Ten-deg off-axis test for shear properties in fiber composites

A combined theoretical and experimental investigation was conducted to assess the suitability of the 10-deg off-axis tensile-test specimen for the intralaminar-shear characterization of unidirectional composites. Composite mechanics, a combined-stress failure criterion and a finiteelement analysis were used to determine theoretically the stress-strain variation across the specimen width and the relative stress and strain magnitudes at the 10-deg plane. Strain gages were used to measure the strain variation across the specimen width at specimen midlength and near the end tabs. Specimens from Mod-I/epoxy. T-300/epoxy, and S-glass/epoxy were used in the experimental program. It was found that the 10-deg off-axis tensile-test specimen is suitable for intralaminar-shear characterization and it, is recommended that it should be considered as a possible standard test specimen for such a characterization.     

On the stress singularities in the plane elasticity of the composite wedge

This paper examines the composite, two-dimensional, linear elastic wedge for singular stresses at its vertex. A full range of wedge boundary and matching conditions is considered. Using separation of variables on the Airy stress function, the usual determinant conditions for singularities of the formO(r ^-) asr 0 are established and further conditions are derived for singularities of the formO(r ^- lnr) asr 0. The order of the determinant involved in these conditions depends upon the number of materials comprising the wedge. Two systematic methods of expanding the determinant for theN-material wedge are presented.

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Résumé Ce papier examine le coin composé, linéaire et élastique, en deux dimensions, pour déterminer les contraintes singulières à son sommet. On va considérer la rangée totale des conditions aux limites du coin, et les conditions correspondantes dans le coin. On se sert de la séparation des variables de la fonction de contrainte d'Airy, pour déterminer les conditions usuelles sur le déterminant pour les singularités de la formeO(r ^-) quandr 0, et on dérive des conditions additionnelles pour les singularités de la formeO(r ^- lnr) quandr 0. L'ordre du déterminant impliqué dans ces conditions dépend du nombre des matériaux dans le coin. D'abord on propose deux méthodes systématiques de développer le déterminant du coin deN-matériaux.

     

Effective medium representation and complex modes in 3D periodic metamaterials made of cubic resonators with large permittivity at mid-infrared frequencies

We review some of the techniques that lead to the effective medium representation of a three-dimensional (3D) periodic metamaterial. We consider a 3D lattice of lead telluride cubic resonators at mid-infrared (MIR) frequencies. Each cubic resonator is modeled with both an electric and a magnetic dipole, through a method called the dual dipole approximation. The electric and magnetic polarizabilities of a cubic resonator are computed via full-wave simulations by mapping the resonator's scattered field under electric/magnetic excitation only to the field radiated by an equivalent electric/magnetic dipole. We then analyze the allowed modes in the lattice, with transverse polarization and complex wavenumber, highlighting the attenuation that each mode experiences after one free space wavelength. We observe the presence of two modes with low attenuation constant, dominant in different frequency ranges, able to propagate inside the lattice: this allows the treatment of the metamaterial as a homogeneous material with effective parameters, evaluated by using various techniques. We then show that the metamaterial under analysis allows for the generation of artificial magnetism (i.e., relative effective permeability different than unity, including negative permeability with low losses) at MIR frequencies.     

A compact UHV package for microfabricated ion-trap arrays with direct electronic air-side access

We have demonstrated a new apparatus for operating microfabricated ion-trap arrays in a compact ultra-high-vacuum setup with excellent optical and electrical access. The approach uses conventional components, materials and techniques in a unique fashion. The microtrap chip is mounted on a modified ceramic leadless chip carrier, the conductors of which serve as the vacuum feedthrough. The chip carrier is indium-sealed to stainless-steel components to form vacuum seals, resulting in short electrical path lengths of ≤20 mm from the trap electrodes under vacuum to air side. The feedthrough contains conductors for the radio-frequency trap drive, as well as 42 conductors for DC electrodes. Vacuum pressures of ～1 × 10^?11 mbar are achieved, and ions have been confined and laser cooled in a microtrap chip. The apparatus enables accurate measurements of radio-frequency voltage amplitudes on the trap electrodes, yielding an excellent agreement between measured and modelled trap efficiencies. This feature is of significant use in establishing initial operation of new devices. The principle of the connectivity scheme presented here is applicable to larger ceramic chip carriers containing many more conductors.     

Erratum to: The Ginibre Ensemble of Real Random Matrices and its Scaling Limits

We correct an error in Theorem 12 of the original article concerning the edge scaling limit of the law of real eigenvalues for the real Ginibre ensemble.     

