Bending of Euler–Bernoulli nanobeams based on the strain-driven and stress-driven nonlocal integral models: a numerical approach

Eringen’s nonlocal elasticity theory is extensively employed for the analysis of nanostructures because it is able to capture nanoscale effects. Previous studies have revealed that using the differential form of the strain-driven version of this theory leads to paradoxical results in some cases, such as bending analysis of cantilevers, and recourse must be made to the integral version. In this article, a novel numerical approach is developed for the bending analysis of Euler–Bernoulli nanobeams in the context of strain- and stress-driven integral nonlocal models. This numerical approach is proposed for the direct solution to bypass the difficulties related to converting the integral governing equation into a differential equation. First, the governing equation is derived based on both strain-driven and stress-driven nonlocal models by means of the minimum total potential energy. Also, in each case, the governing equation is obtained in both strong and weak forms. To solve numerically the derived equations, matrix differential and integral operators are constructed based upon the finite difference technique and trapezoidal integration rule. It is shown that the proposed numerical approach can be efficiently applied to the strain-driven nonlocal model with the aim of resolving the mentioned paradoxes. Also, it is able to solve the problem based on the strain-driven model without inconsistencies of the application of this model that are reported in the literature.     

Vibration analysis of two-dimensional structures using micropolar elements

Based on the micropolar theory(MPT), a two-dimensional(2 D) element is proposed to describe the free vibration response of structures. In the context of the MPT, a 2 D formulation is developed within the ABAQUS finite element software. The user-defined element(UEL) subroutine is used to implement a micropolar element. The micropolar effects on the vibration behavior of 2 D structures with arbitrary shapes are studied. The effect of micro-inertia becomes dominant, and by considering the micropolar effects, the frequencies decrease. Also, there is a considerable discrepancy between the predicted micropolar and classical frequencies at small scales, and this difference decreases when the side length-to-length scale ratio becomes large.     

Size-dependent axial buckling analysis of functionally graded circular cylindrical microshells based on the modified strain gradient elasticity theory

In this paper, a size-dependent first-order shear deformable shell model is developed based upon the modified strain gradient theory (MSGT) for the axial buckling analysis of functionally graded (FG) circular cylindrical microshells. It is assumed that the material properties of FG materials, which obey a simple power-law distribution, vary through the thickness direction. The principle of virtual work is utilized to formulate the governing equations and corresponding boundary conditions. Numerical results are presented for the axial buckling of FG circular cylindrical microshells subject to simply-supported end conditions and the effects of material length scale parameter, material property gradient index, length-to-radius ratio and circumferential mode number on the size-dependent critical buckling load are extensively studied. For comparison purpose, the critical buckling loads predicted by modified couple stress theory (MCST) and classical theory (CT) are also presented. Results show that the size effect plays an important role for lower values of dimensionless length scale parameter. Moreover, it is observed that the critical buckling loads obtained based on MSGT are greater than those obtained based on MCST and CT.     

Post modification of zinc based coordination polymer to prepare Zn‐Mo‐ICP nanoparticles as efficient self‐supported catalyst for olefin epoxidation

Preparation, characterization, and catalytic properties of bimetallic coordination polymer constructed from 2‐aminoterephthalic acid as linker, zinc cations as node, and cis‐dioxo molybdenum units as catalytic active sites are reported via two pathways. Molybdenum centers were placed in N,O positions created by condensation reaction of 2‐aminoterephthalic acid with salicylaldehyde while zinc cations coordinated via carboxylic acid groups of linker to achieve infinite chains of metalo‐ligand. The obtained coordination polymer was fully characterized and its catalytic properties in the epoxidation of olefins with tert‐butyl hydroperoxide (TBHP) described. In comparison with previously reported heterogenized molybdenum catalysts, this new coordination polymer exhibited good conversion as well as high selectivity in the epoxidation of olefins. The catalyst is stable under ambient conditions and could be reused as active catalyst for at least five times.     

