Analysis of the free vibration of rectangular plates with central cut-outs using the discrete Ritz method

We present an analysis of the free vibration of plates with internal discontinuities due to central cut-outs. A numerical formulation for a basic L-shaped element which is divided into appropriate sub-domains that are dependent upon the location of the cut-out is used as the basic building element. Trial functions formed to satisfy certain boundary conditions are employed to define the transverse deflection of each sub-domain. Mathematical treatments in terms of the continuities in displacement, slope, moment, and higher derivatives between the adjacent sub-domains are enforced at the interconnecting edges. The energy functional results, from the proper assembly of the coupled strain and kinetic energy contributions of each sub-domain, are minimized via the Ritz procedure to extract the vibration frequencies and. mode shapes of the plates. The procedures are demonstrated by considering plates with central cut-outs that are subjected to two types of boundary conditions. (C) 2003 Elsevier Ltd. All rights reserved.

Aquatic passive sampling of herbicides on naked particle loaded membranes: Accelerated measurement and empirical estimation of kinetic parameters

Water-sampler equilibrium partitioning coefficients and aqueous boundary layer mass transfer coefficients for atrazine, diuron, hexazionone and fluometuron onto C18 and SDB-RPS Empore disk-based aquatic passive samplers have been determined experimentally under a laminar flow regime (Re = 5400). The method involved accelerating the time to equilibrium of the samplers by exposing them to three water concentrations, decreasing stepwise to 50% and then 25% of the original concentration. Assuming first-order Fickian kinetics across a rate-limiting aqueous boundary layer, both parameters are determined computationally by unconstrained nonlinear optimization. In addition, a method of estimation of mass transfer coefficients-therefore sampling rates-using the dimensionless Sherwood correlation developed for laminar flow over a flat plate is applied. For each of the herbicides, this correlation is validated to within 40% of the experimental data. The study demonstrates that for trace concentrations (sub 0.1 mu g/L) and these flow conditions, a naked Empore disk performs well as an integrative sampler over short deployments (up to 7 days) for the range of polar herbicides investigated. The SDB-RPS disk allows a longer integrative period than the C18 disk due to its higher sorbent mass and/or its more polar sorbent chemistry. This work also suggests that for certain passive sampler designs, empirical estimation of sampling rates may be possible using correlations that have been available in the chemical engineering literature for some time.

Stoichiometric and kinetic characterisation of Nitrosomonas sp in mixed culture by decoupling the growth and energy generation processes

A novel method that relies on the decoupling of the energy production and biosynthesis processes was used to characterise the maintenance, cell lysis and growth processes of Nitrosomonas sp. A Nitrosolnonas culture was enriched in a sequencing batch reactor (SBR) with ammonium as the sole energy source. Fluorescent in situ hybridization (FISH) showed that Nitrosomonas bound to the NEU probe constituted 82% of the bacterial population, while no other known ammonium or nitrite oxidizing bacteria were detected. Batch tests were carried out under conditions that both ammonium and CO, were in excess, and in the absence of one of these two substrates. The oxygen uptake rate and nitrite production rate were measured during these batch tests. The results obtained from these batch tests, along with the SBR performance data, allowed the determination of the maintenance coefficient and the in situ cell lysis rate, as well as the maximum specific growth rate of the Nitrosomonas culture. It is shown that, during normal growth, the Nitrosomonas culture spends approximately 65% of the energy generated for maintenance. The maintenance coefficient was determined to be 0.14 - 0.16 mgN mgCOD(biomass)(-1) h(-1), and was shown to be independent of the specific growth rate. The in situ lysis rate and the maximum specific growth rate of the Nitrosomonas culture were determined to be 0.26 and 1.0 day(-1) (0.043 h(-1)), respectively, under aerobic conditions at 30 degrees C and pH7. (c) 2006 Elsevier B.V. All rights reserved.