Vibration of rectangular orthotropic plates

An approximate analytical procedure has been given to solve the problem of a vibrating rectangular orthotropic plate, with various combinations of simply supported and clamped boundary conditions. Numerical results have been given for the case of a clamped square plate. Nomenclature 2a, 2b sides of the rectangular plate h plate thickness Eprime x , Eprime y , EPrime, G elastic constants of te orthotropic material D x Eprime x h 3/12 D y Eprime y h 3/12 H xy EPrimeh 3/12+Gh 3/6 D x , D y and H xy are rigidity constants of the orthotropic platergr mass of the plate per unit area ngr Poisson's ratio W deflection of the plate p circular frequency gamma b/a ratio X m , Y characteristic functions of the vibrating beam problem -lambda rgrp 2 a 2 b 2/H xy the frequency parameter.

Synthetic investigations in the sesamin group - Part I. Synthesis of samin, a degradation product of sesamolin

Ethylα-bromovinylacetate (VII) was condensed with the sodio derivative of ethyl piperonoylacetate (VIII) to give diethylα-vinyl-α′-piperonoylsuccinate (IX). The latter on reduction with lithium aluminium hydride furnished the triol (X), which underwent smooth cyclisation with 1% ethanolic hydrogen chloride to 2-(3′, -methylenedioxyphenyl)-hydroxymethyl-4-vinyltetrahydrofuran (XIa). The structure of XIa was established by Oppenauer oxidation to an aldehyde. Ozonolysis of XIa afforded samin (I).

Synthesis of 1,3-dimethyl-1,3-dicarboxycyclohexane-2-acetic acid. An isomer of the degradation product of abietic acid

A synthesis of 1,3-dimethyl-1,3-dicarboxycyclohexane-2-acetic acid has been described, and proved to be an isomer of the C12-acid-an oxidative degradation product of abietic acid.

Reaction of dialkyl 2-butynoate with aniline and formaldehyde: revision of the structure of the product

Dimethyl 3-(aryl)-3,6-dihydro-2H-1,3-oxazine4,5-dicarboxylate structure assigned for the products obtained in the Bronsted acid catalyzed reaction of dimethyl but-2-ynoates with anilines and an excess of formaldehyde in methanol has been revised to methyl 1-(aryl)-3-(methoxymethyl)-4,5-dioxopyrrolidine-3-carboxylate. (C) 2010 Elsevier Ltd. All rights reserved.

Application of D transforms in the analysis of nonlinear distributed parameter systems

The scope of application of Laplace transforms presently limited to the study of linear partial differential equations, is extended to the nonlinear domain by this study. This has been achieved by modifying the definition of D transforms, put forth recently for the study of classes of nonlinear lumped parameter systems. The appropriate properties of the new D transforms are presented to bring out their applicability in the analysis of nonlinear distributed parameter systems.

Equivalence conditions for classes of linear and non-linear distributed parameter systems

Equivalence of certain classes of second-order non-linear distributed parameter systems and corresponding linear third-order systems is established through a differential transformation technique. As linear systems are amenable to analysis through existing techniques, this study is expected to offer a method of tackling certain classes of non-linear problems which may otherwise prove to be formidable in nature.

Anomalous behavior of hydrodynamic modes in the two dimensional shear flow of a granular material

The growth rates of the hydrodynamic modes in the homogeneous sheared state of a granular material are determined by solving the Boltzmann equation. The steady velocity distribution is considered to be the product of the Maxwell Boltzmann distribution and a Hermite polynomial expansion in the velocity components; this form is inserted into them Boltzmann equation and solved to obtain the coeificients of the terms in the expansion. The solution is obtained using an expansion in the parameter epsilon =(1 - e)(1/2), and terms correct to epsilon(4) are retained to obtain an approximate solution; the error due to the neglect of higher terms is estimated at about 5% for e = 0.7. A small perturbation is placed on the distribution function in the form of a Hermite polynomial expansion for the velocity variations and a Fourier expansion in the spatial coordinates: this is inserted into the Boltzmann equation and the growth rate of the Fourier modes is determined. It is found that in the hydrodynamic limit, the growth rates of the hydrodynamic modes in the flow direction have unusual characteristics. The growth rate of the momentum diffusion mode is positive, indicating that density variations are unstable in the limit k--> 0, and the growth rate increases proportional to kslash} k kslash}(2/3) in the limit k --> 0 (in contrast to the k(2) increase in elastic systems), where k is the wave vector in the flow direction. The real and imaginary parts of the growth rate corresponding to the propagating also increase proportional to kslash k kslash(2/3) (in contrast to the k(2) and k increase in elastic systems). The energy mode is damped due to inelastic collisions between particles. The scaling of the growth rates of the hydrodynamic modes with the wave vector I in the gradient direction is similar to that in elastic systems. (C) 2000 Elsevier Science B.V. All rights reserved.

