/stainless steel layers. It is shown that the vibration frequencies are very much dependent on the vibration amplitude and the imperfection mode and its magnitude. While most of the imperfect laminated plates show the well-known hard-spring vibration, those with free edges can display soft-spring vibration behavior at certain imperfection levels. The influences of material composition, temperature-dependence of material properties and side-to-thickness ratio are also discussed. (C) 2004 Elsevier Ltd. All rights reserved.

An Analytical Solution for the Elastic Lateral-Distortional Buckling of I-section Beams

Lateral-distortional buckling may occur in I-section beams with slender webs and stocky flanges. A computationally efficient method is presented in this paper to study this phenomenon. Previous studies on distortional buckling have been on the use of 3(rd) and 5(th) order polynomials to model the displacements. The present study provides an alternative way, using Fourier Series, to model the behaviour. Beams of different cross-sectional dimensions, load cases and restraint conditions are examined and compared. The accuracy and versatility of the method are verified by calibrating against the results of other published studies. The present method is believed to be a simple and efficient way of determining the buckling load and mode shapes of I-section beams that are susceptible to lateral-distortional buckling modes.

Modelling trickle irrigation: Comparison of analytical and numerical models for estimation of wetting front position with time

Irrigation practices that are profligate in their use of water have come under closer scrutiny by water managers and the public. Trickle irrigation has the propensity to increase water use efficiency but only if the system is designed to meet the soil and plant conditions. Recently we have provided a software tool, WetUp (http://www.clw.csiro.au/products/wetup/), to calculate the wetting patterns from trickle irrigation emitters. WetUp uses an analytical solution to calculate the wetted perimeter for both buried and surface emitters. This analytical solution has a number of assumptions, two of which are that the wetting front is defined by water content at which the hydraulic conductivity (K) is I mm day(-1) and that the flow occurs from a point source. Here we compare the wetting patterns calculated with a 2-dimensional numerical model, HYDRUS2D, for solving the water flow into typical soils with the analytical solution. The results show that the wetting patterns are similar, except when the soil properties result in the assumption of a point source no longer being a good description of the flow regime. Difficulties were also experienced with getting stable solutions with HYDRUS2D for soils with low hydraulic conductivities. (c) 2005 Elsevier Ltd. All rights reserved.

Distortion product otoacoustic emissions in children at school entry: A comparison with pure tone screening and tympanometry results

This study examined the test performance of distortion product otoacoustic emissions (DPOAEs) when used as a screening tool in the school setting. A total of 1003 children (mean age 6.2 years, SD = 0.4) were tested with pure-tone screening, tympanometry, and DPOAE assessment. Optimal DPOAE test performance was determined in comparison with pure-tone screening results using clinical decision analysis. The results showed hit rates of 0.86, 0.89, and 0.90, and false alarm rates of 0.52, 0.19, and 0.22 for criterion signal-to-noise ratio (SNR) values of 4, 5, and 11 dB at 1.1, 1.9, and 3.8 kHz respectively. DPOAE test performance was compromised at 1.1 kHz. In view of the different test performance characteristics across the frequencies, the use of a fixed SNR as a pass criterion for all frequencies in DPOAE assessments is not recommended. When compared to pure tone plus tympanometry results, the DPOAEs showed deterioration in test performance, suggesting that the use of DPOAEs alone might miss children with subtle middle ear dysfunction. However, when the results of a test protocol, which incorporates both DPOAEs and tympanometry, were used in comparison with the gold standard of pure-tone screening plus tympanometry, test performance was enhanced. In view of its high performance, the use of a protocol that includes both DPOAEs and tympanometry holds promise as a useful tool in the hearing screening of schoolchildren, including difficult-to-test children.

Dimensionless spray flux in wet granulation: Monte-Carlo simulations and experimental validation

Dimensionless spray flux Ψa is a dimensionless group that characterises the three most important variables in liquid dispersion: flowrate, drop size and powder flux through the spray zone. In this paper, the Poisson distribution was used to generate analytical solutions for the proportion of nuclei formed from single drops (fsingle) and the fraction of the powder surface covered by drops (fcovered) as a function of Ψa. Monte-Carlo simulations were performed to simulate the spray zone and investigate how Ψa, fsingle and fcovered are related. The Monte-Carlo data was an excellent match with analytical solutions of fcovered and fsingle as a function of Ψa. At low Ψa, the proportion of the surface covered by drops (fcovered) was equal to Ψa. As Ψa increases, drop overlap becomes more dominant and the powder surface coverage levels off. The proportion of nuclei formed from single drops (fsingle) falls exponentially with increasing Ψa. In the ranges covered, these results were independent of drop size, number of drops, drop size distribution (mono-sized, bimodal and trimodal distributions), and the uniformity of the spray. Experimental data of nuclei size distributions as a function of spray flux were fitted to the analytical solution for fsingle by defining a cutsize for single drop nuclei. The fitted cutsizes followed the spray drop sizes suggesting that the method is robust and that the cutsize does indicate the transition size between single drop and agglomerate nuclei. This demonstrates that the nuclei distribution is determined by the dimensionless spray flux and the fraction of drop controlled nuclei can be calculated analytically in advance.

