Analytical test functions for free vibration analysis of rotating non-homogeneous Timoshenko beams

In this paper, the governing equations for free vibration of a non-homogeneous rotating Timoshenko beam, having uniform cross-section, is studied using an inverse problem approach, for both cantilever and pinned-free boundary conditions. The bending displacement and the rotation due to bending are assumed to be simple polynomials which satisfy all four boundary conditions. It is found that for certain polynomial variations of the material mass density, elastic modulus and shear modulus, along the length of the beam, the assumed polynomials serve as simple closed form solutions to the coupled second order governing differential equations with variable coefficients. It is found that there are an infinite number of analytical polynomial functions possible for material mass density, shear modulus and elastic modulus distributions, which share the same frequency and mode shape for a particular mode. The derived results are intended to serve as benchmark solutions for testing approximate or numerical methods used for the vibration analysis of rotating non-homogeneous Timoshenko beams.

Modeling of Bubble-Size Distribution in Water and Freon Co-Blown Free Rise Polyurethane Foams

A model has been developed to simulate the foam characteristics obtained, when chemical (water) and physical (Freon) blowing agents are used together for the formation of polyurethane foams. The model considers the rate of reaction, the consequent rise in temperature of the reaction mixture, nucleation of bubbles, and mass transfer of CO2 and Freon to them till the time of gelation. The model is able to explain the experimental results available in literature. It further predicts that the nucleation period gets reduced with increase in water (at constant Freon content), whereas with increase in Freon (at constant water) concentration nucleation period decreases marginally leading to narrower bubble-size distribution. By the use of uniform sized nuclei added initially, the model predicts that the bubble-size distribution can be made independent of the rate of homogeneous nucleation and can, thus, offer an extra parameter for its control. (C) 2014 Wiley Periodicals, Inc.

Dynamics of the reaction between the free end of a tethered self-avoiding polymer and a flat penetrable surface: A renormalization group study

The average time tau(r) for one end of a long, self-avoiding polymer to interact for the first time with a flat penetrable surface to which it is attached at the other end is shown here to scale essentially as the square of the chain's contour length N. This result is obtained within the framework of the Wilemski-Fixman approximation to diffusion-limited reactions, in which the reaction time is expressed as a time correlation function of a ``sink'' term. In the present work, this sink-sink correlation function is calculated using perturbation expansions in the excluded volume and the polymer-surface interactions, with renormalization group methods being used to resum the expansion into a power law form. The quadratic dependence of tau(r) on N mirrors the behavior of the average time tau(c) of a free random walk to cyclize, but contrasts with the cyclization time of a free self-avoiding walk (SAW), for which tau(r) similar to N-2.2. A simulation study by Cheng and Makarov J. Phys. Chem. B 114, 3321 (2010)] of the chain-end reaction time of an SAW on a flat impenetrable surface leads to the same N-2.2 behavior, which is surprising given the reduced conformational space a tethered polymer has to explore in order to react. (C) 2014 AIP Publishing LLC.

Propensity to Form Amyloid Fibrils Is Encoded as Excitations in the Free Energy Landscape of Monomeric Proteins

Protein aggregation, linked to many of diseases, is initiated when monomers access rogue conformations that are poised to form amyloid fibrils. We show, using simulations of src SH3 domain, that mechanical force enhances the population of the aggregation-prone (N*) states, which are rarely populated under force free native conditions but are encoded in the spectrum of native fluctuations. The folding phase diagrams of SH3 as a function of denaturant concentration (C]), mechanical force (f), and temperature exhibit an apparent two-state behavior, without revealing the presence of the elusive N* states. Interestingly, the phase boundaries separating the folded and unfolded states at all C] and f fall on a master curve, which can be quantitatively described using an analogy to superconductors in a magnetic field. The free energy profiles as a function of the molecular extension (R), which are accessible in pulling experiments, (R), reveal the presence of a native-like N* with a disordered solvent-exposed amino-terminal beta-strand. The structure of the N* state is identical with that found in Fyn SH3 by NMR dispersion experiments. We show that the timescale for fibril formation can be estimated from the population of the N* state, determined by the free energy gap separating the native structure and the N* state, a finding that can be used to assess fibril forming tendencies of proteins. The structures of the N* state are used to show that oligomer formation and likely route to fibrils occur by a domain-swap mechanism in SH3 domain. (C) 2014 Elsevier Ltd. All rights reserved.