Ensemble averages when β is a square integer

We give a hyperpfaffian formulation of partition functions and ensemble averages for Hermitian and circular ensembles when L is an arbitrary integer and ???=?L ² and when L is an odd integer and ???=?L ²?+?1.     

Multiple scattering of an obliquely incident plane acoustic wave from a grating of immersed cylindrical shells

The study of the interaction of acoustic waves with cylindrical structures has numerous applications including the ultrasonic nondestructive testing of materials. In this paper, using a new mathematical model presented for the scattering of obliquely incident plane acoustic waves from a grating of immersed cylindrical shells, a detailed study of the resonant interaction of A-wave resonances originating from the shells is conducted. The nature of A-wave resonances and the effect of center-to-center distance of the shells on these resonances are examined. It is observed that this resonant interaction not only results in the splitting of A-wave resonances, but also causes an increase in resonance amplitudes. This interaction phenomenon is not seen in Rayleigh, whispering gallery and guided wave resonances. It is also shown that increasing the angle of wave incidence to the grating weakens the A-wave resonant interactions. The numerical results obtained from the mathematical model are compared to experimental results available in the literature for gratings composed of two and three aluminum shells. The numerical results are in very good agreement with their experimental counterparts.     

Correlation between helical surface waves and guided modes of an infinite immersed elastic cylinder

Scattering of obliquely incident plane acoustic waves from immersed infinite solid elastic cylinders is a complex phenomenon that involves generation of various types of surface waves on the body of the cylinder. Mitri [F.G. Mitri, Acoustic backscattering enhancement resulting from the interaction of an obliquely incident plane wave with an infinite cylinder, Ultrasonics 50 (2010) 675-682] recently showed that for a solid aluminum cylinder, there exist acoustic backscattering enhancements at a normalized frequency of ka?0.1. The incidence angle α_c at which these enhancements are observed lies between the first (longitudinal) and second (shear) coupling angles of the cylinder. He also confirmed the observations previously reported by the authors that there exist backscattering enhancements of the dipole mode at large angles of incidence where no wave penetration into the cylinder is expected. In this paper, physical explanations are provided for the aforementioned observations by establishing a correlation between helical surface waves generated by oblique insonification of an immersed infinite solid elastic cylinder and the longitudinal and flexural guided modes that can propagate along the cylinder. In particular, it is shown that the backscattering enhancement observed at ka?0.1 is due to the excitation of the first longitudinal guided mode travelling at the bar velocity along the cylinder. It is also demonstrated that the dipole resonance mode observed at incidence angles larger than the Rayleigh coupling angle is associated with the first flexural guided mode of the cylinder. The correlation established between the scattering and propagation problems can be used in both numerical and experimental studies of interaction of mechanical waves with cylinders.     

Asymmetric and axisymmetric vibrations of finite transversely isotropic circular cylinders

This paper presents an approach for obtaining the exact frequency equations of axisymmetric and asymmetric free vibrations of transversely isotropic circular cylinders. The solution method is based on the three dimensional theory of linear elasticity and uses potential functions. Using this approach, the frequency spectra and vibration mode shapes are plotted for a number of transversely isotropic cylinders. The proposed approach introduces a number of merits compared to earlier approximate and exact solution methods. First, unlike numerically complicated series methods that provide approximate solutions, the proposed approach is exact. Second, combination of scalar functions employed for representing the displacement field is consistent with the physics of the problem. One scalar potential function has been considered for each component of the wave field inside the elastic cylinder. As a result, the solution is systematically divided into coupled and decoupled equations. In addition, by using this approach, there is no need to guess the final of the solution a priori. These merits make the proposed approach suitable for other vibration problems of anisotropic materials.     

Density functional and spectroscopic studies of nitrogen inversion in substituted dizocilpines

While developing a synthesis towards tagged dizocilpine (MK‐801) analogues, we observed highly restricted inversion of a nitrogen centre in a number hydroxylamines obtained as key intermediates. These compounds are shown to possess some of the structural elements which are expected to significantly hinder the nitrogen inversion, potentially leading to hydroxylamines with a chiral nitrogen centre. Free energy barriers (ΔG^≠) of the nitrogen inversion were estimated to be ca. 22 kcal mol^?1 at temperatures near 420 K using variable temperature NMR measurements in DMSO‐d₆. Further density functional studies of a number model systems were undertaken in order to better rationalize the measured inversion barriers and follow the role of various structural factors in raising the barrier height of the nitrogen inversion process. Copyright © 2008 John Wiley & Sons, Ltd.