Environmental Risk Factors for Parkinson's Disease

Parkinson’s disease (PD) is a progressive, degenerative, neurological disease. The progressive disability associated with PD results in substantial burdens for those with the condition, their families and society in terms of increased health resource use, earnings loss of affected individuals and family caregivers, poorer quality of life, caregiver burden, disrupted family relationships, decreased social and leisure activities, and deteriorating emotional well-being. Currently, no cure is available and the efficacy of available treatments, such as medication and surgical interventions, decreases with longer duration of the disease. Whilst the cause of PD is unknown, genetic and environmental factors are believed to contribute to its aetiology. Descriptive and analytical epidemiological studies have been conducted in a number of countries in an effort to elucidate the cause, or causes, of PD. Rural residency, farming, well water consumption, pesticide exposure, metals and solvents have been implicated as potential risk factors for PD in some previous epidemiological studies. However, there is substantial disagreement between the results of existing studies. Therefore, the role of environmental exposures in the aetiology of PD remains unclear. The main component of this thesis consists of a case-control study that assessed the contribution of environmental exposures to the risk of developing PD. An existing, previously unanalysed, dataset from a local case-control study was analysed to inform the design of the new case-control study. The analysis results suggested that regular exposure to pesticides and head injury were important risk factors for PD. However, due to the substantial limitations of this existing study, further confirmation of these results was desirable with a more robustly designed epidemiological study. A new exposure measurement instrument (a structured interviewer-delivered questionnaire) was developed for the new case-control study to obtain data on demographic, lifestyle, environmental and medical factors. Prior to its use in the case-control study, the questionnaire was assessed for test-retest repeatability in a series of 32 PD cases and 29 healthy sex-, age- and residential suburb-matched electoral roll controls. High repeatability was demonstrated for lifestyle exposures, such as smoking and coffee/tea consumption (kappas 0.70-1.00). The majority of environmental exposures, including use of pesticides, solvents and exposure to metal dusts and fumes, also showed high repeatability (kappas >0.78). A consecutive series of 163 PD case participants was recruited from a neurology clinic in Brisbane. One hundred and fifty-one (151) control participants were randomly selected from the Australian Commonwealth Electoral Roll and individually matched to the PD cases on age (± 2 years), sex and current residential suburb. Participants ranged in age from 40-89 years (mean age 67 years). Exposure data were collected in face-to-face interviews. Odds ratios and 95% confidence intervals were calculated using conditional logistic regression for matched sets in SAS version 9.1. Consistent with previous studies, ever having been a regular smoker or coffee drinker was inversely associated with PD with dose-response relationships evident for packyears smoked and number of cups of coffee drunk per day. Passive smoking from ever having lived with a smoker or worked in a smoky workplace was also inversely related to PD. Ever having been a regular tea drinker was associated with decreased odds of PD. Hobby gardening was inversely associated with PD. However, use of fungicides in the home garden or occupationally was associated with increased odds of PD. Exposure to welding fumes, cleaning solvents, or thinners occupationally was associated with increased odds of PD. Ever having resided in a rural or remote area was inversely associated with PD. Ever having resided on a farm was only associated with moderately increased odds of PD. Whilst the current study’s results suggest that environmental exposures on their own are only modest contributors to overall PD risk, the possibility that interaction with genetic factors may additively or synergistically increase risk should be considered. The results of this research support the theory that PD has a multifactorial aetiology and that environmental exposures are some of a number of factors to contribute to PD risk. There was also evidence of interaction between some factors (eg smoking and welding) to moderate PD risk.

Analytical solution of forced convection in a duct of rectangular cross-section saturated by a porous medium

A theoretical analysis is presented to investigate fully developed (both thermally and hydrodynamically) forced convection in a duct of rectangular cross-section filled with a hyper-porous medium. The Darcy-Brinkman model for flow through porous media was adopted in the present analysis. A Fourier series type solution is applied to obtain the exact velocity and temperature distribution within the duct. The case of uniform heat flux on the walls, i.e. the H boundary condition in the terminology of Kays and Crawford [1], is treated. Values of the Nusselt number and the friction factor as a function of the aspect ratio, the Darcy number, and the viscosity ratio are reported.

Pair correlations in a finite-temperature 1D Bose gas

We calculate the two-particle local correlation for an interacting 1D Bose gas at finite temperature and classify various physical regimes. We present the exact numerical solution by using the Yang-Yang equations and Hellmann-Feynman theorem and develop analytical approaches. Our results draw prospects for identifying the regimes of coherent output of an atom laser, and of finite-temperature “fermionization” through the measurement of the rates of two-body inelastic processes, such as photoassociation.

Intuition: Myth or a Decision-making Tool?

Faced with today’s ill-structured business environment of fast-paced change and rising uncertainty, organizations have been searching for management tools that will perform satisfactorily under such ambiguous conditions. In the arena of managerial decision making, one of the approaches being assessed is the use of intuition. Based on our definition of intuition as a non-sequential information-processing mode, which comprises both cognitive and affective elements and results in direct knowing without any use of conscious reasoning, we develop a testable model of integrated analytical and intuitive decision making and propose ways to measure the use of intuition.