beta gamma-fused turn structures in sugar amino acid (SAA) containing cyclic tetrapeptides with alpha 3 delta architecture

The current manuscript describes conformational analysis of 15-membered cyclic tetrapeptides (CTPs), with alpha 3 delta architecture, containing sugar amino acids (SAA) having variation in the stereocenter at C5 carbon. Conformational analyses of both the series, in protected and deprotected forms, were carried out in DMSO-d(6) using various NMR techniques, supported by restrained MD calculations. It was intriguing to notice that the alpha 3 delta macrocycles got stabilized by both 10-membered beta-turn as well as a seven-membered gamma-turn, fused within the same macrocycle. The presence of fused sub-structures within a 15-membered macrocycle is rare to see. Also, the stereocenter variation at C5 did not affect the fused turn structures and exhibited similar conformations in both the series. The design becomes highly advantageous as fused reverse turn structures are occurring in the cyclic structure with minimalistic size macrocycle and this can be applied to develop suitable pharmacophores in the drug development process. (C) 2014 Elsevier Ltd. All rights reserved.

Role of spectator ions in influencing the properties of dopant-free ZnO nanocrystals

Towards fundamental studies and potential applications, achieving precise control over the generation of defects in pure ZnO nanocrystals has been always intriguing. Herein, we explored the rote of spectator ions (Co2+ and Ni2+) in influencing the functional properties of ZnO nanocrystals. The crystalline quality, phase purity, and composition of as-prepared samples were thoroughly established by powder X-ray diffraction, electron microscopy (TEM and STEM), and by Raman and X-ray photoelectron spectroscopies (XPS). Despite the presence of Co2+ and Ni2+ ions in the reaction mixture, STEM-energy dispersive spectroscopy (EDS), XPS analysis, and inductively-coupled plasma mass spectrometry (ICP-MS) revealed that the ZnO nanocrystals formed are dopant-free. Even so, their luminescence and magnetic properties were substantially different from those of pure ZnO nanocrystals synthesized using a similar methodology. We attribute the origin of these properties to the defects associated with ZnO nanocrystals generated under different but optimized conditions.

Finite element analysis of free vibration of the delaminated composite plate with variable kinematic multilayered plate elements

Composite laminates are prone to delamination. Implementation of delamination in the Carrera Unified Formulation frame work using nine noded quadrilateral MITC9 element is discussed in this article. MITC9 element is devoid of shear locking and membrane locking. Delaminated as well as healthy structure is analyzed for free mode vibration. The results from the present work are compared with the available experimental or/and research article or/and the three dimensional finite element simulations. The effect of different kinds and different percentages of area of delamination on the first three natural frequencies of the structure is discussed. The presence of open-mode delamination mode shape for large delaminations within the first three natural frequencies is discussed. Also, the switching of places between the second bending mode, with that of the first torsional mode frequency is discussed. Results obtained from different ordered theories are compared in the presence of delamination. Advantage of layerwise theories as compared to equivalent single layer theories for very large delaminations is stated. The effect of different kinds of delamination and their effect on the second bending and first torsional mode shape is discussed. (C) 2014 Elsevier Ltd. All rights reserved.

DIMENSION FREE BOUNDEDNESS OF RIESZ TRANSFORMS FOR THE GRUSHIN OPERATOR

Let G = -Delta(xi) - vertical bar xi vertical bar(2) partial derivative(2)/partial derivative eta(2) be the Grushin operator on R-n x R. We prove that the Riesz transforms associated to this operator are bounded on L-p(Rn+1), 1 < p < infinity, and their norms are independent of dimension n.

