Shear deformation effect in flexural–torsional vibrations of beams by BEM

In this paper, a boundary element method is developed for the general flexural–torsional vibration problem of Timoshenko beams of arbitrarily shaped cross section taking into account the effects of warping stiffness, warping and rotary inertia and shear deformation. The beam is subjected to arbitrarily transverse and/or torsional distributed or concentrated loading, while its edges are restrained by the most general linear boundary conditions. The resulting initial boundary value problem, described by three coupled partial differential equations, is solved employing a boundary integral equation approach. Besides the effectiveness and accuracy of the developed method, a significant advantage is that the displacements as well as the stress resultants are computed at any cross-section of the beam using the respective integral representations as mathematical formulae. All basic equations are formulated with respect to the principal shear axes coordinate system, which does not coincide with the principal bending one in a nonsymmetric cross section. To account for shear deformations, the concept of shear deformation coefficients is used. Six boundary value problems are formulated with respect to the transverse displacements, to the angle of twist, to the primary warping function and to two stress functions and solved using the Analog Equation Method, a BEM based method. Both free and forced vibrations are examined. Several beams are analysed to illustrate the method and demonstrate its efficiency and wherever possible its accuracy.     

Simulation of single mode Rayleigh–Taylor instability by SPH method

A smoothed particle hydrodynamics (SPH) solution to the Rayleigh–Taylor instability (RTI) problem in an incompressible viscous two-phase immiscible fluid with surface tension is presented. The present model is validated by solving Laplace’s law, and square bubble deformation without surface tension whereby it is shown that the implemented SPH discretization does not produce any artificial surface tension. To further validate the numerical model for the RTI problem, results are quantitatively compared with analytical solutions in a linear regime. It is found that the SPH method slightly overestimates the border of instability. The long time evolution of simulations is presented for investigating changes in the topology of rising bubbles and falling spike in RTI, and the computed Froude numbers are compared with previous works. It is shown that the numerical algorithm used in this work is capable of capturing the interface evolution and growth rate in RTI accurately.     

The joint mixing action of the static pre-mixer and the rotating drum mixer – Discrete element method approach

In this study, the mixing performance of coupled mixing action of the Komax static mixer (which is used as a pre-mixer) and rotating drum (applied as the final mixer) was explored in the maize meal mixing operation. The main objective of this paper was to predict the behaviour of the previously grinded maize particles, during the mixing process in static mixer and drum mixer, and to explore the possibilities to shorten the mixing time in the main mixer (in order to reduce the energy consumption).Three different experiments were performed: in the first experiment, possibilities of static mixer were explored, second experiment showed the mixing performance of rotating drum, and the combination of these two mixing devices was investigated in the third experiment. Homogeneity of the obtained mixtures was determined experimentally, by the “Microtracers” method.The Discrete Element Method was used for modelling of granular flow in the pre-mixing and final mixing applications, and to predict the inter-particle mixing quality within a static mixer and the rotating drum mixer. The results of the numerical simulation are compared with appropriate experimental results. The possible industrial application of this model could be the optimization of parameters of mixing systems taking into account the quality and the duration of the mixing process.     

The determination of the permeability of concrete to oxygen by the Cembureau method—a recommendation

A committee was set up in 1981 by the Cembureau Working Party on the Quality of Concrete with the following aims and objectives:

Effect of solvents on the preparation of lithium aluminate by sol–gel method

γ-Lithium aluminate was prepared by sol–gel method using lithium methoxide and aluminum-sec-butoxide precursors in i-propanol, n- and tert-butanol. Clear gels could be obtained due to the addition of ethylacetoacetate and the dried solids were calcined at 550 and 900 °C. The resulting solids were characterized by X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FT-IR), scanning electron microscopy (SEM), thermo-gravimetric analysis/differential thermal analysis (TGA/DTA). γ-Lithium aluminate with the highest purity was obtained with t-butanol solvent and LiAl₅O₈ was the second major phase.     

A Hermite DRK interpolation-based collocation method for the analyses of Bernoulli–Euler beams and Kirchhoff–Love plates

A Hermite differential reproducing kernel (DRK) interpolation-based collocation method is developed for solving fourth-order differential equations where the field variable and its first-order derivatives are regarded as the primary variables. The novelty of this method is that we construct a set of differential reproducing conditions to determine the shape functions of derivatives of the Hermite DRK interpolation, without directly differentiating it. In addition, the shape function of this interpolation at each sampling node is separated into a primitive function possessing Kronecker delta properties and an enrichment function constituting reproducing conditions, so that the nodal interpolation properties are satisfied for the field variable and its first-order derivatives. A weighted least-squares collocation method based on this interpolation is developed for the static analyses of classical beams and plates with fully simple and clamped supports, in which its accuracy and convergence rate are examined, and some guidance for using this method is suggested.     

