Application of Krein’s theorem and bifurcation theory for stability analysis of a bladed rotor

This paper considers the stability and eigenvalue analyses for a bladed rotor which goes under cylindrical and conical whirling. The model consists of a group of flexible blades which are modeled by beams and rigid disk on the elastic bearings. The model is a Hamiltonian system which is perturbed by small dissipative forces. Krein’s theorem reveals that the forward whirling mode and the blade collective motion may cause instability when their frequencies cut themselves in the Campbell diagram. An unstable interaction between the blades and the conical whirling is discovered. The eigenmode and eigenvalue evolutions are determined on the stability boundary. The bifurcation analysis is performed by applying multiple scales method around the stability boundary. It is shown that the damping distribution between the blades and the bearings may shift the unstable mode.     

Stability and Hamiltonian Hopf bifurcation for a nonlinear symmetric bladed rotor

The modal interaction which leads to Hamiltonian Hopf bifurcation is studied for a nonlinear rotating bladed-disk system. The model, which is discussed in the paper, is a Jeffcott rotor carrying a number of planar blades which bend in the plane of the motion. The rigid rotating disk is supported on nonlinear bearings. It is supposed that this dynamical system is a Hamiltonian system which is perturbed by small dissipative and nonlinear forces. Krein’s theorem is employed for obtaining a stability criterion. The nonlinear eigenvalue equations on the stability boundary are turned into ordinary differential equations (ODEs) by differentiating them over the rotating speed. By solving these ODEs, the eigenmodes and the eigenvalues on the stability boundary are obtained. The bifurcation analysis is performed by applying multiple scales method around the boundary. The rotor nonlinear behavior and damping effects are studied for different conditions on the rotating speed and nonlinearity type by the bifurcation equation. It is shown that the damping distribution between the blades and bearings may shift the unstable mode. Depending on the nonlinearity type, subcritical and supercritical Hopf bifurcation are possible.     

The direct effect of interfacial nanolayers on thermal conductivity of nanofluids

One of the most important features of nanofluids is their thermal conductivity. In this article, a new model for thermal conductivity is proposed based on the combination of a statistical model and thermal convection caused by Brownian motion of nanoparticles with considering the effect of interfacial nanolayers among nanoparticles and base fluids. This model is compared with Al₂O₃ in deionized water and CuO in deionized water (based nanofluids of spherical particles) using a number of theoretical and experimental thermal conductivity models, after that the experimental results have been made available in the open literature. In this model, an interfacial nanolayer is influenced directly on both parts of static and dynamic effective thermal conductivity. The present model shows good agreement with the experimental result of nanofluids and gives better predictions compared to models used for nanofluids in this article. This model is purely theoretical and in order to achieve it, experimental results have no effect.     

Design and simulation of neutron radiography system based on 241Am–Be source

Neutron imaging is extended rapidly as a means of non-destructive testing (NDT) of materials. Various effective parameters on the image quality are needed to be studied for neutron radiography system with good resolution. In the present study a portable system of neutron radiography has been designed using ²⁴¹Am–Be neutron source. The effective collimator parameters were calculated to obtain relatively pure, collimated and uniform neutron beam. All simulations were carried out in two stages using MCNPX Monte Carlo code. In the first stage, different collimator configurations were investigated and the appropriate design was selected based on maximum intensity and uniformity of neutron flux at the image plane in the outlet of collimator. Then, the overall system including source, collimator and sample was simulated for achieving radiographic images of standard samples. Normalized thermal neutron fluence of 2.61×10^?5 cm^?2 per source particle with n/γ ratio of 1.92×10⁵ cm^?2 μSv^?1 could be obtained at beam port of the designed collimator. Quality of images was assessed for two standard samples, using radiographic imaging capability in MCNPX. The collimated neutron beam in the designed system could be useful in a transportable exposure module for neutron radiography application.     

Characterization of AZ91D Granules Covered with a Flux during In‐Situ Melting

Oxidation and melting behaviors of AZ91D granules throughout the in‐situ melting process using flux were investigated. The granules were heated under unprotected environment at four different temperatures between 650 and 800 °C, for the durations of 30 and 60 min. The products of heating process were characterized macroscopically and the oxides formed on the granules were examined using field emission scanning electron microscope, energy dispersive X‐ray spectroscopy and X‐ray diffraction analysis. Thermal analysis was used to reveal the response of the granules to heating during the in‐situ melting. The results showed that the granules experienced severe oxidation even in the presence of the flux, and significant amount of them changed to a powdered state due to oxidation and combustion, especially at 800 °C. It was discovered that the granules melted during heating; however, oxides formed on their surface encapsulated the molten metal and prevented the liquids from merging. The results also revealed that increasing heating temperature and time enhanced mold‐magnesium reaction resulted in the entrance of mold materials into the oxidation residues.     

Equations-of-motion method for triplet excitation operators in graphene

The particle-hole continuum in the Dirac sea of graphene has a unique window underneath, which in principle leaves room for bound state formation in the triplet particle-hole channel (Baskaran and Jafari 2002 Phys. Rev. Lett. 89 016402). In this work, we construct appropriate triplet particle-hole operators and, using a repulsive Hubbard-type effective interaction, we employ equations of motion to derive approximate eigenvalue equations for such triplet operators. While the secular equation for the spin density fluctuations gives rise to an equation which is second order in the strength of the short range interaction, the explicit construction of the triplet operators obtained here shows that, in terms of these operators, the second-order equation can be factorized to two first-order equations, one of which gives rise to a solution below the particle-hole continuum of Dirac electrons in undoped graphene.     

Electrochemical Determination of Tyrosine in the Presence of Dopamine and Uric Acid at the Surface of Gold Nanoparticles Modified Carbon Paste Electrode

A gold nanoparticles modified carbon paste electrode (GN‐CPE) was used as a highly sensitive electrochemical sensor for determination of tyrosine (Tyr), dopamine (DA) and uric acid (UA) in phosphate buffer solution (PBS). The study and measurements were carried out by using cyclic voltammetry (CV), differential pulse voltammetry (DPV) and chronoamperometry methods. In DPV, the GN‐CPE could separate the oxidation peak potentials of DA and UA present in the same solution, though at the unmodified CPE the peak potentials were indistinguishable. The prepared electrode showed voltammetric responses with high sensitivity and selectivity for Tyr, DA and UA in optimal conditions, which makes it very suitable for simultaneous determination of these compounds. The calibration curves for Try, DA and UA were linear for the concentrations of each species. The proposed voltammetric approach was also applied to the determination of Tyr concentration in human serum as a real sample.     

A Study on Transreactions of PET/PEN Reactive Blending in a Twin‐Screw Extruder Using an Axial Dispersion Model

Transreactions of PET and PEN melt‐mixed in a twin‐screw extruder are investigated. The extruder is modeled and characterized in the frame of a tubular system of closed type. The kinetic modeling is based on a modified second‐order reversible reaction equation, which allows the dispersion equation to be solved analytically. The analysis shows a good agreement between the model and experiment. The axial dispersion model is employed to predict the extent of transesterification reactions (X) and degree of randomness (RD). ¹H NMR measurements are performed to estimate X and RD. Theoretical and experimental data are in good agreement. The model can thus be exploited to describe the effects of processing parameters, mixing time, mixing temperature, and blend composition on X and RD.