A continuous vibration theory for rotors with an open edge crack

In this paper a new continuous model for flexural vibration of rotors with an open edge crack has been developed. The cracked rotor is considered in the rotating coordinate system attached to it. Therefore, the rotor bending can be decomposed in two perpendicular directions. Two quasi-linear displacement fields are assumed for these two directions and the strain and stress fields are calculated in each direction. Then the final displacement and stress fields are obtained by composing the displacement and stress fields in the two directions. The governing equation of motion for the rotor has been obtained using the Hamilton principle and solved using a modified Galerkin method. The free vibration has been analyzed and the critical speeds have been calculated. Results are compared with the finite element results and an excellent agreement is observed.     

Synthesis and characterization of nanostructured strontium hexaferrite thin films by the sol–gel method

Nanostructured single phase strontium hexaferrite, SrFe₁₂O₁₉, thin films have been synthesized on the (100) silicon substrate using a spin coating sol–gel process. The thin films with various Fe/Sr molar ratios of 8–12 were calcined at different temperatures from 500 to 900 °C. The composition, microstructure and magnetic properties of the SrFe₁₂O₁₉ thin films were characterized using Fourier transform infrared spectroscopy, differential thermal analysis, thermogravimetry, X-ray diffraction, electron microscopy and vibrating sample magnetometer. The results showed that the optimum molar ratio for Fe/Sr was 10 at which the lowest calcination temperature to obtain the single phase strontium hexaferrite thin film was 800 °C. The magnetic measurements revealed that the sample with Fe/Sr molar ratio of 10, exhibited higher saturation magnetization (267.5 emu/cm³) and coercivity (4290 Oe) in comparison with those synthesized under other Fe/Sr molar ratios.     

Selective surface chemistry of allyl alcohol and allyl aldehyde on Si(1 0 0)2×1: Competition of [2 + 2] CC cycloaddition with O-H dissociation and with [2 + 2] CO cycloaddition in bifunctional molecules

Competition between the CC functional group with the OH group in allyl alcohol and with the CO group in allyl aldehyde in the adsorption and thermal chemistry on Si(1 0 0)2×1 has been studied by X-ray photoelectron spectroscopy (XPS) and temperature-programmed desorption (TPD), as well as density-functional theory (DFT) calculations. The similarities found in the C 1s and O 1s spectra for both molecules indicate that the O-H dissociation product for allyl alcohol and [2 + 2] CO cycloaddition product for allyl aldehyde are preferred over the corresponding [2 + 2] CC cycloaddition products. Temperature-dependent XPS and TPD studies further show that thermal evolution of these molecules gives rise to the formation of ethylene, acetylene, and propene on Si(1 0 0)2×1, with additional CO evolution only from allyl alcohol. The formation of these desorption products also supports that the [2 + 2] CC cycloaddition reaction does not occur. In addition, the formation of SiC at 1090 K is observed for both allyl alcohol and allyl aldehyde. We propose plausible surface-mediated reaction pathways for the formation of these thermal evolution products. The present work illustrates the crucial role of the Si(1 0 0)2×1 surface in selective reactions of the Si dimers with the O−H group in allyl alcohol and with the CO group in allyl aldehyde over the CC functional group common to both molecules.     

An alternative method for plotting dispersion curves

Solving the frequency equation and plotting the dispersion curves in problems of wave propagation in cylinders and plates, particularly when the material is anisotropic, are complicated tasks. The traditional numerical methods are usually based on determination of the zeros of the frequency equation by using an iterative find-root algorithm. In this paper, an alternative method is proposed which extracts the solution of the frequency equation in the form of dispersion curves from the three-dimensional illustration of the frequency equation. For this purpose, a three-dimensional representation of the real roots of the frequency equation is first plotted. The dispersion curves, which are the numerical solutions of the frequency equation, are then obtained by a suitable cut in the velocity-frequency plane. The advantages of this method include simplicity, high speed, low possibility of numerical error, and presentation of the results in a graphical form that promotes ease of interpretation. This method is not directly applicable to problems which incorporate high damping or leaky waves. However, if the damping is not very high, it could be a good estimate of the true dispersion curves.     

Comparison between standard and counterpoise-corrected optimization using some hydrogen and halogen bonded systems

The effect of the counterpoise correction on the geometries, stabilization energies, and vibrational harmonic frequencies of some hydrogen- and halogen-bonded systems (B?=?CH₃CN,?HCN,?NH₃,?N₂,?CO,?H₂O,?H₂S,?PH₃;?HX?=?HF,?HCl,?HBr,?HCN,?HCF₃; XY?=?Br₂,?BrCl,?BrF,?Cl₂,?ClF,?F₂) has been analysed at the MP2 level of theory using the popular 6-311++G(d,p) basis set. The optimized B?···?H and B?···?X bond lengths increase with counterpoise (CP) correction. In some cases standard values and in other cases CP-corrected values are close to experimental data. The absolute values of complexation energies of CP-corrected structures are higher than standard by inclusion of BSSE correction. The effect of CP correction on intermolecular bond lengths and complexation energies of B?···?XY series are usually higher than B?···?HX. Also, this effect is higher for H₂S and PH₃ groups. The CP correction changes the vibrational harmonic frequencies by 0–100%. The changes are frequently lower than 20% for frequencies higher than 300?cm^?1.     

