VAM Applied to Dimensional Reduction of Nonlinear Multifunctional Film-fabric Laminates

This work aims at asymptotically accurate dimensional reduction of non-linear multi-functional film-fabric laminates having specific application in design of envelopes for High Altitude Airships (HAA). The film-fabric laminate for airship envelope consists of a woven fabric core coated with thin films on each face. These films provide UV protection and Helium leakage prevention, while the core provides required structural strength. This problem is both geometrically and materially non-linear. To incorporate the geometric non-linearity, generalized warping functions are used and finite deformations are allowed. The material non-linearity is handled by using hyper-elastic material models for each layer. The development begins with three-dimensional (3-D) nonlinear elasticity and mathematically splits the analysis into a one-dimensional through-the-thickness analysis and a two-dimensional (2-D) plate analysis. The through-the-thickness analysis provides the 2-D constitutive law which is then given as an input to the 2-D reference surface analysis. The dimensional reduction is carried out using Variational Asymptotic Method (VAM) for moderate strains and very small thickness-to-wavelength ratio. It features the identification and utilization of additional small parameters such as ratio of thicknesses and stiffness coefficients of core and films. Closed form analytical expressions for warping functions and 2-D constitutive law of the film-fabric laminate are obtained.

Physical Layer Data Fusion Via Distributed Co-Phasing With General Signal Constellations

This paper studies a pilot-assisted physical layer data fusion technique known as Distributed Co-Phasing (DCP). In this two-phase scheme, the sensors first estimate the channel to the fusion center (FC) using pilots sent by the latter; and then they simultaneously transmit their common data by pre-rotating them by the estimated channel phase, thereby achieving physical layer data fusion. First, by analyzing the symmetric mutual information of the system, it is shown that the use of higher order constellations (HOC) can improve the throughput of DCP compared to the binary signaling considered heretofore. Using an HOC in the DCP setting requires the estimation of the composite DCP channel at the FC for data decoding. To this end, two blind algorithms are proposed: 1) power method, and 2) modified K-means algorithm. The latter algorithm is shown to be computationally efficient and converges significantly faster than the conventional K-means algorithm. Analytical expressions for the probability of error are derived, and it is found that even at moderate to low SNRs, the modified K-means algorithm achieves a probability of error comparable to that achievable with a perfect channel estimate at the FC, while requiring no pilot symbols to be transmitted from the sensor nodes. Also, the problem of signal corruption due to imperfect DCP is investigated, and constellation shaping to minimize the probability of signal corruption is proposed and analyzed. The analysis is validated, and the promising performance of DCP for energy-efficient physical layer data fusion is illustrated, using Monte Carlo simulations.

Sound radiation from a perforated panel set in a baffle with a different perforation ratio

A finite flexible perforated panel set in a differently perforated rigid baffle is considered. The radiation efficiency from such a panel is derived using a 2-D wavenumber domain formulation. This generalization is later used to represent a more practical case of a perforated panel fixed in an unperforated baffle. The perforations are in the form of an array of uniformly distributed circular holes. A complex impedance model for the holes available in the literature is used. An averaged fluid particle velocity is derived using the continuity equation and the surface pressure is derived using an appropriate momentum equation. The discontinuity in the perforate impedance (due to different hole dimensions or perforation ratio) at the panel-baffle interface is carefully taken into account. It is found that there exists a `coupling' of different wavenumbers of the spatially mean fluid particle velocity field. The change in the resonance frequencies and the modeshapes of the panel due to the perforations is taken into account using the Receptance method. Analytical expressions for the radiated power and radiation efficiency are derived in an integral form and numerical results are presented. Several comparisons are made to understand the radiation efficiency curves. Since both the resistive and reactive components of the hole impedance are taken into account, the model is directly applicable to micro-perforated panels also. (C) 2016 Elsevier Ltd. All rights reserved.

The Size-Dependent Elastic Properties of Nanofilms with Surface Effects

Size-dependent elastic constants are investigated theoretically with reference to a nanoscale single-crystal thin film. A three-dimensional _3D_ model is presented with the relaxation on the surface of the nanofilm taken into consideration. The constitutive relation of the 3D model is derived by using the energy approach, and analytical expressions for the four nonzero elastic constants of the nanofilm are obtained. The size effects of the four elastic constants are then discussed, and the dependence of these elastic constants on the surface relaxation and the ambiguity in the definition of the thickness of the nanofilm are also analyzed. In addition, the elastic moduli of the nanofilm in two kinds of plane problem are obtained and discussed in the case of a special boundary condition.

