Elasto-plastic vibrational analysis of tapered bars under uniform axial loading considering shear deformation and rotary inertia

The analysis of structures in the plastic regime is important in order to develop an adequate and competitive design in engineering. This paper presents a study of the small-amplitude free vibration of tapered bars under pre-stress in the post-elastic regime due to a uniform axial loading. The plastic behavior is taken into account using an energy approach. The method does not require an iterative procedure, unlike conventional methods used in plasticity. The Timoshenko beam theory and the dynamic version of the principle of virtual work are used to derive the eigenvalue problem. The solution is carried out using beam finite elements. The results are validated using 3D finite element software and results from the open literature. A variety of numerical results are given in order to analyze the influence of plastic behavior for various bar geometries and material parameters. The combined effect of the stiffening due to the axial loading and the plastic softening may produce an increase or decrease of the natural frequencies as the tensile load increases. The plastic softening effect is seen to be pronounced for short bars and for high taper ratios. In addition, axial normal modes are more affected than bending modes.     

Computational fluid dynamics and experimental study of the hydrodynamics of a gas–solid tapered fluidized bed

In the present work, experimental and numerical studies for the hydrodynamics in a gas–solid tapered fluidized bed have been carried out. The experimental results obtained by carrying out experiments in a tapered fluidized bed for glass bead (spherical) of 2.0 mm and dolomite (non-spherical particles) of 2.215 mm in diameter, were compared with the computational fluid dynamics (CFD) simulation results, using a commercial CFD software package, Fluent. The gas–solid flow was simulated using the Eulerian–Eulerian model and applying the kinetic theory of granular flow for solid particles. The Gidaspow drag model was used to calculate the gas–solid momentum exchange coefficients. Pressure drops predicted by the CFD simulations agreed reasonably well with experimental measurements for both types (spherical and non-spherical) of particles. Good agreement was also obtained between experimental and CFD predicted bed expansion ratios for both types of particles. Present study provides a useful basis for further works on the CFD of tapered fluidized bed.     

Analysis of large amplitude free vibrations of clamped tapered beams on a nonlinear elastic foundation

The purpose of this paper is to present efficient and accurate analytical expressions for large amplitude free vibration analysis of single and double tapered beams on elastic foundation. Geometric nonlinearity is considered using the condition of inextensibility of neutral axis. Moreover, the elastic foundation consists of a linear and cubic nonlinear parts together with a shearing layer. The nonlinear governing equation is solved by employing the variational iteration method (VIM). This study shows that the second-order approximation of the VIM leads to highly accurate solutions which are valid for a wide range of vibration amplitudes. The effects of different parameters on the nonlinear natural frequency of the beams are studied under different mode shapes. The results of the present work are also compared with those available in the literature and a good agreement is observed.     

Mathematical modelling of unsteady flow of a Sisko fluid through an anisotropically tapered elastic arteries with time-variant overlapping stenosis

In the present investigation, we have studied the influence of heat and chemical reactions on blood flow through anisotropically tapered elastic artery with time-variant overlapping stenosis. The nature of blood in small arteries are analyzed mathematically by considering it as a Sisko fluid. The analysis is carried out for an artery with a mild stenosis. Analytical expressions for the axial velocity, the stream function, the temperature distribution, the concentration of fluid, the pressure gradient, the resistance impedance and the wall shear stress distribution have been computed numerically and the results were studied for various values of the physical parameters, such as the Sisko parameter b^∗, the power index n, the taper angle ?  , the maximum height of stenosis δ^∗${\delta }^{\ast }$, the Soret number S_r, the Brickmann number B_r, the total mass of the vessel and the surrounding tissues M and the longitudinal contributions of the viscous and elastic constraints to the total tethering C and K respectively. The obtained results show that the magnitude of the axial velocity is higher for a Newtonian fluid than that for a Sisko fluid and it decreases by increasing of the power index n also the transmission of axial velocity curves through a tethered tube is substantially higher than that through the free tube. The wall shear stress distribution and resistance impedance profiles with the time have an oscillation form through the tapered overlapping stenosed arteries and this oscillation decaying as the time increases. The temperature profile increase by increasing the Sisko parameter b^∗ and the power index n   but the concentration profile has an opposite behavior as compared to the temperature profile. For a fixed flux, the magnitude of the pressure drop for a shear-thinning fluid (n<1)$(n<1)$ is much larger than that through a shear-thickening (n>1)$(n>1)$. The stream lines separate and the trapping bolus appear by increasing the maximum height of the stenosis δ^∗${\delta }^{\ast }$. The trapping bolus increase in size toward the line center of the tube as the power index n increases and it appear gradually by increasing the Sisko parameter b^∗. Finally the size of trapped bolus for the stream lines in the free isotropic tube is smaller than those in the tethered tube.     

