Dynamic boundary stabilization of a Reissner–Mindlin plate with Timoshenko beam

This paper is concerned with well‐posedness results for a mathematical model for the transversal vibrations of a two‐dimensional hybrid elastic structure consisting of a rectangular Reissner–Mindlin plate with a Timoshenko beam attached to its free edge. The model incorporates linear dynamic feedback controls along the interface between the plate and the beam. Classical semigroup methods are employed to show the unique solvability of the coupled initial‐boundary‐value problem. We also show that the energy associated with the system exhibits the property of strong stability. Copyright © 2004 John Wiley & Sons, Ltd.     

Well‐posedness of the equations governing the motions of a one‐dimensional hybrid thermo‐elastic structure

In this paper a model for the vibrations of a one‐dimensional hybrid thermo‐elastic structure consisting of an extensible thermo‐elastic beam which is hinged at one end, with a rigid body attached to its free end, is studied with a view to establishing the existence of a unique solution in a weak sense. The model takes account of the effect of stretching on bending and rotational inertia. By treating eigenvalue problems with the spectral parameter also in the boundary conditions, we are able to employ the method of Faedo–Galerkin approximations. Copyright © 2004 John Wiley & Sons, Ltd.     

Heat transfer effects on hydropneumatic suspension systems

One of the problems experienced on hydropneumatic suspension systems, is the effect of temperature change on the spring characteristic, resulting in variations in spring rate and ride height. This problem can be analysed using an appropriate heat transfer model. Two major heat transfer modes are investigated, i.e. heat transfer between the gas and its surroundings and heat transfer between the damper oil and the gas. The analyses performed include the determination of the dynamic spring force characteristic, the effect of heat build-up on the spring force characteristic and the effect of heat build-up on the performance of the hydropneumatic spring and damper unit during vehicle tests. Mathematical modelling of the spring characteristic is performed by solving the energy equation for a gas in a closed container using the thermal time constant approach. The Benedict–Webb–Rubin equation of state is used for real gas behaviour. The mathematical model is verified against experimental data and good correlation is achieved. It is shown that hydropneumatic suspension systems have a significant amount of inherent damping due to heat transfer which produces no nett temperature change or heat build-up. The effect of heat build-up in the damper on the spring force characteristic is determined by laboratory tests. It is shown that heat generation in the damper, accompanied by a rise in gas temperature, has a detrimental effect on the spring force characteristic. Tests performed on experimental hydropneumatic spring and damper systems fitted to a test vehicle indicate that the effect is smaller in practice than anticipated. Heat build-up is strongly influenced by terrain roughness, vehicle speed, mission profile and damping levels.     

Strong stability for a fluid–structure interaction model

In this paper we consider the question of stabilization of a fluid–structure model that describes the interaction between a 3‐D incompressible fluid and a 2‐D plate, the interface, which coincides with a flat flexible part of the surface of the vessel containing the fluid. The mathematical model comprises the Stokes equations and the equations for the longitudinal deflections of the plate with inclusion of the shear stress, which the fluid exerts on the plate. We show that the energy associated with the model decays strongly when the interface is equipped with a locally supported dissipative mechanism. Our main tool is an abstract resolvent criterion due to Tomilov. Copyright © 2008 John Wiley & Sons, Ltd.     

Uniform stabilization of a nonlinear structural acoustic model with a Timoshenko beam interface

This paper is concerned with a nonlinear model which describes the interaction of sound and elastic waves in a two‐dimensional acoustic chamber in which one flat ‘wall’, the interface, is flexible. The composite dynamics of the structural acoustic model is described by the linearized equations for a gas defined on the interior of the chamber and the nonlinear Timoshenko beam equations on the interface. Uniform stability of the energy associated with the interactive system of partial differential equations is achieved by incorporating a nonlinear feedback boundary damping scheme in the equations for the gas and the beam. Copyright © 2006 John Wiley & Sons, Ltd.     