Quasi-static three-point bending of carbon fiber sandwich beams with square honeycomb cores

Sandwich beams comprising identical face sheets and a square honeycomb core were manufactured from carbon fiber composite sheets. Analytical expressions were derived for four competing collapse mechanisms of simply supported and clamped sandwich beams in three-point bending: core shear, face microbuckling, face wrinkling, and indentation. Selected geometries of sandwich beams were tested to illustrate these collapse modes, with good agreement between analytic predictions and measurements of the failure load. Finite element (FE) simulations of the three-point bending responses of these beams were also conducted by constructing a FE model by laying up unidirectional plies in appropriate orientations. The initiation and growth of damage in the laminates were included in the FE calculations. With this embellishment, the FE model was able to predict the measured load versus displacement response and the failure sequence in each of the composite beams. © 2011 American Society of Mechanical Engineers.

The Surface- And Size-Dependent Elastic Moduli Of Nanostructures

A theoretical model is presented to investigate the size-dependent elastic moduli of nanostructures with the effects of the surface relaxation surface energy taken into consideration. At nanoscale, due to the large ratios of the surface-to-volume, the surface effects, which include surface relaxation surface energy, etc., can play important roles. Thus, the elastic moduli of nanostructures become surface- and size-dependent. In the research, the three-dimensional continuum model of the nanofilm with the surface effects is investigated. The analytical expressions of five nonzero elastic moduli of the nanofilm are derived, and then the dependence of the elastic moduli is discussed on the surface effects and the characteristic dimensions of nanofilms.

Fractal dimensions for unsaturated porous media

The analytical expressions of the fractal dimensions for wetting and non-wetting phases for unsaturated porous media are derived and are found to be a function of porosity, maximum and minimum pore sizes as well as saturation. There is no empirical constant in the proposed fractal dimensions. It is also found that the fractal dimensions increase with porosity of a medium and are meaningful only in a certain range of saturation S-w, i.e. S-w > S-min for wetting phase and S-w < S-max for non-wetting phase at a given porosity, based on real porous media for requirements from both fractal theory and experimental observations. The present analysis of the fractal dimensions is verified to be consistent with the existing experimental observations and it makes possible to analyze the transport properties such as permeability, thermal dispersion in unsaturated porous media by fractal theory and technique.

A note on the heat-transfer to nonspherical particles from plasma

Heat transfer from plasma to a nonspherical partical in the free-molecular regime is studied in the present paper under thin plasma sheath condition. Analytical expressions for the floating potential charge and heat fluxes of an ellipsoid particle of revolution are derived and curves are given for key parameters for arbitrary plasma flow direction. On the basis of these results, an equivalent sphere with the same surface area as the nonspherical particle is suggested to be used for calculating the total heat flux of nonspherical particle in engineering application with acceptable accuracy. Furthermore, the effects of particle rotation, which occurs in most aerosol systems, on the heat transfer are also discussed.

Complex stress functions and plastic zone sizes for notch cracks subjected to various loading conditions

In this paper, the conformal mapping method is used to solve the plane problem of an infinite plate containing a central lip-shaped notch subjected to biaxial loading at a remote boundary or a surface uniform pressure on the notch. The stress intensity factors KI and KII are obtained by the derived complex stress functions. The simple analytical expressions can be applied to the situation of cracks originating from a circular or an elliptical notch. The plastic zone sizes for such notch cracks are subsequently evaluated in light of the Dugdale strip yield concept. The results are consistent with available numerical data.

The effect of variable currents on internal solitary waves

The effect of variable currents on internal solitary waves is described within the context of a variable coefficient Korteweg-de Vries (KdV) equation, and the approximate slowly varying, solitary-wave solution of this equation. The general theory which leads to the variable coefficient KdV equation is described; a derivation for the special case when the solitary wave and the current are aligned in the same direction is given in the Appendix. Using further simplifications and approximations, a number of analytical expressions are obtained for the variation in the solitary wave amplitude resulting from variable shear in the basic current or from when the basic current is a depth-independent flow which is a simple representation of a geostrophic current, tidal flow or inertial wave.

The surface- and size-dependent elastic moduli of nanostructures

A theoretical model is presented to investigate the size-dependent elastic moduli of nanostructures with the effects of the surface relaxation surface energy taken into consideration. At nanoscale, due to the large ratios of the surface-to-volume, the surface effects, which include surface relaxation surface energy, etc., can play important roles. Thus, the elastic moduli of nanostructures become surface- and size-dependent. In the research, the three-dimensional continuum model of the nanofilm with the surface effects is investigated. The analytical expressions of five nonzero elastic moduli of the nanofilm are derived, and then the dependence of the elastic moduli is discussed on the surface effects and the characteristic dimensions of nanofilms.

