Nonlocal scale effects on wave propagation in multi-walled carbon nanotubes

This paper represents the effect of nonlocal scale parameter on the wave propagation in multi-walled carbon nanotubes (MWCNTs). Each wall of the MWCNT is modeled as first order shear deformation beams and the van der Waals interactions between the walls are modeled as distributed springs. The studies shows that the scale parameter introduces certain band gap region in both flexural and shear wave mode where no wave propagation occurs. This is manifested in the wavenumber plots as the region where the wavenumber tends to infinite (or group speed tends to zero). The frequency at which this phenomenon occurs is called the ``Escape frequency''. The analysis shows that, for a given N-walled carbon nanotube (CNT). the nonlocal scaling parameter has a significant effect on the shear wave modes of the N - 1 walls. The escape frequencies of the flexural and shear wave modes of the N-walls are inversely proportionl to the nonlocal scaling parameter. It is also shown that the cut-off frequencies are independent of the nonlocal scale parameter. (C) 2009 Elsevier B.V. All rights reserved.

CAE-based prediction of projectile residual velocity for impact on single and multi-layered metallic armour plates

The present, paper deals with the CAE-based study Of impact of jacketed projectiles on single- and multi-layered metal armour plates using LS-DYNA. The validation of finite element modelling procedure is mainly based on the mesh convergence study using both shell and solid elements for representing single-layered mild steel target plates. It, is shown that the proper choice of mesh density and the strain rate-dependent material properties are essential for all accurate prediction of projectile residual velocity. The modelling requirements are initially arrived at by correlating against test residual velocities for single-layered mild steel plates of different depths at impact velocities in the ran.-c of approximately 800-870 m/s. The efficacy of correlation is adjudged, in terms of a 'correlation index', defined in the paper: for which values close to unity are desirable. The experience gained for single-layered plates is next; used in simulating projectile impacts on multi-layered mild steel target plates and once again a high degree of correlation with experimental residual velocities is observed. The study is repeated for single- and multi-layered aluminium target plates with a similar level of success in test residual velocity prediction. TO the authors' best knowledge, the present comprehensive study shows in particular for the first time that, with a. proper modelling approach, LS-DYNA can be used with a great degree of confidence in designing perforation-resistant single and multi-layered metallic armour plates.

Free vibration and wave propagation analysis of uniform and tapered rotating beams using spectrally formulated finite elements

This paper presents a formulation of an approximate spectral element for uniform and tapered rotating Euler-Bernoulli beams. The formulation takes into account the varying centrifugal force, mass and bending stiffness. The dynamic stiffness matrix is constructed using the weak form of the governing differential equation in the frequency domain, where two different interpolating functions for the transverse displacement are used for the element formulation. Both free vibration and wave propagation analysis is performed using the formulated elements. The studies show that the formulated element predicts results, that compare well with the solution available in the literature, at a fraction of the computational effort. In addition, for wave propagation analysis, the element shows superior convergence. (C) 2007 Elsevier Ltd. All rights reserved.

Vave propagation and bandgaps in a parametrically modulated composite laminate

Wave propagation and its frequency bandgaps in a parametrically modulated composite laminate are reported in this paper. The modulated properties under considerations are due to periodic microstructure, for example honeycomb core sandwich composite, which can be parameterized and homogenized in a suitable scale. Wave equations are derived by assuming a third-order shear deformation theory. Homogenization of the wave equations is carried out in the scale of wavelength. In-plane wave and flexural-shear wave dispersions are obtained for a range of values of a stiffness modulation coefficient (alpha). A clear pattern of stop-bands is observed for alpha >= 4. To validate the band-gap phenomena, we take recourse to time domain response obtained from finite element simulation. As predicted by the proposed analytical technique, a distinct correlation between the chosen frequency band and the simulated wave arrival time and amplitude reduction is found. This promises practical applications of the proposed analytical technique to designing parametrically modulated composite laminate for wave suppression. (C) 2009 Elsevier B.V. All rights reserved.

Capturability analysis of a geometric guidance law in relative velocity space

In this paper, a relative velocity approach is used to analyze the capturability of a geometric guidance law. Point mass models are assumed for both the missile and the target. The speeds of the missile and target are assumed to remain constant throughout the engagement. Lateral acceleration, obtained from the guidance law, is applied to change the path of the missile. The kinematic equations for engagements in the horizontal plane are derived in the relative velocity space. Some analytical results for the capture region are obtained for non-maneuvering and maneuvering targets. For non-maneuvering targets it is enough for the navigation gain to be a constant to intercept the target, while for maneuvering targets a time varying navigation gain is needed for interception. These results are then verified through numerical simulations.

