Conditional linearization in nonlinear random vibration

In this paper, an improved probabilistic linearization approach is developed to study the response of nonlinear single degree of freedom (SDOF) systems under narrow-band inputs. An integral equation for the probability density function (PDF) of the envelope is derived. This equation is solved using an iterative scheme. The technique is applied to study the hardening type Duffing's oscillator under narrow-band excitation. The results compare favorably with those obtained using numerical simulation. In particular, the bimodal nature of the PDF for the response envelope for certain parameter ranges is brought out.

Investigations of the reduction behavior of Iron-impregnated alumina gels (Fe/AlOOH) and the formation of Fe0-Al2O3 metal-ceramic composites

Fe/AlOOH gels calcined and reduced at different temperatures have been investigated by a combined use of Mossbauer spectroscopy, x-ray diffraction, and electron microscopy in order to obtain information on the nature of the iron species formed as well as the various reduction processes. Calcination at or below 1070 K mainly gives reducible Fe3+ while calcination at higher temperatures gives substitutional Fe3+ in the form of Al2-xFexO3. The Fe3+ species in the calcined samples are, by and large, present in the form of small superparamagnetic particles. Crystallization of Al2O3 from the gels is catalyzed by Fe2O3 as well as FeAl2O4. Fe (20 wt. %)/AlOOH gels calcined at or below 870 K give FeAl2O4 when reduced in hydrogen at 1070 K or lower and a ferromagnetic Fe0-Al2O3 composite (with the metallic Fe particles >100 angstrom) when reduced at 1270 K. Samples calcined at 1220 K or higher give the Fe0-Al2O3 composite when reduced in the 870-12,70 K range, but a substantial proportion of Fe3+ remains unreduced in the form of Al2-xFexO3, showing thereby the extraordinary stability of substitutional Fe3+ to reduction even at high temperatures. Besides the ferromagnetic Fe0-Al2O3 composite, high-temperature reduction of Al2-xFexO3 yields a small proportion of superparamagnetic Fe0-Al2O3 wherein small metallic particles (<100 angstrom) are embedded in the ceramic matrix. In order to preferentially obtain the Fe0-Al2O3 composite on reduction, Fe/AlOOH gels should be calcined at low temperatures (less-than-or-equal-to 1100 K); high-temperature calcination results in Al2-xFexO3. Several modes of formation of FeAl2O4 are found possible during reduction of the gels, but a novel one is that involving the reaction, 2Fe3+ + Fe0 --> 3Fe2+.

Linear and nonlinear optical properties of cumulenes and polyenynes: a model exact study

Model exact static and frequency-dependent polarizabilities, static second hyperpolarizabilities and THG coefficents of cumulenes and polyenynes, calculated within the correlated Pariser-Parr-Pople (PPP) model defined over the pi-framework are reported and compared with the results for the polyenes. It is found that for the same chain length, the polarizabilities and THG coefficients of the cumulenes are largest and those of the polyenynes smallest with the polyenes having an intermediate value. The optical gap of the infinite cumulene is lowest (0.75 eV) and is associated with a low transition dipole moment for an excitation involving transfer of an electron between the two orthogonal conjugated pi-systems. The polyenynes have the largest optical gap (4.37 eV), with the magnitude being nearly independent of the chain length. This excitation involves charge transfer between the conjugated bonds in the terminal triple bond. Chain length and frequency dependence of alpha(ij) and gamma(ijkl) of these systems are also reported. The effect of a heteroatom on the polarizability and THG coefficients of acetylenic systems is also reported. It has been found that the presence of the heteroatom reduces the polarizability and THG coefficients of these systems, an effect opposite to that found in the polyenes and cyanine dyes. This result has been associated with the different nature of the charge transfer in the acetylenic systems.

Generation of novel materials for nonlinear optics: Analysis of hydrogen-bonded networks in haloaromatic and aliphatic amine-tartrate complexes

Five tartrate-amine complexes have been studied in terms of crystal packing and hydrogen bonding frameworks. The salts are 3-bromoanilinium-L-monohydrogen tartrate 1, 3-fluoroanilinium-D-dibenzoylmonohydrogen tartrate 2, 1-nonylium-D-dibenzoylmonohydrogen tartrate 3, 1 -decylium-D-dibenzoylmonohydrogen tartrate 4, and 1,4-diaminobutanium-D-dibenzoyl tartrate trihydrate 5. The results indicate that there are no halogen-halogen interactions in the haloaromatic-tartrate complexes. The anionic framework allows accomodation of ammonium ions that bear alkyl chain residues of variable lengths. The long chain amines in these structures remain disordered while the short chain amines form multidirectional hydrogen bonds on either side.

