The low-frequency reflection and scattering of the S0 Lamb mode from a circular through-thickness hole in a plate: Finite Element,analytical and experimental studies

A study of the interaction of the S0 Lamb wave with a circular through-thickness hole in a plate is presented. The study is limited to the nondispersive frequency range of this wave, in which the distributions of stress and displacement are simple. This allows a Finite Element analysis to be undertaken using a two-dimensional membrane discretization. Predictions of the direct reflection of the S0 mode and the lateral scattering of the SH0 mode are made for a range of diameters of the hole. At the same time, an analytical solution based on modal superposition is developed, and this is also used to predict the reflection and scattering coefficients. Both sets of predictions are validated by experimental measurements. It is found that the trends of the reflection coefficients for different hole diameters, frequencies and distances from the hole satisfy a simple normalization. On a detailed scale, the functions exhibit undulations which are shown to result from the interference of the direct reflection with secondary reflections which arrive slightly later.     

Ultrasonic interferometry for the measurement of shear velocity and attenuation in viscoelastic solids

A method for the measurement of the shear properties of solid viscoelastic materials is presented. The viscoelastic material is cut into a cylindrical sample which is clamped between two rods. The transmission and reflection coefficient spectra of the fundamental torsional mode through the sample are measured by means of two pairs of piezoelectric transducers placed at the free ends of the rod-sample-rod system. Such spectra exhibit maxima and minima which occur approximately at the resonance frequencies of the free viscoelastic cylinder. Therefore, the shear velocity can be obtained by measuring the frequency interval between two consecutive maxima or minima. The shear attenuation is derived by best fitting the analytical expression of the reflection and transmission coefficients to the experimental spectra. The test is very quick to set up as the sample is simply clamped between the two rods.     

A remarkable [2.2.2]propellane

To explore the effects of fluorine substitution on the highly strained [2.2.2]propellane skeleton, a new representative of this ring system, perfluorotricyclo[2.2.2.01,4]octan-2-one ethylene ketal, was prepared by a rapid and quantitative [2+2] cycloaddition to the strained alkene perfluorobicyclo[2.2.0]hex-1(4)-ene. The propellane displays impressive thermal stability, and the vulnerable C-C bond joining the bridgeheads is very resistant to attack by electrophilic reagents. On the other hand, that electron-deficient bond is cleaved quickly at room temperature by a variety of nucleophiles and mild reducing agents. The behavior of this compound contrasts dramatically with that of the only known [2.2.2]propellane lacking fluorine substituents.     

Time evolving theory of the mechanics of single particles and single photons

We introduce space-time ensemble methods to formulate definitions of single particles and single photons as local abstractions of constant processes. We find the general form of the corresponding Stueckelberg Lagrangian for Riemannian and Newtonian spacetimes and supply a physical interpretation for the worldline parameter. We develop the corresponding mechanical theories over the extended configuration space and the extended phase space. We suppose that the background can be represented by an external field and we study several general examples. Certain phenomenological forms do not describe particles, others do not seem to describe theories in which the representation of the background is process independent (Riemannian case). At the canonical level the elimination of second-class constraints associated with null processes generates restrictions on the domain of definition of photon coordinates which correspond to the absence of zero energies. The requirement that the canonical process-anti-process classification exist leads to a factorization condition on the extended phase space which is satisfied for all the cases studied in which the configuration formalisms entail no difficulties, except one, which is the minimally coupled external vector field case over Riemannian space-times. We discuss the observation theoretical significance of our results.     

Development of a practical Buchwald-Hartwig amine arylation protocol using a conveniently prepared (NHC)Pd(R-allyl)Cl catalyst

Continuing efforts to establish a more general "user-friendly" protocol for the palladium-catalysed arylation of amines (Buchwald-Hartwig reaction) are described herein. Significant advances have been made through the use of the versatile (SIPr)Pd(methallyl)Cl complex in conjunction with the reliable base lithium hexamethyldisilazide (LHMDS).     

The scattering of guided waves in partly embedded cylindrical structures

The scattering of ultrasonic guided waves at a point where a free cylindrical waveguide enters an embedding material is investigated. A modal solution that is valid when the guided waves are incident from the free section of the waveguide is developed. It is shown that in this case it is valid to consider only the modal fields over the cross section of the waveguide, neglecting the fields in the embedding material. As an application, the scattering of the lowest-order longitudinal mode in a cylindrical waveguide, L(0,1), is examined in detail. As well as considering epoxy resin as an embedding material, the case where the embedding material is replaced by a perfectly rigid boundary is discussed. The latter gives some insight into the role of nonpropagating and inhomogeneous waveguide modes in the scattering process. The results from the modal solution are validated using Finite Element modeling, very good agreement being obtained.