Mapping of Average Shear Wave Velocity for Bangalore Region: A Case Study

Mapping the shear wave velocity profile is an important part in seismic hazard and microzonation studies. The shear wave velocity of soil in the city of Bangalore was mapped using the Multichannel Analysis of Surface Wave (MASW) technique. An empirical relationship was found between the Standard Penetration Test (SPT) corrected N value ((N1)60cs) and measured shear wave velocity (Vs). The survey points were selected in such a way that the results represent the entire Bangalore region, covering an area of 220 km2. Fifty-eight 1-D and 20 2-D MASW surveys were performed and their velocity profiles determined. The average shear wave velocity of Bangalore soils was evaluated for depths of 5 m, 10 m, 15 m, 20 m, 25 m and 30 m. The sub-soil classification was made for seismic local site effect evaluation based on average shear wave velocity of 30-m depth (Vs30) of sites using the National Earthquake Hazards Reduction Program (NEHRP) and International Building Code (IBC) classification. Mapping clearly indicates that the depth of soil obtained from MASW closely matches with the soil layers identified in SPT bore holes. Estimation of local site effects for an earthquake requires knowledge of the dynamic properties of soil, which is usually expressed in terms of shear wave velocity. Hence, to make use of abundant SPT data available on many geotechnical projects in Bangalore, an attempt was made to develop a relationship between Vs (m/s) and (N1)60cs. The measured shear wave velocity at 38 locations close to SPT boreholes was used to generate the correlation between the corrected N values and shear wave velocity. A power fit model correlation was developed with a regression coefficient (R2) of 0.84. This relationship between shear wave velocity and corrected SPT N values correlates well with the Japan Road Association equations.

Prediction of flame liftoff height of diffusion/partially premixed jet flames and modeling of mild combustion burners

In this article, a new flame extinction model based on the k/epsilon turbulence time scale concept is proposed to predict the flame liftoff heights over a wide range of coflow temperature and O-2 mass fraction of the coflow. The flame is assumed to be quenched, when the fluid time scale is less than the chemical time scale ( Da < 1). The chemical time scale is derived as a function of temperature, oxidizer mass fraction, fuel dilution, velocity of the jet and fuel type. The present extinction model has been tested for a variety of conditions: ( a) ambient coflow conditions ( 1 atm and 300 K) for propane, methane and hydrogen jet flames, ( b) highly preheated coflow, and ( c) high temperature and low oxidizer concentration coflow. Predicted flame liftoff heights of jet diffusion and partially premixed flames are in excellent agreement with the experimental data for all the simulated conditions and fuels. It is observed that flame stabilization occurs at a point near the stoichiometric mixture fraction surface, where the local flow velocity is equal to the local flame propagation speed. The present method is used to determine the chemical time scale for the conditions existing in the mild/ flameless combustion burners investigated by the authors earlier. This model has successfully predicted the initial premixing of the fuel with combustion products before the combustion reaction initiates. It has been inferred from these numerical simulations that fuel injection is followed by intense premixing with hot combustion products in the primary zone and combustion reaction follows further downstream. Reaction rate contours suggest that reaction takes place over a large volume and the magnitude of the combustion reaction is lower compared to the conventional combustion mode. The appearance of attached flames in the mild combustion burners at low thermal inputs is also predicted, which is due to lower average jet velocity and larger residence times in the near injection zone.

The partition of unity finite element method for elastic wave propagation in Reissner-Mindlin plates

This paper reports a numerical method for modelling the elastic wave propagation in plates. The method is based on the partition of unity approach, in which the approximate spectral properties of the infinite dimensional system are embedded within the space of a conventional finite element method through a consistent technique of waveform enrichment. The technique is general, such that it can be applied to the Lagrangian family of finite elements with specific waveform enrichment schemes, depending on the dominant modes of wave propagation in the physical system. A four-noded element for the Reissner-indlin plate is derived in this paper, which is free of shear locking. Such a locking-free property is achieved by removing the transverse displacement degrees of freedom from the element nodal variables and by recovering the same through a line integral and a weak constraint in the frequency domain. As a result, the frequency-dependent stiffness matrix and the mass matrix are obtained, which capture the higher frequency response with even coarse meshes, accurately. The steps involved in the numerical implementation of such element are discussed in details. Numerical studies on the performance of the proposed element are reported by considering a number of cases, which show very good accuracy and low computational cost. Copyright (C)006 John Wiley & Sons, Ltd.