Entropy generation for forced convection in a porous saturated circular tube with uniform wall temperature

A numerical study is reported to investigate both the First and the Second Law of Thermodynamics for thermally developing forced convection in a circular tube filled by a saturated porous medium, with uniform wall temperature, and with the effects of viscous dissipation included. A theoretical analysis is also presented to study the problem for the asymptotic region applying the perturbation solution of the Brinkman momentum equation reported by Hooman and Kani [1]. Expressions are reported for the temperature profile, the Nusselt number, the Bejan number, and the dimensionless entropy generation rate in the asymptotic region. Numerical results are found to be in good agreement with theoretical counterparts.

Turbulence in Hydraulic Jumps: Experimental Measurements

A hydraulic jump is the transition from a supercritical open channel flow to a subcritical regime. It is characterised by a highly turbulent flow with macro-scale vortices, some kinetic energy dissipation and a bubbly two-phase flow structure. New air-water flow measurements were performed in hydraulic jump flows for a range of inflow Froude numbers. The experiments were conducted in a large-size facility using two types of phase-detection intrusive probes: i.e., single-tip and double-tip conductivity probes. These were complemented by some measurements of free-surface fluctuations using ultrasonic displacement meters. The present study was focused on the turbulence characteristics of hydraulic jumps with partially-developed inflow conditions. The void fraction measurements showed the presence of an advective diffusion shear layer in which the void fractions profiles matched closely an analytical solution of the advective diffusion equation for air bubbles. The present results highlighted some influence of the inflow Froude number onto the air bubble entrainment process. At the largest Froude numbers, the advected air bubbles were more thoroughly dispersed vertically, and larger amount of air bubbles were detected in the turbulent shear layer. In the air-water mixing layer, the maximum void fraction and bubble count rate data showed some longitudinal decay function in the flow direction. Such trends were previously reported in the literature. The measurements of interfacial velocity and turbulence level distributions provided new information on the turbulent velocity field in the highly-aerated shear region. The present data suggested some longitudinal decay of the turbulence intensity. The velocity profiles tended to follow a wall jet flow pattern. The air–water turbulent time and length scales were deduced from some auto- and cross-correlation analyses based upon the method of CHANSON (2006,2007). The results provided the integral turbulent time and length scales of the eddy structures advecting the air bubbles in the developing shear layer. The experimental data showed that the auto-correlation time scale Txx was larger than the transverse cross-correlation time scale Txz. The integral turbulence length scale Lxz was a function of the inflow conditions, of the streamwise position (x-x1)/d1 and vertical elevation y/d1. Herein the dimensionless integral turbulent length scale Lxz/d1 was closely related to the inflow depth: i.e., Lxz/d1 = 0.2 to 0.8, with Lxz increasing towards the free-surface. The free-surface fluctuations measurements showed large turbulent fluctuations that reflected the dynamic, unsteady structure of the hydraulic jumps. A linear relationship was found between the normalized maximum free-surface fluctuation and the inflow Froude number.

Review of recent results on excursion set models

Many images consist of two or more 'phases', where a phase is a collection of homogeneous zones. For example, the phases may represent the presence of different sulphides in an ore sample. Frequently, these phases exhibit very little structure, though all connected components of a given phase may be similar in some sense. As a consequence, random set models are commonly used to model such images. The Boolean model and models derived from the Boolean model are often chosen. An alternative approach to modelling such images is to use the excursion sets of random fields to model each phase. In this paper, the properties of excursion sets will be firstly discussed in terms of modelling binary images. Ways of extending these models to multi-phase images will then be explored. A desirable feature of any model is to be able to fit it to data reasonably well. Different methods for fitting random set models based on excursion sets will be presented and some of the difficulties with these methods will be discussed.

Substrate-inhibited kinetics with catalyst deactivation in an isothermal CSTR

Analytical expressions are developed for the time-dependent reactant concentration and catalyst activity in an isothermal CSTR with Langmuir-Hinshelwood kinetics of deactivation and reaction. Several parallel and series posioning mechanisms are considered for a reactor which, without poisoning, would operate at a unique steady state. The use of matched asymptotic expansions and abandonment of the usual initial-steady-state assumption give results, valid from startup to final loss of activity, whose accuracy can be improved systematically.

Approximate analytical solutions for porous catalysts with nonuniform activity

Using a novel finite integral transform technique, the problem of diffusion and chemical reaction in a porous catalyst with general activity profile is investigated theoretically. Analytical expressions for the effectiveness factor are obtained for pth order and Michaelis-Menten kinetics. Perturbation methods are employed to provide useful asymptotic solutions for large or small values of Thiele modulus and Biot number.

An improved novel method for solving nonlinear boundary value problems

A modified formula for the integral transform of a nonlinear function is proposed for a class of nonlinear boundary value problems. The technique presented in this paper results in analytical solutions. Iterations and initial guess, which are needed in other techniques, are not required in this novel technique. The analytical solutions are found to agree surprisingly well with the numerically exact solutions for two examples of power law reaction and Langmuir-Hinshelwood reaction in a catalyst pellet.