Free Vibration Analysis of Moderately Thick Rectangular Plates on Pasternak Foundation with Point Supports and Elastically Restrained Edges by Using the Rayleigh–Ritz Method

In the present paper, free vibration analysis of moderately thick rectangular plates resting on an elastic foundation of Pasternak model with point supports and elastically restrained edges based on the first-order shear deformation plate theory is presented. The Rayleigh–Ritz method is applied to derive the eigenvalue equation of the plate. The Chebyshev polynomials multiplied by a boundary function which define the displacement components are adopted in this method as the admissible functions. The accuracy of the present method is examined via lots of convergence and comparison studies with the available data in the literature, and it is demonstrated that the present method has a rapid convergence rate and high accuracy. Many numerical results are presented in tabular and graphical forms in order to investigate the effects of various parameters such as thickness–span ratio, foundation parameters, the lateral and rotational stiffness of the edge supports, and locations of the point supports on the natural frequencies.     

Spectral element model for axially loaded bending–shear–torsion coupled composite Timoshenko beams

The use of frequency-dependent spectral element matrix (or exact dynamic stiffness matrix) in structural dynamics is known to provide extremely accurate solutions, while reducing the total number of degrees-of-freedom to resolve the computational and cost problems. Thus, in this paper, the spectral element model is developed for an axially loaded bending–shear–torsion coupled composite laminated beam which is represented by the Timoshenko beam model based on the first-order shear deformation theory. The high accuracy of the spectral element model is then numerically verified by comparing with exact theoretical solutions or the solutions obtained by conventional finite element method. For the numerical verification, the finite element model is also provided for the composite laminated beam.     

Conservation of energy of non-Newtonian media for the Rayleigh–Stokes problem

The energetic balance of the Rayleigh–Stokes problem for Newtonian-, second grade- and Maxwell fluids is studied for different initial and boundary conditions. We get the solutions of the differential equations by Fourier sine transform or by series expansion. The result for the kinetic energy E _kin, the dissipation Φ and the power of the shear stresses at the wall L are important for nature and technology.     

Analysis of the ellipse of polarization by the senarmont method as the phase difference varies in the range 0–2π

An analysis of the Senarmont method is performed using Müller marices and Stokes, vectors. It is proved that the traditional undrstanding of the Senarmont method is applicable in the case of phase differences not exceeding one-half wave. For measurements of phase differences in the range 0–2π, a preliminary identification of the rapid and slow axes of the phase plate is required. A method is presented by means of which it is possible to distinguish the axes on the basis of the direction of the rotation of the resultant plane oscillations in the case of continuous variation of the phase differences. Translated from Izmeritel'naya Tekhnika, No. 11, pp. 22–25, November, 1999.     

Synthesis of B–C–N nanotubes by means of gas arc discharge with a rotating anode

B–C–N nanotubes were synthesized by plasma rotating electrode process (PREP) and examined by scanning electron microscope (SEM) and X-ray diffraction (XRD). Compared with results at 0 rpm of the anode, the number of B–C–N nanotubes was increased by rotating the anode. In addition, peak intensity ratio of h-(BN)_0.26C_0.74 to graphite was increased with rotation of the anode and/or the increase of metal concentration. That indicates the yield of B–C–N nanotubes was increased. These results could be explained by an increase of plasma temperature and a swirl in the plasma by rotation of the anode that promote the mixing to aid chemical reactions between evaporated species and atomic nitrogen.     

Preparation of chitosan–hyaluronate double-walled microspheres by emulsification-coacervation method

Chitosan (CHS)−hyaluronate (HA) double-walled microspheres were prepared by emulsification-coacervation method. Tripolyphosphate (TPP) acted as ion crosslinker. The effects of oil/water volume ratio, surfactant, solution pH, TPP concentration, HA concentration, and emulsification time on microspheres fabrication and morphology were examined by Zeta (ζ) potential, Scanning electron microscopy (SEM) and Fourier-transform infrared spectrometry (FT-IR). It was found that TPP concentration, solution pH, surfactant and emulsification time were crucial factors for microspheres fabrication. Spherical microspheres with smooth surface were formed when TPP concentration was 8% or higher. The optimal pH for microspheres formation ranged from 6.0 to 7.0. As for surfactant, the microspheres obtained when span80 was applied alone were shapelier compared with those obtained when both span80 and tween80 were applied. With insufficient emulsification time, vacuous microcapsules, but not compact microspheres were formed. In addition, oil/water volume ratio and HA concentration also affected the microspheres morphology, but less importantly.     