Growth and characterization of germanium nanowires by electron beam evaporation

Germanium nanowires were grown on Au coated Si substrates at 380 degrees C in a high vacuum (5 x 10(-5) Torr) by e-beam evaporation of Germanium (Ge). The morphology observation by a field emission scanning electron microscope (FESEM) shows that the grown nanowires are randomly oriented with an average length and diameter of 600 nm and 120 nm respectively for a deposition time of 60 min. The nanowire growth ratewas measured to be similar to 10 nm/min. Transmission electron microscope (TEM) studies revealed that the Ge nanowires were single crystalline in nature and further energy dispersive X-ray analysis(EDAX) has shown that the tip of the grown nanowires was capped with Au nanoparticles, this shows that the growth of the Ge nanowires occurs by the vapour liquid solid (VLS) mechanism. HRTEM studies on the grown Ge nanowire show that they are single crystalline in nature and the growth direction was identified to be along [110]. (C) 2010 Elsevier B.V. All rights reserved.

Effect of insertion of buffer-strip on the response of carbon-epoxy system in short beam tests

dThe work looks at the response to three-point loading of carbon-epoxy (CF-EP) composites with inserted buffer strip (BS) material. Short beam Shear tests were performed to study the load-deflection response as well as fracture features through macroscopy on the CF-EP system containing the interleaved PTFE-coated fabric material. Significant differences were noticed in the response of the CF-EP system to the bending process consequent to the architectural modification. It was inferred that introduction of small amounts of less adherent layers of material at specific locations causes a decrement in the load carrying capability. Further the number and the ease with which interface separation occurs is found to depend on the extent to which the inserted layer is present in either single or multiple layer positions.

Effect of interaction of macrocracks on the stress intensity factor in a beam

Beams with a central edge crack, as well as other noncentral vertical and inclined edge cracks distributed symmetrically, subjected to three-point as well as four-point bending, are analysed using the finite element technique. Values of stress intensity factor K1 at the central crack tip for a crack-to-beam depth ratio Image equal to 0.5, are calculated for various cracked-beam configurations, using the compliance calibration technique as well as method of strain energy release rate. These are compared with the value of K1 for the case of a beam with central edge crack alone. Results of the present parametric study are used to specify the range of values pertaining to basic parameters such as crack-to-beam depth ratios, geometry and position with respect to central edge crack, of other macrocracks for which interaction exists. Accordingly, the macrocracks are classified as either interacting or noninteracting types. Hence for noninteracting types of cracks, analytical expressions available for the determination of K1 in the case of beam with a central edge crack alone, are applicable.

Characterization of compact ICP ion source for focused ion beam applications

A compact, high brightness 13.56 MHz inductively coupled plasma ion source without any axial or radial multicusp magnetic fields is designed for the production of a focused ion beam. Argon ion current of density more than 30 mA/cm(2) at 4 kV potential is extracted from this ion source and is characterized by measuring the ion energy spread and brightness. Ion energy spread is measured by a variable-focusing retarding field energy analyzer that minimizes the errors due t divergence of ion beam inside the analyzer. Brightness of the ion beam is determined from the emittance measured by a fully automated and locally developed electrostatic sweep scanner. By optimizing various ion source parameters such as RF power, gas pressure and Faraday shield, ion beams with energy spread of less than 5 eV and brightness of 7100 Am(-2)sr(-1)eV(-1) have been produced. Here, we briefly report the details of the ion source, measurement and optimization of energy spread and brightness of the ion beam. (C) 2010 Elsevier B.V. All rights reserved.

Electron-beam melting and centrifugal splat-quenching technique for rapid solidification of titanium alloys

An electron-beam melting and centrifugal splat-quenching technique for the production of microflakes of Ti-6A1-4V (wt%) alloy quenched at an average cooling rate of about 105 K sec–1 is described. The effect of substrate angle on the shape, size, microstructure and average cooling rate of the flakes of major sieve fractions is discussed. Morphologies of particles of minor sieve fractions are dealt with briefly.