An improved free surface modeling for incompressible SPH

In Incompressible Smooth Particle Hydrodynamics (ISPH), a pressure Poisson equation (PPE) is solved to obtain a divergence free velocity field. When free surfaces are simulated using this method a Dirichlet boundary condition for pressure at the free surface has to be applied. In existing ISPH methods this is achieved by identifying free surface particles using heuristically chosen threshold of a parameter such as kernel sum, density or divergence of the position, and explicitly setting their pressure values. This often leads to clumping of particles near the free surface and spraying off of surface particles during splashes. Moreover, surface pressure gradients in flows where surface tension is important are not captured well using this approach. We propose a more accurate semi-analytical approach to impose Dirichlet boundary conditions on the free surface. We show the efficacy of the proposed algorithm by using test cases of elongation of a droplet and dam break. We perform two dimensional simulations of water entry and validate the proposed algorithm with experimental results. Further, a three dimensional simulation of droplet splash is shown to compare well with the Volume-of-Fluid simulations. (C) 2014 Elsevier Ltd. All rights reserved.

Multidimensional free energy surface of unfolding of HP-36: Microscopic origin of ruggedness

The protein folding funnel paradigm suggests that folding and unfolding proceed as directed diffusion in a multidimensional free energy surface where a multitude of pathways can be traversed during the protein's sojourn from initial to final state. However, finding even a single pathway, with the detail chronicling of intermediates, is an arduous task. In this work we explore the free energy surface of unfolding pathway through umbrella sampling, for a small globular a-helical protein chicken-villin headpiece (HP-36) when the melting of secondary structures is induced by adding DMSO in aqueous solution. We find that the unfolding proceeds through the initial separation or melting of aggregated hydrophobic core that comprises of three phenylalanine residues (Phe7, Phe11, and Phe18). This separation is accompanied by simultaneous melting of the second helix. Unfolding is found to be a multistage process involving crossing of three consecutive minima and two barriers at the initial stage. At a molecular level, Phe18 is observed to reorient itself towards other hydrophobic grooves to stabilize the intermediate states. We identify the configuration of the intermediates and correlate the intermediates with those obtained in our previous works. We also give an estimate of the barriers for different transition states and observe the softening of the barriers with increasing DMSO concentration. We show that higher concentration of DMSO tunes the unfolding pathway by destabilizing the third minimum and stabilizing the second one, indicating the development of a solvent modified, less rugged pathway. The prime outcome of this work is the demonstration that mixed solvents can profoundly transform the nature of the energy landscape and induce unfolding via a modified route. A successful application of Kramer's rate equation correlating the free energy simulation results shows faster rate of unfolding with increasing DMSO concentration. This work perhaps presents the first systematic theoretical study of the effect of a chemical denaturant on the microscopic free energy surface and rates of unfolding of HP-36. (C) 2014 AIP Publishing LLC.

Flexibility in flapping foil suppresses meandering of induced jet in absence of free stream