Growth and characterization of single crystal cored fibers of organic nonlinear optical materials

The recent development of several organic materials with large nonlinear susceptibilities, high damage threshold and low melting points encouraged researchers to employ these materials in fiber form to efficiently couple diode laser pumps and obtain enhanced second harmonic generation (SHG). In this paper we report the growth of single crystal cored fibers of 4-nitro-4'-methylbenzylidene aniline, ethoxy methoxy chalcone and (-)2-((alpha) -methylbenzylamino)-5- nitropyridine by inverted Bridgman-Stockbarger technique. The fibers were grown in glass capillaries with varying internal diameters and lengths and were characterized using x-ray and polarizing microscope techniques. The propagation loss at 632.8 nm and 1300 nm were measured and SHG was studied using 1064 nm pump.

Nonlinear static and dynamic damped response of a composite rectangular plate resting on a two-parameter elastic foundation

Nonlinear static and dynamic response analyses of a clamped. rectangular composite plate resting on a two-parameter elastic foundation have been studied using von Karman's relations. Incorporating the material damping, the governing coupled, nonlinear partial differential equations are obtained for the plate under step pressure pulse load excitation. These equations have been solved by a one-term solution and by applying Galerkin's technique to the deflection equation. This yields an ordinary nonlinear differential equation in time. The nonlinear static solution is obtained by neglecting the time-dependent variables. Thc nonlinear dynamic damped response is obtained by applying the ultraspherical polynomial approximation (UPA) technique. The influences of foundation modulus, shear modulus, orthotropy, etc. upon the nonlinear static and dynamic responses have been presented.

High swirl-inducing piston bowls in small diesel engines for emission reduction

Detailed three-dimensional CFD simulations involving flow and combustion chemistry are used to study the effect of swirl induced by re-entrant piston bowl geometries on pollutant emissions from a single-cylinder diesel engine. The baseline engine configuration consists of a hemispherical piston bowl and an injector with finite sac volume. The first iteration involved using a torroidal, slightly re-entrant bowl geometry, and a sac-less injector. Pollutant emission measurements indicated a reduction in emissions with this modification. Simulations on both configurations were then conducted to understand the effect of the changes. The simulation results indicate that the selected piston bowl geometry could actually be reducing the in-cylinder swirl and turbulence and the emission reduction may be entirely due to the introduction of the sac-less injector. In-cylinder air motion was then studied in a number of combustion chamber geometries, and a geometry which produced the highest in-cylinder swirl and Turbulence Kinetic Energy (TKE) around the compression top dead centre (TDC) was identified. The optimal nature of this re-entrant piston bowl geometry is confirmed by detailed combustion simulations and emission predictions. (C) 2010 Elsevier Ltd. All rights reserved.

Model Hamiltonians for nonlinear optical properties of conjugated polymers

Quantum cell models for delocalized electrons provide a unified approach to the large NLO responses of conjugated polymers and pi-pi* spectra of conjugated molecules. We discuss exact NLO coefficients of infinite chains with noninteracting pi-electrons and finite chains with molecular Coulomb interactions V(R) in order to compare exact and self-consistent-field results, to follow the evolution from molecular to polymeric responses, and to model vibronic contributions in third-harmonic-generation spectra. We relate polymer fluorescence to the alternation delta of transfer integrals t(1+/-delta) along the chain and discuss correlated excited states and energy thresholds of conjugated polymers.

Nonlinear dynamics of a rigid block on a rigid base

The planar rocking of a prismatic rectangular rigid block about either of its corners is considered. The problem of homoclinic intersections of the stable and unstable manifolds of the perturbed separatrix is addressed to and the corresponding Melnikov functions are derived. Inclusion of the vertical forcing in the Hamiltonian permits the construction of a three-dimensional separatrix. The corresponding modified Melnikov function of Wiggins for homoclinic intersections is derived. Further, the 1-period symmetric orbits are predicted analytically using the method of averaging and compared with the simulation results. The stability boundary for such orbits is also established.

