Nonlinear free vibration analysis of simply supported piezo-laminated plates with random actuation electric potential difference and material properties

Studies are made on nonlinear free vibrations of simply supported piezo-laminated rectangular plates with immovable edges utilizing Kirchoff’s hypothesis and von Kármán strain–displacement relations. The effect of random material properties of the base structure and actuation electric potential difference on the nonlinear free vibration of the plate is examined. The study is confined to linear-induced strain in the piezoelectric layer applicable to low electric fields. The von Kármán’s large deflection equations for generally laminated elastic plates are derived in terms of stress function and transverse deflection function. A deflection function satisfying the simply supported boundary conditions is assumed and a stress function is then obtained after solving the compatibility equation. Applying the modified Galerkin’s method to the governing nonlinear partial differential equations, a modal equation of Duffing’s type is obtained. It is solved by exact integration. Monte Carlo simulation has been carried out to examine the response statistics considering the material properties and actuation electric potential difference of the piezoelectric layer as random variables. The extremal values of response are also evaluated utilizing the Convex model as well as the Multivariate method. Results obtained through the different statistical approaches are found to be in good agreement with each other.     

Void-fraction measurements in a steady-state mercury-nitrogen flow loop

 A steady-state vertical mercury-nitrogen flow system has been investigated using three tomographic algorithms. Void-fraction profiles have been reconstructed by the data collected by a 60 mCi gamma-ray source and a single Na(Tl) detector. The results indicate excellent agreement (within ±1%) between the least-squares-solution and the chord-segment-inversion algorithms. The data-collection time for each data-ray was varied so that in each case 3000 counts could be collected to reduce the detrimental effect of Poisson statistics in the reconstructed profiles. Eleven sets of data have been collected for nitrogen flow-rates between 0.00123 and 0.00884  kg/s. The mercury flow-rates were between 17.6 and 34.1 kg/s. The resulting cross-sectional average void varied between 0.10 and 0.38. Received: 13 March 1997/Accepted: 12 September 1997     

Generation of stable mixed-compact-toroid rings by inducing plasmacurrents in strong E rings

In the RECE-Christa device, hybrid-type compact toroid rings are generated by inducing large toroidal plasma currents I_p in strong electron rings using a thin induction coil positioned along the ring axis. Starting from field-reversal values δ_p =50-120% of the original pure fast-electron ring, the induced plasma current I_p raises δ to a maximum value of up to 240% with I_p contributing more than 50% of the total ring current. The generated hybrid compact toroid configurations appear gross-stable during the full I_p pulse length (half-amplitude width about 100 μs)     

Simple and efficient methods of synthesis of 3,3-diarylcyclobutanone and 3,3-diarylcyclobutylamine derivatives using the TiCl4/R3N reagent system

[reaction: see text] The iminium ions generated in situ by the oxidation of N,N-diisopropyl-N-benzylamine using iodine react with diaryl ketones in the presence of TiCl4/R3N to give the corresponding 3,3-diarylcyclobutanones in moderate to good yields (49-86%). The 3,3-diarylcyclobutanone iminium ions formed in this transformation was reduced in situ with B2H6 to produce the corresponding 3,3-diarylcyclobutylamines (52-79% yields), a class of compounds with potential antidepressant activity. In addition, a series of N,N-dimethyl-3,3-diarylcyclobutylamines were synthesized by the reductive amination of the corresponding 3,3-diarylcyclobutanone derivatives.     

Dendrimers based on a three-dimensionally disposed AB4 monomer

[reaction: see text] Design and synthesis of a novel class of dendrons based on an AB(4) monomer are described. These dendrons have been evaluated by using dendritic encapsulation of a redox active core. The electrochemical properties of symmetric ferrocene-cored dendrimers show that significant alterations in redox potential and heterogeneous electron-transfer rate constants could be achieved even at lower generations.     