Evaluation of flow restrictors for open-tubular supercritical fluid chromatography at pressures up to 560 atm

Proper performance of the flow restrictor is of crucial importance in supercritical fluid chromatography. This is especially the case when the restrictor is the interface between the chromatographic column and a detector operating at lower pressure than the column. The performance of three types of fixed flow restrictor, the “tapered”, the “integral”, and the “frit”, was examined. The test mixtures chosen covered a range of polarities and molecular weights. Polydimethylsiloxane with an average molecular weight of 10,000 was used as a low polarity probe. Two polyethylene glycol mixtures were chosen as higher polarity probes. One consisted of a mixture of polyethylene glycol standards with average molecular weights ranging from 200 to 1450. The other polyethylene glycol mixture had an average molecular weight of 2000. The polydimethylsiloxane standard did not elute when the frit restrictor was used. Satisfactory results were obtained when the tapered and integral restrictors were employed. All three restrictors provided satisfactory results for polyethylene glycol oligomers eluting up to approximately 40.5 MPa (400 atm). However, for oligomers eluting above this pressure, the peaks merged into a broad hump with the frit restrictor, while the tapered and integral restrictors provided satisfactory separations. The integral restrictor produced more evenly spaced, more well resolved peaks at the high-pressure end of the chromatograms than did the tapered restrictor. This is shown to be due to differences in the rates of increase in mobile-phase velocity with increasing pressure for the two restrictors.     

Higher order mode propagation in an optical nanofiber

The propagation of higher modes, such as the LP₁₁ mode, in optical nanofibers using the exponentially tapered optical fiber as a basic model is investigated. In order to preserve the LP₁₁ mode in the downtaper as far as the nanofiber waist, the effect of varying the cladding-core radius ratio on the LP₁₁ adiabatic criterion is modeled. A Laguerre-Gaussian beam is created in free space using a spatial light modulator (SLM) and coupled to a few-mode fiber. This device allows convenient switching between the fundamental and LP₁₁ fiber modes. By selecting a few-mode fiber with a relatively low cladding-core ratio, the propagation of the LP₁₁ mode down to a submicron waist has been maintained. Furthermore, by observing the transmission profile during tapering, it is possible to decisively terminate the pulling process in order to eliminate the two degenerate HE₂₁ modes of the LP₁₁ mode. As a result, a nanofiber can be fabricated through which only the TE₀₁ and TM₀₁ components of the LP₁₁ mode propagate. Such a nanofiber has promising applications in the area of mode interference for controlled particle trapping sites.     

Mesoscopic effect of spectral modulation for the light transmitted by a SNOM tip

The effect of a tapered metal-coated optical fiber terminated by a sub-wavelength aperture (SWA) on the spectrum of the transmitted light is investigated experimentally. Under certain conditions a remarkable spectral modulation of the transmitted light can be observed. This effect is of a mesoscopic origin, occurring only for a certain interval of SWA diameters. One can conclude that a noticeable modulation appears when the number of the transmitted fiber modes is small but exceeds unity, thus indicating the presence of a phase shift between different modes. To discern between two possible sources of such phase shift, the fiber length dependence of the output spectrum has been studied. According to the results obtained for the used sample of 200 nm SNOM tip, the observed phase shift is mostly caused rather by the inherent modal dispersion of the multimode fiber than by the mode-dependent light slowdown in the tapered region close to SWA due to the coupling to surface plasmons of the metal coating. The SWA acts here mainly as an effective mode filter.     

Nylon-6 capillary-channeled polymer (C-CP) fibers as a hydrophobic interaction chromatography stationary phase for the separation of proteins

Nylon-6 capillary-channeled polymer (C-CP) fibers are used as the stationary phase for the hydrophobic interaction chromatography (HIC) separation of a synthetic protein mixture composed of ribonuclease A, lysozyme, and holotransferrin. Nylon is a useful polymer phase for HIC as it has an alkyl backbone, while the amide functionality is hydrophilic (in fact ionic) in nature. The combination of a nonporous polymer surface of the fiber phases and high column permeability yields very efficient mass transfer characteristics, as exhibited by narrowing of peak widths with increases in mobile phase linear velocity. Retention factors and resolution were evaluated at flow rates ranging from 0.5 to 9 mL/min (linear velocities of ca. 2 to 15 mm/s) and at gradient slopes between 3.3 and 20 %B/min. Optimum resolution was achieved by employing fast flow rates (9 mL/min) and slow gradients (3 %B/min), also resulting in the highest peak capacities.     

Electrospinning of α,β-poly(N-2-hydroxyethyl)-dl-aspartamide-graft-polylactic acid to produce a fibrillar scaffold

α,β-Poly(N-2-hydroxyethyl)-dl-aspartamide grafted with polylactic acid (PHEA-g-PLA) is a biocompatible and biodegradable amphiphilic copolymer that has been already employed to prepare a drug delivery system.In this study we have prepared for the first time a fibrillar scaffold from PHEA-g-PLA by the electrospinning of a solution of this copolymer in a mixture of N,N-dimethyl formamide (DMF) and acetone (80:20 vol/vol). The average diameter and the morphology of electrospun fibers were detected by scanning electron microscopy.Chemical degradation studies in phosphate buffer solution pH 7.4 have been performed until 15 days in order to obtain a preliminary information about the hydrolytic resistance of the prepared scaffold.