Novel reduction (Zn-AcOH) of DDHQ esters - A new route to tropone synthesis

Zn/acetic acid reaction of DDHQ esters 1 a-d gave the saturated acids 3 a-d and the hydrocarbons 7 a-d. The intermediacy of the aldehydes 10 and 11 in the formation of the products has been established. Oxidation of hydrocarbons 7a and 7b gave the corresponding tropones (5a and 5b).

Crystal growth and defects characterization of zinc tris (thiourea) sulfate: a novel metalorganic nonlinear optical crystal

Single crystals of the metalorganic nonlinear optical material zinc tris (thiourea) sulfate (ZTS) were grown from aqueous solution. The morphology of the crystals was indexed. The grown crystals were characterized by recording the powder X-ray diffraction pattern and by identifying the diffracting planes. Spectrophotometric studies on ZTS reveal that it has good transparency for the Nd: YAG laser fundamental wavelength. Differential thermal analysis of ZTS indicates that the material does not sublime before melting but decomposes immediately after melting. The defect content of the crystals was estimated using etching and X-ray topography. The mechanical hardness anisotropy was evaluated in the (100) plane, which indicates the presence of soft directions.

Reduction of quinolines to 1,2,3,4-tetrahydro derivatives employing a combination of NaCNBH3 and BF3.OEt(2)

A regiospecific reduction of quinolines (and 1,10-phenanthroline) into the corresponding 1,2,3,4-tetrahydro derivatives using a combination of sodium cyanoborohydride and boron trifluoride etherate in refluxing methanol is described. Under the same conditions indole and acridine reduced to the corresponding dihydroderivatives, whereas acyl group transfer from oxygen to nitrogen atom is also noticed in the case of 8-acyloxyquinolines.

Optimization of Helicopter Rotor Using Polynomial and Neural Network Metamodels

This study aims to determine optimal locations of dual trailing-edge flaps and blade stiffness to achieve minimum hub vibration levels in a helicopter, with low penalty in terms of required trailing-edge flap control power. An aeroelastic analysis based on finite elements in space and time is used in conjunction with an optimal control algorithm to determine the flap time history for vibration minimization. Using the aeroelastic analysis, it is found that the objective functions are highly nonlinear and polynomial response surface approximations cannot describe the objectives adequately. A neural network is then used for approximating the objective functions for optimization. Pareto-optimal points minimizing both helicopter vibration and flap power ale obtained using the response surface and neural network metamodels. The two metamodels give useful improved designs resulting in about 27% reduction in hub vibration and about 45% reduction in flap power. However, the design obtained using response surface is less sensitive to small perturbations in the design variables.

Reduction of DDHQ and TCC esters by NaBH4-its specificity in the presence of Alkyl/Aryl esters

DDHQ/TCC esters 3a–f, 7a–g were prepared either by oxidation of spiroketones 1 with DDQ/Image -chloranil or by condensation of acid chloride with DDHQ/TCC. NaBH4 reduction of unsaturated DDHQ 3a–b and TCC 7a–c esters gave the corresponding allylic alcohols in good yield without any observable 1,4-addition products. Reduction of saturated esters 3e, 7d, gave the corresponding alcohols. Alkyl esters 5 and 6, methyl benzoate and phenyl benzoate remained unaffected under these reduction conditions. In the reduction of compound 7e containing both alkyl and TCC esters, TCC ester is selectively reduced. Reduction of TCC mono esters 7f–g gave the lactones. The observed facile reduction has been rationalised.

Relationship between nonlinear resistivity and the varistor forming mechanism in ZnO ceramics

The use of a number of perovskite phases M� M�O3-x, as the only forming additive in ZnO ceramics, produces a high nonlinearity index, ?(up to 45), where M� is a multivalent transition?metal ion and M� is an alkaline earth or a rare?earth ion. From this study, the formation parameters crucial to high nonlinearity, such as nonstoichiometry in the as?received ZnO powder, low x values of the additives and fast cooling rate after the sintering, are explainable on the basis of a depletion layer formation at the presintering stage. This is because of the surface states arising out of the chemisorbed oxygen. The depletion layer is retained during sintering as a result of the higher valence state of M� ions, preferentially present at the grain?boundary regions. The fast cooling freezes in the high?temperature concentration of donor?type defects, thereby decreasing the depletion layer width.