Bending and vibration analyses of coupled axially functionally graded tapered beams

The nonlinear bending and vibrations of tapered beams made of axially functionally graded (AFG) material are analysed numerically. For a clamped–clamped boundary conditions, Hamilton’s principle is employed so as to balance the potential and kinetic energies, the virtual work done by the damping, and that done by external distributed load. The nonlinear strain–displacement relations are employed to address the geometric nonlinearities originating from large deflections and induced nonlinear tension. Exponential distributions along the length are assumed for the mass density, moduli of elasticity, Poisson’s ratio, and cross-sectional area of the AFG tapered beam; the non-uniform mechanical properties and geometry of the beam along the length make the system asymmetric with respect to the axial coordinate. This non-uniform continuous system is discretised via the Galerkin modal decomposition approach, taking into account a large number of symmetric and asymmetric modes. The linear results are compared and validated with the published results in the literature. The nonlinear results are computed for both static and dynamic cases. The effect of different tapered ratios as well as the gradient index is investigated; the numerical results highlight the importance of employing a high-dimensional discretised model in the analysis of AFG tapered beams.     

Nonlinear vibration behavior and resonance of a Cartesian manipulator system carrying an intermediate end effector

This paper studied the nonlinear vibration and resonance of a Cartesian manipulator system carrying an intermediate end effector under mixed excitations. The multiple scales method is applied to get the approximate solutions of this system of the second-order differential equation. Furthermore, the analytical solution obtained the amplitudes and phases of the response from the first-order differential equation governing. We extracted all worst resonance cases and studied it numerically. The numerical solutions and response amplitude of this system are also studied and discussed. We analyzed the stability of the steady-state solution of a Cartesian manipulator system using frequency response equations and phase plane technique at the worst resonance cases. Comparison between analytical and numerical solutions is obtained. We determined both bifurcation diagrams and stability using Poincaré maps. Also, the numerical results are obtained using MAPLE and MATLAB algorithms.     

Analytical parametric study of bi-linear hysteretic model of dry friction under harmonic,impulse and random excitations

Hysteretic behavior due to some nonlinear sources is a common phenomenon in many dynamical systems. One of the sources of this behavior in mechanical systems is dry friction. Dry friction in bolted or riveted joints of mechanical structures makes their dynamic behavior hysteretic. Bi-linear hysteresis is one of the models that can be used to study these systems which is used in this paper. A SDOF system containing a bi-linear hysteretic element called Jenkins element under harmonic, impulse and random excitations is considered. For all three types of excitations, the effects of system and excitation parameters on the defined equivalent system parameters and the response specifications are studied. Harmonic balance method is employed for harmonic excitation studies, and optimum friction threshold for minimizing response amplitude is obtained versus other system parameters and response amplitude. Energy balance method is used for impulse excitation through which the desired decaying ratio can be achieved by tuning the friction threshold, depending on stiffness ratio. System under random excitation is investigated by equivalent linearization technique in two steps. At the first step, equivalent properties are obtained versus instantaneous amplitude of response. In this step, the paper contains the parametric study of system in which the variations of equivalent parameters are described when physical parameters of system or input intensity vary. Overall variance of system response is determined in the second step, and optimum sliding threshold is obtained to have minimum overall variance of system response.     

Binding of the Zn2+ ion to ferric uptake regulation protein from E. coli and the competition with Fe2+ binding: a molecular modeling study of the effect on DNA binding and conformational changes of Fur

The three dimensional structure of Ferric uptake regulation protein dimer from E. coli, determined by molecular modeling, was docked on a DNA fragment (iron box) and Zn²⁺ ions were added in two steps. The first step involved the binding of one Zn²⁺ ion to what is known as the zinc site which consists of the residues Cys 92, Cys 95, Asp 137, Asp141, Arg139, Glu 140, His 145 and His 143 with an average metal-Nitrogen distance of 2.5 Å and metal-oxygen distance of 3.1–3.2 Å. The second Zn²⁺ ion is bound to the iron activating site formed from the residues Ile 50, His 71, Asn 72, Gly 97, Asp 105 and Ala 109. The binding of the second Zn²⁺ ion strengthened the binding of the first ion as indicated by the shortening of the zinc-residue distances. Fe²⁺, when added to the complex consisting of 2Zn²⁺/Fur dimer/DNA, replaced the Zn²⁺ ion in the zinc site and when a second Fe²⁺ was added, it replaced the second zinc ion in the iron activating site. The binding of both zinc and iron ions induced a similar change in Fur conformations, but shifted residues closer to DNA in a different manner. This is discussed along with a possible role for the Zn²⁺ ion in the Fur dimer binding of DNA in its repressor activity. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Physiochemical properties of various polymer substrates and their effects on microchip electrophoresis performance

A suite of polymers were evaluated for their suitability as viable substrate materials for microchip electrophoresis applications, which were fabricated via replication technology. The relevant physiochemical properties investigated included the glass transition temperature (T(g)), UV-vis absorption properties, autofluorescence levels, electroosmotic flow (EOF) and hydrophobicity/hydrophilicity as determined by sessile water contact angle measurements. These physiochemical properties were used as a guide to select the proper substrate material for the intended microchip electrophoretic application. The T(g) of these polymers provided a guide for optimizing embossing parameters to minimize replication errors (REs), which were evaluated from surface profilometer traces. RE values ranged from 0.4 to 13.6% for the polymers polycarbonate (PC) and low-density polyethylene (LDPE), respectively. The absorption spectra and autofluorescence levels of the polymers were also measured at several different wavelengths. In terms of optical clarity (low absorption losses and small autofluorescence levels), poly(methyl methacrylate), PMMA (clear acrylic), provided ideal characteristics with autofluorescence levels comparable to glass at excitation wavelengths that ranged from 488-780 nm. Contact angle measurements showed a maximum (i.e., high degree of hydrophobicity) for polypropylene (PP), with an average contact angle of 104 degrees +/-3 degrees and a minimum exhibited by gray acrylic, G-PMMA, with an average contact angle of 27 degrees +/-2 degrees. The EOF was also measured for thermally assembled chips both before and after treatment with bovine serum albumin (BSA). The electrophoretic separation of a mixture of dye-labeled proteins including; carbonic anhydrase, phosphorylase B, beta-galactosidase, and myosin, was performed on four different polymer microchips using laser-induced fluorescence (LIF) excitation at 632.8 nm. A maximum average resolution of 5.04 for several peak pairs was found with an efficiency of 6.68 x 10(4) plates for myosin obtained using a BSA-treated PETG microchip.     

