Analysis of vibration of clamped square plates by the Rayleigh-Ritz method with asymptotic solutions from a modified Bolotin method

Estimates of flexural frequencies of clamped square plates are initially obtained by the modified Bolotin's method. The mode shapes in “each direction” are then determined and the product functions of these mode shapes are used as admissible functions in the Rayleigh-Ritz method. The data for the first twenty eigenvalues in each of the three (four) symmetric groups obtained by the (i) Bolotin, (ii) Rayleigh and (iii) Rayleigh-Ritz methods are reported here. The Rayleigh estimates are found to be much closer to the true eigenvalues than the Bolotin estimates. The present product functions are found to be much superior to the conventional beam eigenmodes as admissible functions in the Rayleigh-Ritz method of analysis.

Oxidation of bis-(2-hydroxy-1-naphthyl)methane with 2,3-dichloro-5,6-dicyano-1,4-benzoquinone. X-Ray crystal structure of a novel product

A novel compound obtained by the oxidation of the title compound with 2,3-dichloro-5,6-dicyano-1,4-benzoquinone has been assigned structure (5) on the basis of spectral data and X-ray crystal structure analysis.

Interaction of metal ions with 6-oxopurine nucleotides. Part 2. X-Ray structures of ternary nickel(II) complexes with 2'-deoxyguanosine 5'-monophosphate or guanosine 5'-monophosphate

The ternary metal nucleotide complexes [Ni(en)1.3(H2O)1.4(H2O)2][Ni(5?-dGMP)2(en)0.7-(H2O)0.6(H2O)2]·7H2O (1) and [Ni(en)2(H2O)2][Ni(5?-GMP)2(H2O)4]·6H2O (2)(en = ethylenediamine, 5?-dGMP = 2?-deoxyguanosine 5?-monophosphate, 5?-GMP = guanosine 5?-monophosphate) have been prepared and their structures analyzed by X-ray diffraction methods. Both compounds crystallise in the space group C2221 with a= 8.810(1), b= 25.090(4), c= 21.084(1)Å, and Z= 4 for (1) and a= 8.730(1), b= 25.691(4), c= 21.313(5)Å, and Z= 4 for (2). The structures were deduced from the analogous CoIII complexes and refined by full-matrix least-squares methods to final R values of 0.087 and 0.131 for 1 211 and 954 reflections for (1) and (2) respectively. An interesting feature of the deoxyribonucleotide complex (1) is that en is not totally labilized from the metal centre on nucleotide co-ordination, as observed in corresponding ribonucleotide complexes. Apart from extensive intra- and inter-molecular hydrogen bonding, the structures are stabilized by significant intracomplex base�base and base�sugar interactions. The nucleotides in both complexes have an anti base, C(2?)-endo sugar pucker, and gauche�gauche conformation about the C(4?)�C(5?) bond.

Oxidation Of Spiroalcohols With 2,3-Dichloro-5,6-Dicyano-1,4-Benzoquinone (Ddq) .4. Structure Of A Novel Dioxepin Derivative

DDQ oxidation of the spiroalcohol 7a gives exclusively a compound to which the 13a-methyl-13aH-7a, 15-methano-15H-dinaphtho[2,1-b:2',1'-e][1,4]-dioxepin structure 8a has been assigned on the basis of two-dimensional homonuclear (H-1-H-1) and heteronuclear (H-1-C-13; FUCOUP) correlation spectroscopy experiments. Similar oxidation of spiroalcohols 7b-h gives the dioxepin derivatives 8b-h.

A characteristic based numerical method with tracking for nonlinear wave equations

Many physical problems can be modeled by scalar, first-order, nonlinear, hyperbolic, partial differential equations (PDEs). The solutions to these PDEs often contain shock and rarefaction waves, where the solution becomes discontinuous or has a discontinuous derivative. One can encounter difficulties using traditional finite difference methods to solve these equations. In this paper, we introduce a numerical method for solving first-order scalar wave equations. The method involves solving ordinary differential equations (ODEs) to advance the solution along the characteristics and to propagate the characteristics in time. Shocks are created when characteristics cross, and the shocks are then propagated by applying analytical jump conditions. New characteristics are inserted in spreading rarefaction fans. New characteristics are also inserted when values on adjacent characteristics lie on opposite sides of an inflection point of a nonconvex flux function, Solutions along characteristics are propagated using a standard fourth-order Runge-Kutta ODE solver. Shocks waves are kept perfectly sharp. In addition, shock locations and velocities are determined without analyzing smeared profiles or taking numerical derivatives. In order to test the numerical method, we study analytically a particular class of nonlinear hyperbolic PDEs, deriving closed form solutions for certain special initial data. We also find bounded, smooth, self-similar solutions using group theoretic methods. The numerical method is validated against these analytical results. In addition, we compare the errors in our method with those using the Lax-Wendroff method for both convex and nonconvex flux functions. Finally, we apply the method to solve a PDE with a convex flux function describing the development of a thin liquid film on a horizontally rotating disk and a PDE with a nonconvex flux function, arising in a problem concerning flow in an underground reservoir.

