Dimensionless analysis of constrained damping treatments

One of the most effective ways of controlling vibrations in plate or beam structures is by means of constrained viscoelastic damping treatments. Contrary to the unconstrained configuration, the design of constrained and integrated layer damping treatments is multifaceted because the thickness of the viscoelastic layer acts distinctly on the two main counterparts of the strain energy the volume of viscoelastic material and the shear strain field. In this work, a parametric study is performed exploring the effect that the design parameters, namely the thickness/length ratio, constraining layer thickness, material modulus, natural mode and boundary conditions have on these two counterparts and subsequently, on the treatment efficiency. This paper presents five parametric studies, namely, the thickness/length ratio, the constraining layer thickness, material properties, natural mode and boundary conditions. The results obtained evidence an interesting effect when dealing with very thin viscoelastic layers that contradicts the standard treatment efficiency vs. layer thickness relation; hence, the potential optimisation of constrained and integrated viscoelastic treatments through the use of properly designed thin multilayer configurations is justified. This work presents a dimensionless analysis and provides useful general guidelines for the efficient design of constrained and integrated damping treatments based on single or multi-layer configurations. (C) 2012 Elsevier Ltd. All rights reserved.

The effect of the angle of incidence on the aqueous corrosion of ion implanted M50 steel substrates

Following work on tantalum and chromium implanted flat M50 steel substrates, this work reports on the electrochemical behaviour of M50 steel implanted with tantalum and chromium and the effect of the angle of incidence. Proposed optimum doses for resistance to chloride attack were based on the interpretation of results obtained during long-term and accelerated electrochemical testing. After dose optimization from the corrosion viewpoint, substrates were implanted at different angles of incidence (15°, 30°, 45°, 60°, 75°, 90°) and their susceptibility to localized corrosion assessed using open-circuit measurements, step by step polarization and cyclic voltammetry at several scan rates (5–50 mV s-1). Results showed, for tantalum implanted samples, an ennoblement of the pitting potential of approximately 0.5 V for an angle of incidence of 90°. A retained dose of 5 × 1016 atoms cm-2 was found by depth profiling with Rutherford backscattering spectrometry. The retained dose decreases rapidly with angle of incidence. The breakdown potential varies roughly linearly with the angle of incidence up to 30° falling fast to reach -0.1 V (vs. a saturated calomel electrode (SCE)) for 15°. Chromium was found to behave differently. Maximum corrosion resistance was found for angles of 45°–60° according to current densities and breakdown potentials. Cr+ depth profiles ((p,γ) resonance broadening method), showed that retained doses up to an angle of 60° did not change much from the implanted dose at 90°, 2 × 1017 Cr atoms cm-2. The retained implantation dose for tantalum and chromium was found to follow a (cos θ)8/3 dependence where θ is the angle between the sample normal and the beam direction.

Positive radial solutions of the Dirichlet problem for the Minkowski-Curvature equation in a ball

We study the existence and multiplicity of positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation { -div(del upsilon/root 1-vertical bar del upsilon vertical bar(2)) in B-R, upsilon=0 on partial derivative B-R,B- where B-R is a ball in R-N (N >= 2). According to the behaviour off = f (r, s) near s = 0, we prove the existence of either one, two or three positive solutions. All results are obtained by reduction to an equivalent non-singular one-dimensional problem, to which variational methods can be applied in a standard way.

Redox-active cytotoxic diorganotin(IV) cycloalkylhydroxamate complexes with different ring sizes: Reduction behaviour and theoretical interpretation

Two series of new diorganotin(IV) cycloalkylhydroxamate complexes with different ring sizes (cyclopropyl, cyclobutyl, cyclopentyl and cyclohexyl), formulated as the mononuclear [R2Sn(HL)(2)] (1:2) (a, R=Bu-n and Ph) and the polymeric [R2SnL](n) (1:1) (b, R=Bu-n) compounds, were prepared and fully characterized. Single crystal X-ray diffraction for [(Bu2Sn)-Bu-n{C5H9C(O)NHO}(2)] (3a) discloses the cis geometry and strong intermolecular NH center dot center dot center dot O interactions. The in vitro cytotoxic activities of the complexes were evaluated against HL-60, Bel-7402, BGC-823 and KB human tumour cell lines, the greater activity concerning [(Bu2Sn)-Bu-n(HL)(2)] [HL=C3H5C(O)NHO (1a), C6H11C(O)NHO (4a)] towards BGC-823. The complexes undergo, by cyclic voltammetry and controlled-potential electrolysis, one irreversible overall two-electron cathodic process at a reduction potential that does not appear to correlate with the antitumour activity. The electrochemical behaviour of [R2Sn(C5H9C(O)NHO)(2)] [R=Bu-n (3a), Ph (7a)] was also investigated using density functional theory (DFT) methods, showing that the ultimate complex structure and the mechanism of its formation are R dependent: for the aromatic (R = Ph) complex, the initial reduction step is centred on the phenyl ligands and at the metal, being followed by a second reduction with Sn-O and Sn-C ruptures, whereas for the alkyl (R=Bu-n) complex the first reduction step is centred on one of the hydroxamate ligands and is followed by a second reduction with Sn-O bond cleavages and preservation of the alkyl ligands. In both cases, the final complexes are highly coordinative unsaturated Sn-II species with the cis geometry, features that can be of biological significance.