Effect of pH value on the structural and magnetic properties of nanocrystalline strontium hexaferrite thin films

Strontium hexaferrite SrFe₁₂O₁₉ thin films have been synthesized at different pH, adjusted by NH₄OH, on the Si (1 0 0) substrate using a spin coating sol-gel process. Fourier transform infrared spectroscopy analysis and theoretical calculations were conducted for determination and controlling metal citrates in solution precursors. X-ray diffraction, scanning electron microscopy and vibrating sample magnetometer were applied to evaluate the composition, microstructure, crystallite size and magnetic properties of the SrFe₁₂O₁₉ thin films. Using the solution with pH 7, the approximately single phase strontium hexaferrite thin films with optimum physical properties can be obtained at calcination temperature of 800 °C. The SrFe₁₂O₁₉ thin films derived from the solution with pH 7 after calcination at 800 °C exhibited crystallite size of 42 nm and magnetic properties of M_s=267 emu/cm³ (at 10 kOe), M_r=134 emu/cm³ and H_c=4290 Oe.     

Investigation of a mutual interaction force at different pressure amplitudes in sulfuric acid

This paper investigates the secondary Bjerknes force for two oscillating bubbles in various pressure amplitudes in a concentration of 95% sulfuric acid.The equilibrium radii of the bubbles are assumed to be smaller than 10 μm at a frequency of 37 kHz in various strong driving acoustical fields around 2.0 bars (1 bar=10 5 Pa).The secondary Bjerknes force is investigated in uncoupled and coupled states between the bubbles,with regard to the quasi-adiabatic model for the bubble interior.It finds that the value of the secondary Bjerknes force depends on the driven pressure of sulfuric acid and its amount would be increased by liquid pressure amplitude enhancement.The results show that the repulsion area of the interaction force would be increased by increasing the driven pressure because of nonlinear oscillation of bubbles.     

Metric and Complete Metric σ-Frames

A -frame is a lattice in which countable joins exist and binary meets distribute over countable joins. In this paper, the category MFrm, of metric -frames, is introduced, and it is shown to be equivalent to the category MLFrm _u, of metric Lindelöf frames.Finally, it is shown that the complete metric -frames are exactly the cozero parts of complete metric Lindelöf frames.     

Synthesis and magnetic properties of hard/soft SrFe12O19/Ni0.7Zn0.3Fe2O4 nanocomposite magnets

Magnetic nanocomposite SrFe₁₂O₁₉/Ni_0.7Zn_0.3Fe₂O₄ powders with different weight fractions of the Ni_0.7Zn_0.3Fe₂O₄ soft ferrite were synthesized by a combination of the sol–gel self-propagation and glyoxilate precursor methods. The results of magnetic measurements revealed the higher Mr/Ms ratio for the nanocomposites than that for the single phase SrFe₁₂O₁₉ which proves the existence of the intergrain exchange coupling between hard and soft magnetic phases with the exchange spring behavior. The highest Mr/Ms ratio of 0.63 was obtained in the composite consisting of 80 wt% of SrFe₁₂O₁₉ and 20 wt% Ni_0.7Zn_0.3Fe₂O₄. The microstructural studies of this sample exhibited the average dimensions of hard and soft phases about 20 nm and 15 nm, respectively which are small enough for strong exchange coupling according to the theoretical studies. The variations of the reduced remanence (Mr/Ms) with increasing the weight fraction of the soft phase could be also explained by the role of the exchange and dipolar interactions in tuning the magnetic properties of the nanocomposites.     

Scale-dependent effects on wave propagation in magnetically affected single/double-layered compositionally graded nanosize beams

This article deals with the wave propagation analysis of single/double layered functionally graded (FG) size-dependent nanobeams in elastic medium and subjected to a longitudinal magnetic field employing nonlocal elasticity theory. Material properties of nanobeam change gradually according to the sigmoid function. Applying an analytical solution, the acoustical and optical dispersion relations are explored for various wave number, nonlocality parameter, material composition, elastic foundation constants, and magnetic field intensity. It is found that frequency and phase velocity of waves propagating in S-FGM nanobeam are significantly affected by these parameters. Also, presence of cut-off and escape frequencies in wave propagation analysis of embedded S-FGM nanobeams is investigated.