Thrust-generating flapping foils are known to produce jets inclined to the free stream at high Strouhal numbers St = fA/U-infinity, where f is the frequency and A is the amplitude of flapping and U-infinity is the free-stream velocity. Our experiments, in the limiting case of St —> infinity (zero free-stream speed), show that a purely oscillatory pitching motion of a chordwise flexible foil produces a coherent jet composed of a reverse Benard-Karman vortex street along the centreline, albeit over a specific range of effective flap stiffnesses. We obtain flexibility by attaching a thin flap to the trailing edge of a rigid NACA0015 foil; length of flap is 0.79 c where c is rigid foil chord length. It is the time-varying deflections of the flexible flap that suppress the meandering found in the jets produced by a pitching rigid foil for zero free-stream condition. Recent experiments (Marais et al., J. Fluid Mech., vol. 710, 2012, p. 659) have also shown that the flexibility increases the St at which non-deflected jets are obtained. Analysing the near-wake vortex dynamics from flow visualization and particle image velocimetry (PIV) measurements, we identify the mechanisms by which flexibility suppresses jet deflection and meandering. A convenient characterization of flap deformation, caused by fluid-flap interaction, is through a non-dimensional effective stiffness', EI* = 8 EI/(rho V-TEmax(2) s(f) c(f)(3)/2), representing the inverse of the flap deflection due to the fluid-dynamic loading; here, EI is the bending stiffness of flap, rho is fluid density, V-TEmax is the maximum velocity of rigid foil trailing edge, s(f) is span and c(f) is chord length of the flexible flap. By varying the amplitude and frequency of pitching, we obtain a variation in EI* over nearly two orders of magnitude and show that only moderate EI*. (0.1 less than or similar to EI * less than or similar to 1 generates a sustained, coherent, orderly jet. Relatively `stiff' flaps (EI* greater than or similar to 1), including the extreme case of no flap, produce meandering jets, whereas highly `flexible' flaps (EI* less than or similar to 0.1) produce spread-out jets. Obtained from the measured mean velocity fields, we present values of thrust coefficients for the cases for which orderly jets are observed.

Impact of Stone-Wales and lattice vacancy defects on the electro-thermal transport of the free standing structure of metallic ZGNR

We report the effect of topological as well as lattice vacancy defects on the electro-thermal transport properties of the metallic zigzag graphene nano ribbons at their ballistic limit. We employ the density function theory-Non equilibrium green's function combination to calculate the transmission details. We then present an elaborated study considering the variation in the electrical current and the heat current transport with the change in temperature as well as the voltage gradient across the nano ribbons. The comparative analysis shows, that in the case of topological defects, such as the Stone-Wales defect, the electrical current transport is minimum. Besides, for the voltage gradient of 0.5 Volt and the temperature gradient of 300 K, the heat current transport reduces by similar to 62 % and similar to 50% for the cases of Stones-Wales defect and lattice vacancy defect respectively, compared to that of the perfect one.

Hexamethylenetetramine mediated simultaneous nitrogen doping and reduction of graphene oxide for a metal-free SERS substrate

We report a one-pot hydrothermal synthesis of nitrogen doped reduced graphene oxide (N-rGO) and Ag nanoparticle decorated N-rGO hybrid nanostructures from graphene oxide (GO), metal ions and hexamethylenetetramine (HMT). HMT not only reduces GO and metal ions simultaneously but also acts as the source for the nitrogen (N) dopant. We show that the N-rGO can be used as a metal-free surface enhanced Raman spectroscopy (SERS) substrate, while the Ag nano-particles decorated N-rGO can be used as an effective SERS substrate as well as a template for decorating various other nanostructures on N-rGO.

Beyond classical dynamic structural plasticity using mesh-free modelling techniques

The problem of modelling the transient response of an elastic-perfectly-plastic cantilever beam, carrying an impulsively loaded tip mass, is,often referred to as the Parkes cantilever problem 25]; The permanent deformation of a cantilever struck transversely at its tip, Proc. R. Soc. A., 288, pp. 462). This paradigm for classical modelling of projectile impact on structures is re-visited and updated using the mesh-free method, smoothed particle hydrodynamics (SPH). The purpose of this study is to investigate further the behaviour of cantilever beams subjected to projectile impact at its tip, by considering especially physically real effects such as plastic shearing close to the projectile, shear deformation, and the variation of the shear strain along the length and across the thickness of the beam. Finally, going beyond macroscopic structural plasticity, a strategy to incorporate physical discontinuity (due to crack formation) in SPH discretization is discussed and explored in the context of tip-severance of the cantilever beam. Consequently, the proposed scheme illustrates the potency for a more refined treatment of penetration mechanics, paramount in the exploration of structural response under ballistic loading. The objective is to contribute to formulating a computational modelling framework within which transient dynamic plasticity and even penetration/failure phenomena for a range of materials, structures and impact conditions can be explored ab initio, this being essential for arriving at suitable tools for the design of armour systems. (C) 2014 Elsevier Ltd. All rights reserved.