Regioselective bond cleavage in the dissociative electron transfer to benzyl thiocyanates: the role of radical/ion pair formation

Important aspects of the electrochemical reduction of a series of substituted benzyl thiocyanates were investigated. A striking change in the reductive cleavage mechanism as a function of the substituent on the aryl ring of the benzyl thiocyanate was observed, and more importantly, a regioselective bond cleavage was encountered. A reductive alpha-cleavage (CH(2)-S bond) was seen for cyano and nitro-substituted benzyl thiocyanates leading to the formation of the corresponding nitro-substituted dibenzyls. With other substituents (CH(3)O, CH(3), H, Cl, and F), both the alpha (CH(2)-S) and the beta (S-CN) bonds could be cleaved as a result of an electrochemical reduction leading to the formation of the corresponding substituted monosulfides, disulfides, and toluenes. These final products are generated through either a protonation or a nucleophilic reaction of the two-electron reduction-produced anion on the parent molecule. The dissociative electron transfer theory and its extension to the formation/dissociation of radical anions, as well as its extension to the case of strong in-cage interactions between the produced fragments ("sticky" dissociative electron transfer (ET)), along with the theoretical calculation results helped rationalize (i) the observed change in the ET mechanism, (ii) the dissociation of the radical anion intermediates formed during the electrochemical reduction of the nitro-substituted benzyl thiocyanates, and more importantly (iii) the regioselective reductive bond cleavage.     

Self-organized Segregation on the Grid

We consider an agent-based model with exponentially distributed waiting times in which two types of agents interact locally over a graph, and based on this interaction and on the value of a common intolerance threshold \(\tau \), decide whether to change their types. This is equivalent to a zero-temperature ising model with Glauber dynamics, an asynchronous cellular automaton with extended Moore neighborhoods, or a Schelling model of self-organized segregation in an open system, and has applications in the analysis of social and biological networks, and spin glasses systems. Some rigorous results were recently obtained in the theoretical computer science literature, and this work provides several extensions. We enlarge the intolerance interval leading to the expected formation of large segregated regions of agents of a single type from the known size \(\epsilon >0\) to size \(\approx 0.134\). Namely, we show that for \(0.433< \tau < 1/2\) (and by symmetry \(1/2<\tau <0.567\)), the expected size of the largest segregated region containing an arbitrary agent is exponential in the size of the neighborhood. We further extend the interval leading to expected large segregated regions to size \(\approx 0.312\) considering “almost segregated” regions, namely regions where the ratio of the number of agents of one type and the number of agents of the other type vanishes quickly as the size of the neighborhood grows. In this case, we show that for \(0.344 < \tau \le 0.433\) (and by symmetry for \(0.567 \le \tau <0.656\)) the expected size of the largest almost segregated region containing an arbitrary agent is exponential in the size of the neighborhood. This behavior is reminiscent of supercritical percolation, where small clusters of empty sites can be observed within any sufficiently large region of the occupied percolation cluster. The exponential bounds that we provide also imply that complete segregation, where agents of a single type cover the whole grid, does not occur with high probability for \(p=1/2\) and the range of intolerance considered.     

Supercontinuum generation with femtosecond optical pulse compression in silicon photonic crystal fibers at 2500 nm

In this paper, femtosecond optical pulses compression and supercontinuum generation in a triangular silicon photonic crystal fiber at 2500 nm are investigated. A region of large minimum anomalous group velocity dispersion, negligible higher order dispersions and unique nonlinearity of silicon are used to demonstrate compression of 100 fs initial input optical pulses to 2.5 fs and ultra-broadband supercontinuum generation with very low input pulse energy over short distances of the fiber.     

All optical NOR and NAND gate based on nonlinear photonic crystal ring resonators

In this paper we proposed optical NOR and NAND gates. By combining nonlinear Kerr effect with photonic crystal ring resonators first we designed a structure, whose optical behavior can be controlled via input power intensity. The switching power threshold obtained for this structure equal to 2 kW/μm². For designing the proposed optical logic gates we employed two resonant rings with the same structures, both rings at the logic gates were designed such that their resonant wavelength be at λ = 1550 nm. Every proposed logic gate has one bias and two logic input ports. We used plane wave expansion and finite difference time domain methods for analyzing the proposed structures.     

T-shaped channel drop filter based on photonic crystal ring resonator

Photonic crystal ring resonators are promising candidates for realizing all optical filters with acceptable transmission efficiency and quality factor values. In this paper, by putting a12-fold quasi crystal at the middle of on 7 × 7 square cavity we created a ring resonator structure and designed a T-shaped channel drop filter. The drop wavelength of our filter is at 1551 nm, with transmission efficiency and quality factor equal to 90% and 387. Our structure is composed of dielectric rods immersed in air. Because in this kind of structures the dominant band gap is in TM mode, all of our simulations have been done in TM mode. The total footprint of our filter is 242.4 μm², which makes it suitable for all optical integrated circuits.