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.

Non-linear analysis of the thermo-electro-mechanical behaviour of shear deformable FGM plates with piezoelectric actuators

This paper investigates the non-linear bending behaviour of functionally graded plates that are bonded with piezoelectric actuator layers and subjected to transverse loads and a temperature gradient based on Reddy's higher-order shear deformation plate theory. The von Karman-type geometric non-linearity, piezoelectric and thermal effects are included in mathematical formulations. The temperature change is due to a steady-state heat conduction through the plate thickness. The material properties are assumed to be graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. The plate is clamped at two opposite edges, while the remaining edges can be free, simply supported or clamped. Differential quadrature approximation in the X-axis is employed to convert the partial differential governing equations and the associated boundary conditions into a set of ordinary differential equations. By choosing the appropriate functions as the displacement and stress functions on each nodal line and then applying the Galerkin procedure, a system of non-linear algebraic equations is obtained, from which the non-linear bending response of the plate is determined through a Picard iteration scheme. Numerical results for zirconia/aluminium rectangular plates are given in dimensionless graphical form. The effects of the applied actuator voltage, the volume fraction exponent, the temperature gradient, as well as the characteristics of the boundary conditions are also studied in detail. Copyright (C) 2004 John Wiley Sons, Ltd.

An expert system on design of liquid-retaining structures with blackboard architecture

The design of liquid-retaining structures involves many decisions to be made by the designer based on rules of thumb, heuristics, judgement, codes of practice and previous experience. Structural design problems are often ill structured and there is a need to develop programming environments that can incorporate engineering judgement along with algorithmic tools. Recent developments in artificial intelligence have made it possible to develop an expert system that can provide expert advice to the user in the selection of design criteria and design parameters. This paper introduces the development of an expert system in the design of liquid-retaining structures using blackboard architecture. An expert system shell, Visual Rule Studio, is employed to facilitate the development of this prototype system. It is a coupled system combining symbolic processing with traditional numerical processing. The expert system developed is based on British Standards Code of Practice BS8007. Explanations are made to assist inexperienced designers or civil engineering students to learn how to design liquid-retaining structures effectively and sustainably in their design practices. The use of this expert system in disseminating heuristic knowledge and experience to practitioners and engineering students is discussed.

Structure of a cellulose degrading bacterial community during anaerobic digestion

It is widely accepted that cellulose is the rate-limiting substrate in the anaerobic digestion of organic solid wastes and that cellulose solubilisation is largely mediated by surface attached bacteria. However, little is known about the identity or the ecophysiology of cellulolytic microorganisms from landfills and anaerobic digesters. The aim of this study was to investigate an enriched cellulolytic microbial community from an anaerobic batch reactor. Chemical oxygen demand balancing was used to calculate the cellulose solubilisation rate and the degree of cellulose solubilisation. Fluorescence in situ hybridisation (FISH) was used to assess the relative abundance and physical location of three groups of bacteria belonging to the Clostridium lineage of the Firmicutes that have been implicated as the dominant cellulose degraders in this system. Quantitation of the relative abundance using FISH showed that there were changes in the microbial community structure throughout the digestion. However, comparison of these results to the process data reveals that these changes had no impact on the cellulose solubilisation in the reactor. The rate of cellulose solubilisation was approximately stable for much of the digestion despite changes in the cellulolytic population. The solubilisation rate appears to be most strongly affected by the rate of surface area colonisation and the biofilm architecture with the accepted model of first order kinetics due to surface area limitation applying only when the cellulose particles are fully covered with a thin layer of cells. (c) 2005 Wiley Periodicals, Inc.

Evaluation by respirometry of the degradability of retort water using a shale ash and overburden packed column

Oil shale processing produces an aqueous wastewater stream known as retort water. The fate of the organic content of retort water from the Stuart oil shale project (Gladstone, Queensland) is examined in a proposed packed bed treatment system consisting of a 1:1 mixture of residual shale from the retorting process and mining overburden. The retort water had a neutral pH and an average unfiltered TOC of 2,900 mg l(-1). The inorganic composition of the retort water was dominated by NH4+. Only 40% of the total organic carbon (TOC) in the retort water was identifiable, and this was dominated by carboxylic acids. In addition to monitoring influent and effluent TOC concentrations, CO2 evolution was monitored on line by continuous measurements of headspace concentrations and air flow rates. The column was run for 64 days before it blocked and was dismantled for analysis. Over 98% of the TOC was removed from the retort water. Respirometry measurements were confounded by CO2 production from inorganic sources. Based on predictions with the chemical equilibrium package PHREEQE, approximately 15% of the total CO2 production arose from the reaction of NH4+ with carbonates. The balance of the CO2 production accounted for at least 80% of the carbon removed from the retort water. Direct measurements of solid organic carbon showed that approximately 20% of the influent carbon was held-up in the top 20cm of the column. Less than 20% of this held-up carbon was present as either biomass or as adsorbed species. Therefore, the column was ultimately blocked by either extracellular polymeric substances or by a sludge that had precipitated out of the retort water.