Mo (CO)6‐assisted Pd‐supported magnetic graphene oxide‐catalyzed carbonylation‐cyclization as an efficient way for the synthesis of 4(3H)‐quinazolinones

In this paper, a novel catalyst is introduced based on the immobilization of palladium on modified magnetic graphene oxide nanoparticles. The catalyst is characterized by several methods, including transmission electron microscopy, scanning electron microscopy, X‐ray fluorescence, vibrating‐sample magnetometer, Fourier transform‐infrared and dynamic light scattering (DLS) analysis. The activity of the catalyst was investigated in the synthesis of 4(3H)‐quinazolinones via Pd‐catalyzed carbonylation‐cyclization of N‐(2‐bromoaryl) benzimidamides by Mo (CO)₆. The Mo (CO)₆ is used as a carbon monoxide source for performing the reaction under mild conditions. The catalyst showed good reusability, and no change in activity was observed after 10 cycles of recovery.     

Intense Upconversion Luminescence of Yb<Superscript>3+</Superscript>-Er<Superscript>3+</Superscript> in Li<Subscript>2</Subscript>O Content Tungsten-tellurite Glasses

The Er³⁺ -Yb³⁺ codoped in Li₂O content tungsten -tellurite (TWL) transparent glasses are synthesized and measured the absorption, Raman and upconversion luminescence (UPL) spectra. At room temperature intense green emission peak at 560 nm ( ⁴S_3/2→⁴I_15/2) and red emission peak at 670 nm ( ⁴F_9/2→⁴I_15/2) of Er³⁺ observed even at minimum 86 mW pumping power of infrared 980 nm excitation. For structure of the TWL glass, Raman spectrum result revealed that an important role of WO₃ in the formation of glass network linkage with Li₂O. Under this influence estimated lifetime of the ⁴I_11/2 of Er³⁺ was 1.89 μs and due to lower phonon energy of the glass produce strong upconversion signal. The effect of Er₂O₃ concentration on emission intensity result indicated that green emission intensity initially increase in compare to red emission. Under the 980 nm pump power variation measured the relatively increases the red emission to the green emission intensity and analyze the possible upconversion mechanism and process.     

A theorem on asymptotic behaviour of functional equations and its applications

A method for the determination of rate of decay of a solution of a stable functional equation is discussed. A method for establishing a bound on an unstable, but bounded, solution is also discussed. Some applications are considered as examples.     

Optical absorption and NMR spectroscopic studies on paramagnetic trivalent lanthanide complexes with 2,2'-bipyridine.; The solvent effect on 4f-4f hypersensitive transitions

The optical absorption and NMR studies of trivalent lanthanide chloride complexes with 2,2'-bipyridine (bpy) are presented and discussed. The NMR spectra of paramagnetic complexes exhibit lower as well as higher field shifts of bpy resonances that reflect change in geometry and reveals importance of the factor (3 cos2 theta - 1 ) in changing sign of the shift. The paramagnetic shifts recorded have been analyzed and the intramolecular shift ratios suggest that the paramagnetic shift is predominantly dipolar in origin. Electronic spectral studies of the Pr, Nd, Ho, Er and Dy complexes in different solvents (viz. methanol, pyridine, DMSO and DMF), which differ with respect to donor atoms, reveal that the chemical environment around the lanthanide ion has great impact on f-f transitions and any change in the environment results in modifications of the spectra. The oscillator strength for the hypersensitive and non-hypersensitive transitions have been determined and changes in the oscillator strength and band shape with respect to solvent type is rationalized in terms of ligand (solvent) structure and coordination properties.     

A comparative study of first-derivative spectrophotometry and high-performance liquid chromatography applied to the determination of losartan potassium in tablets

Losartan, a highly effective blood pressure-lowering agent, has been widely used for the treatment of hypertension. A fast and reliable method for the determination of losartan was highly desirable to support formulation screening and quality control. A first-derivative UV spectroscopic method and HPLC were developed for the determination of losartan in the tablet dosage form. The first-derivative spectrum recorded between 220 and 320 nm and a zero-crossing technique for first-derivative measurement at 232.5 nm were selected. The selectivity and sensitivity of the method was in desirable range. In comparison with the direct UV method, first-derivative UV spectroscopy has a definite trough without any interference from UV absorbing-excipients. This method is also fast and economical in comparison with the more time-consuming HPLC method regularly used for formulation screening and quality control and can be used routinely by any laboratory possessing a spectrophotometer with a derivative accessory. The linear concentration ranges were 2-50 microg ml(-1), (D(1)=-0.0159C-0.0056, r=0.9994, n=6). Between-days CV of < or =2.9%, within-day CV of < or =2.1%, and analytical recovery close to 98.1% show the suitability of the method for determination in quality control.