Errors in measuring the directivity of a field by the method of a reference field in the range of 25–400 MHZ

Conclusions The cited data on error components in measuring the field-strength lead to the conclusions that the reference field (provided that the distances are measured with an error of ±2%) can be determined with an error of 6%, at frequencies up to 150 MHz, and of ±7% in the range from 150 to 400 MHz. The error in determining the resulting field-strength is smaller for small angles of elevation, since the beam reflected from the ground has a substantial effect on the value of the field.     

Propagation properties of vectorial Hermite–cosine–Gaussian beams beyond the paraxial approximation

Starting from the vectorial Rayleigh–Sommerfeld diffraction integrals, the analytical propagation expressions of vectorial nonparaxial Hermite–cosine–Gaussian (HCosG) beams in free space are derived. The on-axis intensity, far-field equation and, in particular, paraxial expressions are given and treated as special cases of our result. It is shown that for vectorial nonparaxial HCosG beams, the parameter f = 1/kw ₀, with k being the wave number and w ₀ being the waist width, determines their nonparaxiality. What is more, the decentered parameter also affects their intensity distribution and nonparaxial behavior. The calculation results indicate that the position of maximum on-axis intensity changes with the mode indices.     

The semi-elliptical surface crack—A solution by the alternating method

A numerical solution to the three-dimensional equations of elasticity is presented for the problem of a semi-elliptical surface crack in the surface of a finite thickness solid. The alternating method is used to develop the numerical results which incorporate the effects on the stress intensity factor due to the presence of both the front and the back surfaces. The stress intensity factor is presented as a function of position along the crack border for a variety of crack shapes and crack depths. A comparison of the results of this study is made with previous theoretical and experimental work.

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Résumé Une solution numérique à équations tridimensionnelles d'élasticité est présentée pour le problème de la fissure de surface semi-elliptique située en surface ou en solide d'épaisseurs finies.La méthode proposée est utilisée pour développer des résultats numériques qui incorporent les effets des facteurs d'intensité des contraintes associée à la fois des surfaces recto et verso du solide. Le facteur d'intensité des contraintes est décrit pour diverses positions de la fissure et ce dans divers cas de formes et de profondeurs de fissuration. Une comparaison est faite entre les résultats de cette étude et des travaux théoriques et expérimentaux antérieurs.

     

Enhanced hydrophilicity of the Si substrate for deposition of VO2 film by sol–gel method

We have illustrated the role of hydrophilic nature of Si substrate played in the improvement of the contact performance between the vanadium dioxide (VO₂) film and Si substrate. The VO₂ films were fabricated by sol–gel method on single crystal Si substrate, which was pre-treated with hydrophilic solution and obtained a quite improved hydrophilicity. The bonding of Si substrate with precursor V₂O₅ gel was interpreted. The morphology and crystalline structure of the films were investigated by field-emission scanning electron microscopy, atomic force microscopy and X-ray diffraction. It is shown that the surface of the film on Si substrate with enhanced hydrophilicity is quite homogeneous and uniform. The film exhibits the formation of VO₂ phase with (011) preferred orientation. Moreover, the optical pump induced phase transition property of the film was studied by terahertz time-domain spectroscopy, which revealed around 70% reduction of transmission at 0.1–1.5?THz in the VO₂ film across the phase transition.     

Focusing of radially polarized Lorentz–Gauss beams with the power–exponent–phase vortex

Using the vector diffraction theory, the optical field of the focusing radially polarized Lorentz–Gauss beam with the power–exponent–phase vortex is derived. The normalized intensity distributions of the focusing radially polarized Lorentz–Gauss beam with the power–exponent–phase vortex are numerically demonstrated. The influences of the power order n and the topological charge m on the normalized intensity distribution are examined. The beam centre and the effective beam size, which are defined by the first- and the second-order moments of the intensity distribution, are the important parameters for focus. Therefore, the quantitative effects of the power order n and the topological charge m on the beam centre and the effective beam size are further investigated. This research is beneficial to the optical manipulation which is involved in the radially polarized Lorentz–Gauss beam with the power–exponent–phase vortex.     

Optical method using rotating Glan–Thompson polarizers to independently vary the power of the excitation and repumping lasers in laser cooling experiments

A simple optical technique consisting in the rotation of Glan–Thompson polarizers is applied to independently vary and control the power of the cooling laser and the repumping laser in laser cooling experiments of ⁸⁷Rb. For our experimental conditions, which include initial laser powers of approximately 48 mW (for each laser), it was observed that the atom cloud was still visible after reducing the power of the cooling laser to ～10 mW while keeping the power of the repumping laser at its initial level. On the other hand, the atom cloud maintained visibility after reducing the power of the repumping laser to ～103 µW while keeping the power of the excitation laser at its initial level. In both cases the power variation of the lasers is achieved without altering the frequency or tuning characteristics of the lasers.