Semi-empirical procedures for estimation of residual velocity and ballistic limit for impact on mild steel plates by projectiles

This paper deals with the development of simplified semi-empirical relations for the prediction of residual velocities of small calibre projectiles impacting on mild steel target plates, normally or at an angle, and the ballistic limits for such plates. It has been shown, for several impact cases for which test results on perforation of mild steel plates are available, that most of the existing semi-empirical relations which are applicable only to normal projectile impact do not yield satisfactory estimations of residual velocity. Furthermore, it is difficult to quantify some of the empirical parameters present in these relations for a given problem. With an eye towards simplicity and ease of use, two new regression-based relations employing standard material parameters have been discussed here for predicting residual velocity and ballistic limit for both normal and oblique impact. The latter expressions differ in terms of usage of quasi-static or strain rate-dependent average plate material strength. Residual velocities yielded by the present semi-empirical models compare well with the experimental results. Additionally, ballistic limits from these relations show close correlation with the corresponding finite element-based predictions.

Terahertz wave characteristics of a single-walled carbon nanotube containing a fluid flow using the nonlocal Timoshenko beam model

This paper presents the effect of nonlocal scaling parameter on the terahertz wave propagation in fluid filled single walled carbon nanotubes (SWCNTs). The SWCNT is modeled as a Timoshenko beam,including rotary inertia and transverse shear deformation by considering the nonlocal scale effects. A uniform fluid velocity of 1000 m/s is assumed. The analysis shows that, for a fluid filled SWCNT, the wavenumbers of flexural and shear waves will increase and the corresponding wave speeds will decrease as compared to an empty SWCNT. The nonlocal scale parameter introduces certain band gap region in both flexural and shear wave mode where no wave propagation occurs. This is manifested in the wavenumber plots as the region where the wavenumber tends to infinite (or wave speed tends to zero). The frequency at which this phenomenon occurs is called the ``escape frequency''. The effect of fluid density on the terahertz wave propagation in SWCNT is also studied and the analysis shows that as the fluid becomes denser, the wave speeds will decrease. The escape frequency decreases with increase in nonlocal scaling parameter, for both wave modes. We also show that the effect of fluid density and velocity are negligible on the escape frequencies of flexural and shear wave modes. (C) 2010 Elsevier B.V. All rights reserved.

Velocity-Space Contours of Collision Integrals

Based on the recently found closed-form expressions of the Boltzmann collision integrals in a rigid-sphere gas for multi-Maxwellian distributions, a few typical sets of contour surfaces of the integrals in the space of molecular velocities are presented. These show graphically the tendency toward equilibrium under the influence of collisions. A brief preliminary comparison with Monte Carlo results is also given.

Sound Velocity Anomaly at the Mott Transition: Application to Organic Conductors and V2O3

Close to the Mott transition, lattice degrees of freedom react to the softening of electron degrees of freedom. This results in a change of lattice spacing, a diverging compressibility, and a critical anomaly of the sound velocity. These effects are investigated within a simple model, in the framework of dynamical mean-field theory. The results compare favorably to recent experiments on the layered organic-conductor kappa-(BEDT-TTF)(2)Cu[N(CN)(2)]Cl. We predict that effects of a similar magnitude are expected for V2O3, despite the much larger value of the elastic modulus of this material.

Theory of laminar flame propagation with non-normal diffusion.

A study has been made of the problem of steady, one-dimensional, laminar flame propagation in premixed gases, with the Lewis number differing from (and equal to) unity. Analytical solutions, using the method of matched asymptotic expansions, have been obtained for large activation energies. Numerical solutions have been obtained for a wide range of the reduced activation temperature parameter (n {geometrically equal to} E/RTb), and the Lewis number δ. The studies reveal that the flame speed eigenvalue is linear in Lewis number for first order and quadratic in Lewis number for second order reactions. For a quick determination of flame speeds, with reasonable accuracy, a simple rule, expressing the flame speed eigenvalue as a function of the Lewis number and the centroid of the reaction rate function, is proposed. Comparisons have been made with some of the earlier works, for both first and second order reactions.