HOMOTOPY PERTURBATION SOLUTION AND PERIODICITY ANALYSIS OF NONLINEAR VIBRATION OF THIN RECTANGULAR FUNCTIONALLY GRADED PLATES

In this paper nonlinear analysis of a thin rectangular functionally graded piate is formulated in terms of von-Karman＇s dynamic equations. Functionaily Graded Material （FGM） properties vary through the constant thickness of the plate at ambient temperature. By expansion of the solution as a series of mode functions, we reduce the governing equations of motion to a Duffing＇s equation. The homotopy perturbation solution of generated Duffing＇s equation is also obtained and compared with numerical solutions. The sufficient conditions for the existence of periodic oscillatory behavior of the plate are established by using Green＇s function and Schauder＇s fixed point theorem.     

Analytical second derivatives of molecular electronic energy integrals obtained by spherical gaussian orbital

In this research, the complete general formulas for the analytical second derivative of the molecular integrals for spherical gaussian orbitals of electronic energy are presented. Formulas were given for the second derivative for orbital exponent, orbital and nuclear cartesian coordinates and coefficients of contracted gaussians. In order to save computational time, the formulas for the second derivative are written in terms of the original integrals. Although the formulas were presented in general for any type of application, the Floating Spherical Gaussian Orbital (FSGO) method is applied to some molecules such as LiH, H₂O and CH₂ (singlet) to check the formulas. The results were compared with the results of the finite difference method. Besides the accuracy of the analytical derivative, the saving in computational time is significant.     

Assessment of the effect of N-oxide group in a new high-performance energetic tetrazine derivative on its physicochemical and thermodynamic properties,sensitivity, and combustion and detonation performance

Chemistry of Heterocyclic Compounds - This work uses density functional theory and suitable predictive methods to assess the effect of N-oxide group in 1,2-bis(6-nitro-1,2,4,5-tetrazin-3-yl)diazene...     

Analyzing the effects of jump phenomenon in nonlinear vibration of thin circular functionally graded plates

In this paper, the nonlinear vibration of a thin circular functionally graded material plates is studied. The plate thickness is constant, and the material properties of the plate are assumed to vary continuously through the thickness. The governing equations and boundary conditions are extracted. The assumed-time-mode method is used to analyze these equations. The time variable is eliminated by assuming a harmonic response for nonlinear vibration and using Kantorovich time averaging technique. Utilizing shooting and Runge–Kutta methods, the set of first-order nonlinear differential equations are solved. The effect of volume fraction index in free and forced vibration response and jump phenomenon is studied. The results show that jump phenomenon occur according to volume fraction index and uniform temperature in the special frequencies of forced vibration response.     

Fabrication of highly efficient dye-sensitized solar cell and CO2 reduction photocatalyst using TiO2 nanoparticles prepared by spin coating-assisted sol–gel method

A sol?Cgel method was applied for fabrication of nanocrystalline anatase TiO₂ thin films on ITO glass substrates and followed by rapid thermal annealing for application as the work electrode for dye-sensitized solar cells (DSSC). TiO₂ nanoparticles were characterized by X-ray diffraction (XRD) pattern and scanning electron microscopy (SEM) and the absorption of dye on the TiO₂ electrode was shown by UV?Cvis spectroscopy. By controlling different parameters including numbers of coated layers, the gap between two electrodes, sensitization time, and light source power, TiO₂-based solar cells with high efficiency was achieved. The results show that a five time spin-coated TiO₂ electrode with applying sealant and sensitization time of 24?h in N3 dye under illumination of 100?W?cm^?2 tungsten lamp give the optimum power conversion efficiency (??) of 6.61%. The increases in thickness of TiO₂ films by increasing the numbers of coated layers can improve adsorption of the N3 dye through TiO₂ layers to increase the open-circuit voltage (V _oc). However, short-circuit photocurrents (J _sc) of DSSCs with a one-coated layer of TiO₂ films are smaller than those of DSSCs with five-coated layer of TiO₂ films. It could be due to the fact that the increased thickness of TiO₂ thin films also resulted in a decrease in the transmittance of TiO₂ thin films. Also, this electrode was employed to photoreduce CO₂ with H₂O under tungsten lamp as light source.     

A novel cubically convergent iterative method for computing complex roots of nonlinear equations

A fast and simple iterative method with cubic convergent is proposed for the determination of the real and complex roots of any function F(x) = 0. The idea is based upon passing a defined function G(x) tangent to F(x) at an arbitrary starting point. Choosing G(x) in the form of x^k or k^x, where k is obtained for the best correlation with the function F(x), gives an added freedom, which in contrast to all existing methods, accelerates the convergence. Also, this new method can find complex roots just by a real initial guess. This is in contrast to many other methods like the famous Newton method that needs complex initial guesses for finding complex roots. The proposed method is compared to some new and famous methods like Newton method and a modern solver that is fsolve command in MATLAB. The results show the effectiveness and robustness of this new method as compared to other methods.     

KF/Al2O3-Mediated Michael Addition of Thiols to Electron‐Deficient Olefins

Potassium fluoride supported on alumina efficiently catalyzes Michael addition of aromatic and aliphatic thiols to a variety of conjugated alkenes such as α,β‐unsaturated carbonyl compounds, carboxylic esters, amides, nitriles and chalcones. The Michael adducts are produced in good to excellent yields and relatively in short times. The catalyst can be recycled for subsequent reactions without any appreciable loss of efficiency.