Uniform stabilization of a one‐dimensional hybrid thermo‐elastic structure

This paper is concerned with the stabilization of a one‐dimensional hybrid thermo‐elastic structure consisting of an extensible thermo‐elastic beam which is hinged at one end with a rigid body attached to its free end. The model takes account of the effect of stretching on bending and rotational inertia. The property of uniform stability of the energy associated with the model is asserted by constructing an appropriate Lyapunov functional for an abstract second order evolution problem. Critical use is made of a multiplier of an operator theoretic nature, which involves the fractional power A^?1/2 of the bi‐harmonic operator pair A acting in the abstract evolution problem. An explicit decay rate of the energy is obtained. Copyright © 2003 John Wiley & Sons, Ltd.     

A kinetic investigation of the oxidative addition reactions of the dimeric Bu4N[Ir2(μ-Dcbp)(CO)2(PCy3)2] complex with iodomethane

The IR and UV/visible kinetic results of the oxidative addition of iodomethane to Bu₄N[Ir₂(μ-Dcbp)(CO)₂(PCy₃)₂] (Dcbp = 3,5-dicarboxylatepyrazolate anion) showed three time separable reactions. The first, very fast reaction corresponds to the a Ir(I)-Ir(III) alkyl species formation within 10⁻³ s. The second, relative fast reaction corresponds to Ir(III)-Ir(III) alkyl formation with a rate constant of 3.25(4) × 10⁻² M⁻¹ s⁻¹ while the third and slowest reaction corresponds to Ir(III)-Ir(III) acyl formation with a rate constant of 1.42 × 10⁻⁵ s⁻¹. The IR data clearly show the existence of a number of equilibria with the formation of an Ir(I)-Ir(III) alkyl product which then react to form the Ir(III)-Ir(III) which then slowly react to form the Ir(III)-Ir(III) acyl product. A solvent study indicated increased oxidative addition activity in the presence of polar solvents, which is indicative of a polar transition state. The large negative entropy of activation for the Ir(III)-Ir(III) alkyl formation step (k₂) of −178(23) JK⁻¹ mol⁻¹ is indicative of an associative process. DFT calculations successfully identified the stereochemistry of the starting complex, [Ir₂(μ-Dcbp)(CO)₂(PCy₃)₂]⁻ as well as that of the Ir-alkyl and acyl isomers. A reaction pathway, using the IR data and DFT calculations, is proposed for the reaction.     

Quantification of testosterone and epitestosterone in human urine samples by stir bar sorptive extraction--thermal desorption--gas chromatography/mass spectrometry: application to HIV-positive urine samples

A simple method is described for the measurement of testosterone (T) and epitestosterone (ET) in human urine samples. The deconjugated steroids were extracted directly from the samples by stir bar sorptive extraction (SBSE) and derivatized in situ on the stir bar by headspace acylation prior to thermal desorption and GC/MS. Extraction and derivatization parameters, namely salt addition, temperature, and time, were optimized to improve the recovery of T and ET by SBSE. The limits of quantification (S/N 10) were 0.9 ng/mL for T and 2.8 ng/mL for ET. Quantification of the steroids in urine samples was performed using standard addition to avoid the influence of matrix effects. The method was applied for the measurement of urinary T and ET in a group of healthy volunteers and HIV+ patients. Decreased levels of T were detected in the HIV+ group, whereas the excretion of ET was comparable for the two groups. Further clinical research is required to elucidate the biomarker significance of the T/ET ratio in HIV infection.     

Strong stabilization of a structural acoustic model,which incorporates shear and thermal effects in the structural component

In this paper we consider the question of stabilization of a linear three‐dimensional structural acoustic model, which incorporates displacement, rotational inertia, shear and thermal effects in the flat flexible structural component of the model. We show strong stabilization of the coupled model without incorporating viscous or boundary damping in the equations for the gas dynamics and without imposing geometric conditions. It turns out that damping is needed in the interior of the plate. Our main tool is an abstract resolvent criterion due to Y. Tomilov. Copyright © 2009 John Wiley & Sons, Ltd.