Vibration and Stability of Fluid Conveying Pipes with Stochastic Parameters

Flexible cantilever pipes conveying fluids with high velocity are analysed for their dynamic response and stability behaviour. The Young's modulus and mass per unit length of the pipe material have a stochastic distribution. The stochastic fields, that model the fluctuations of Young's modulus and mass density are characterized through their respective means, variances and autocorrelation functions or their equivalent power spectral density functions. The stochastic non self-adjoint partial differential equation is solved for the moments of characteristic values, by treating the point fluctuations to be stochastic perturbations. The second-order statistics of vibration frequencies and mode shapes are obtained. The critical flow velocity is-first evaluated using the averaged eigenvalue equation. Through the eigenvalue equation, the statistics of vibration frequencies are transformed to yield critical flow velocity statistics. Expressions for the bounds of eigenvalues are obtained, which in turn yield the corresponding bounds for critical flow velocities.

Numerical studies on quasilinear and linear elliptic equations

We explore here the acceleration of convergence of iterative methods for the solution of a class of quasilinear and linear algebraic equations. The specific systems are the finite difference form of the Navier-Stokes equations and the energy equation for recirculating flows. The acceleration procedures considered are: the successive over relaxation scheme; several implicit methods; and a second-order procedure. A new implicit method—the alternating direction line iterative method—is proposed in this paper. The method combines the advantages of the line successive over relaxation and alternating direction implicit methods. The various methods are tested for their computational economy and accuracy on a typical recirculating flow situation. The numerical experiments show that the alternating direction line iterative method is the most economical method of solving the Navier-Stokes equations for all Reynolds numbers in the laminar regime. The usual ADI method is shown to be not so attractive for large Reynolds numbers because of the loss of diagonal dominance. This loss can however be restored by a suitable choice of the relaxation parameter, but at the cost of accuracy. The accuracy of the new procedure is comparable to that of the well-tested successive overrelaxation method and to the available results in the literature. The second-order procedure turns out to be the most efficient method for the solution of the linear energy equation.

Charge transfer complexes of crown ethers with neutral organic gyama-acceptor, 2-dicyanoethylene 1,3-indane dione

The interaction of benzo-15-crown-5, dibenzo-18-crown-6 and dibenzo-24-crown-8 with 2-dicyanoethylene 1,3-indane dione in CH2Cl2 has been described in terms of the formation of 1 : 1 molecular complexes. The magnitude of association constants and thermodynamic parameters indicate cooperative interactions of oxygens with the acceptors. The 1H and 13C NMR spectra of the complexes show that gyama-gyama interactions are a major source of ground state stabilization in these complexes.

Phase Equilibria in the System $Al_{2}O_{3}-CaO-CoO$ and Gibbs Energy of Formation of $Ca_{3}CoAl_{4}O_{10}$

The floating-zone method with different growth ambiences has been used to selectively obtain hexagonal or orthorhombic DyMnO3 single crystals. The crystals were characterized by x-ray powder diffraction of ground specimens and a structure refinement as well as electron diffraction. We report magnetic susceptibility, magnetization and specific heat studies of this multiferroic compound in both the hexagonal and the orthorhombic structure. The hexagonal DyMnO3 shows magnetic ordering of Mn3+ (S = 2) spins on a triangular Mn lattice at T-N(Mn) = 57 K characterized by a cusp in the specific heat. This transition is not apparent in the magnetic susceptibility due to the frustration on the Mn triangular lattice and the dominating paramagnetic susceptibility of the Dy3+ (S = 9/2) spins. At T-N(Dy) = 3 K, a partial antiferromagnetic order of Dy moments has been observed. In comparison, the magnetic data for orthorhombic DyMnO3 display three transitions. The data broadly agree with results from earlier neutron diffraction experiments, which allows for the following assignment: a transition from an incommensurate antiferromagnetic ordering of Mn3+ spins at T-N(Mn) = 39 K, a lock-in transition at Tlock-in = 16 K and a second antiferromagnetic transition at T-N(Dy) = 5 K due to the ordering of Dy moments. Both the hexagonal and the orthorhombic crystals show magnetic anisotropy and complex magnetic properties due to 4f-4f and 4f-3d couplings.

The Influence of Processing Parameters on Characteristics of an Aluminum Alloy Spray Deposition

In the present investigation, two nozzle configurations are used for spray deposition, convergent nozzle (nozzle-A), and convergent nozzle with 2 mm parallel portion attached at its end (nozzle-C) without changing the exit area. First, the conditions for subambient aspiration pressure, i.e., pressure at the tip of the melt delivery tube, are established by varying the protrusion length of the melt delivery tube at different applied gas pressures for both of the nozzles. Using these conditions, spray deposits in a reproducible manner are successfully obtained for 7075 Al alloy. The effect of applied gas pressure, flight distance, and nozzle configuration on various characteristics of spray deposition, viz., yield, melt flow rate, and gas-to-metal ratio, is examined. The over-spray powder is also characterized with respect to powder size distribution, shape, and microstructure. Some of the results are explained with the help of numerical analysis presented in an earlier article.