Surface-enhanced Raman scattering and the adsorption behavior of (RS)-phenylsuccinic acid

The surface geometry of (RS)-phenylsuccinic acid molecule was studied by analysis of the SERS spectra of aromatic dicarboxylic acid adsorbed on silver colloid surfaces. For a reliable analysis of the SERS spectrum, we also performed density functional theoretical calculations. The SERS spectral features indicated that the RSPSA molecules should bound to the silver as dicarboxylate, with a strongly tilted orientation with respect to the normal to the surface. Such a tilted orientation was presumed to occur by the simultaneous sigma and pi-type coordination of carboxylate groups to silver surface caused by the steric hindrance and electrostatic repulsion between the two carboxylate groups, and thereby RSPSA on silver was easily displaced with aromatic carboxylic acids. A sigma-type coordination therefore seemed to be more important than a pi-type coordination for aromatic carboxylic acid derivatives to assemble on a silver surface. The large enhancement of in-plane bending, out of plane bending and ring breathing modes in the surface-enhanced Raman scattering spectrum indicates that the molecule is adsorbed on the silver surface in a 'at least vertical' configuration, with the ring perpendicular to the silver surface.     

One‐Pot Synthesis of Highly Substituted Polyheteroaromatic Compounds by Rhodium(III)‐Catalyzed Multiple CH Activation and Annulation

A new method for the synthesis of highly substituted naphthyridine‐based polyheteroaromatic compounds in high yields proceeds through rhodium(III)‐catalyzed multiple C? H bond cleavage and C? C and C? N bond formation in a one‐pot process. Such highly substituted polyheteroaromatic compounds have attracted much attention because of their unique π‐conjugation, which make them suitable materials for organic semiconductors and luminescent materials. Furthermore, a possible mechanism, which involves multiple chelation‐assisted ortho C? H activation, alkyne insertion, and reductive elimination, is proposed for this transformation.     

Non-random cation distribution in hexagonal Al0.5Ga0.5PO4

Based on powder X-ray diffraction and ³¹P Magic Angle Spinning Nuclear Magnetic Resonance (MAS NMR) investigations of mixed phosphate Al_0.5Ga_0.5PO₄, prepared by co-precipitation method followed by annealing at 900 °C for 24 h, it is shown that Al_0.5Ga_0.5PO₄ phase crystallizes in hexagonal form with lattice parameter a=0.491(2) and c=1.106(4) nm. This hexagonal phase of Al_0.5Ga_0.5PO₄ is similar to that of pure GaPO₄. The ³¹P MAS NMR spectrum of the mixed phosphate sample consists of five peaks with systematic variation of their chemical shift values and is arising due to existence of P structural units having varying number of the Al³⁺/Ga³⁺ cations as the next nearest neighbors in the solid solution. Based on the intensity analysis of the component NMR spectra of Al_0.5Ga_0.5PO₄, it is inferred that the distribution of Al³⁺ and Ga³⁺ cations is non-random for the hexagonal Al_0.5Ga_0.5PO₄ sample although XRD patterns showed a well-defined solid solution formation.     

Structure and conformational stability of CH2CHCH2X (X=F, Cl and Br) molecules—post Hartree–Fock and density functional theory methods

The molecular structure and conformational stability of CH₂CHCH₂X (X=F, Cl and Br) molecules were studied using ab initio and density functional theory (DFT) methods. The molecular geometries of 3-fluoropropene were optimized employing BLYP and B3LYP levels of theory of DFT method implementing 6-311+G(d,p) basis set. The MP2/6-31G^*, BLYP and B3LYP levels of theory of ab initio and DFT methods were used to optimize the 3-chloropropene and 3-bromopropene molecules. The structural and physical parameters of the molecules are discussed with the available experimental values. The rotational potential energy surface of the above molecules were obtained at MP2/6-31G^* and B3LYP/6-311+G(d,p) levels of theory. The Fourier decomposition of the rotational potentials were analyzed. The HF/6-31G^* and MP2/6-31G^* levels of theory have predicted the cis conformer as the minimum energy structure for 3-fluoropropene, which is in agreement with the experimental values, whereas the BLYP/6-311+G(d,p) and B3LYP/6-311+G(d,p) levels of theory reverses the order of conformation. The ΔE values calculated for 3-chloropropene at MP2/6-31G^*, BLYP/6-311+G(d,p) and B3LYP/6-311+G(d,p) levels of theory show that the gauche form is more stable than the cis form, which is in agreement with the experimental value. The same levels of theory have also predicted that the gauche form is stable than cis for 3-bromopropene molecule. The maximum hardness principle has been able to predict the stable conformer of 3-fluoropropene at HF/6-31G^* level of theory, but the same level of theory reverses the conformational stability of 3-chloropropene and 3-bromopropene molecules and MP2/6-31G^* level of theory predicted the stable conformer correctly.