Space-time correlations of fluctuating velocities in turbulent shear flows

Space-time correlations or Eulerian two-point two-time correlations of fluctuating velocities are analytically and numerically investigated in turbulent shear flows. An elliptic model for the space-time correlations in the inertial range is developed from the similarity assumptions on the isocorrelation contours: they share a uniform preference direction and a constant aspect ratio. The similarity assumptions are justified using the Kolmogorov similarity hypotheses and verified using the direct numerical simulation DNS of turbulent channel flows. The model relates the space-time correlations to the space correlations via the convection and sweeping characteristic velocities. The analytical expressions for the convection and sweeping velocities are derived from the Navier-Stokes equations for homogeneous turbulent shear flows, where the convection velocity is represented by the mean velocity and the sweeping velocity is the sum of the random sweeping velocity and the shearinduced velocity. This suggests that unlike Taylor’s model where the convection velocity is dominating and Kraichnan and Tennekes’ model where the random sweeping velocity is dominating, the decorrelation time scales of the space-time correlations in turbulent shear flows are determined by the convection velocity, the random sweeping velocity, and the shear-induced velocity. This model predicts a universal form of the spacetime correlations with the two characteristic velocities. The DNS of turbulent channel flows supports the prediction: the correlation functions exhibit a fair good collapse, when plotted against the normalized space and time separations defined by the elliptic model.

Movement of a Spherical Brownian Particle Between Infinite Parallel Plates: Hindered Dispersion and Sedimentation

The dispersion of an isolated, spherical, Brownian particle immersed in a Newtonian fluid between infinite parallel plates is investigated. Expressions are developed for both a 'molecular' contribution to dispersion, which arises from random thermal fluctuations, and a 'convective' contribution, arising when a shear flow is applied between the plates. These expressions are evaluated numerically for all sizes of the particle relative to the bounding plates, and the method of matched asymptotic expansions is used to develop analytical expressions for the dispersion coefficients as a function of particle size to plate spacing ratio for small values of this parameter.

It is shown that both the molecular and convective dispersion coefficients decrease as the size of the particle relative to the bounding plates increase. When the particle is small compared to the plate spacing, the coefficients decrease roughly proportional to the particle size to plate spacing ratio. When the particle closely fills the space between the plates, the molecular dispersion coefficient approaches zero slowly as an inverse logarithmic function of the particle size to plate spacing ratio, and the convective dispersion coefficent approaches zero approximately proportional to the width of the gap between the edges of the sphere and the bounding plates.

Atom localization in a four-level alkaline earth atomic system

We propose an atom localization scheme for a four-level alkaline earth atom via a classical standing-wave field, and give the analytical expressions of the localization peak positions as well as the widths versus the parameters of the optical fields. We show that the probability of finding the atom at a particular position can be increased from 1/4 to 1/3 or 1/2 by adjusting the detuning of the probe field and the Rabi frequencies of the optical fields. Furthermore, the localization precision can be dramatically enhanced by increasing the intensity of the standing-wave field or decreasing the detuning of the probe field. The analytical results are quite accordant to the numerical solutions.

Wave interactions in periodic structures and periodic dielectric waveguides

This work is concerned with a general analysis of wave interactions in periodic structures and particularly periodic thin film dielectric waveguides.

The electromagnetic wave propagation in an asymmetric dielectric waveguide with a periodically perturbed surface is analyzed in terms of a Floquet mode solution. First order approximate analytical expressions for the space harmonics are obtained. The solution is used to analyze various applications: (1) phase matched second harmonic generation in periodically perturbed optical waveguides; (2) grating couplers and thin film filters; (3) Bragg reflection devices; (4) the calculation of the traveling wave interaction impedance for solid state and vacuum tube optical traveling wave amplifiers which utilize periodic dielectric waveguides. Some of these applications are of interest in the field of integrated optics.

A special emphasis is put on the analysis of traveling wave interaction between electrons and electromagnetic waves in various operation regimes. Interactions with a finite temperature electron beam at the collision-dominated, collisionless, and quantum regimes are analyzed in detail assuming a one-dimensional model and longitudinal coupling.

The analysis is used to examine the possibility of solid state traveling wave devices (amplifiers, modulators), and some monolithic structures of these devices are suggested, designed to operate at the submillimeter-far infrared frequency regime. The estimates of attainable traveling wave interaction gain are quite low (on the order of a few inverse centimeters). However, the possibility of attaining net gain with different materials, structures and operation condition is not ruled out.

The developed model is used to discuss the possibility and the theoretical limitations of high frequency (optical) operation of vacuum electron beam tube; and the relation to other electron-electromagnetic wave interaction effects (Smith-Purcell and Cerenkov radiation and the free electron laser) are pointed out. Finally, the case where the periodic structure is the natural crystal lattice is briefly discussed. The longitudinal component of optical space harmonics in the crystal is calculated and found to be of the order of magnitude of the macroscopic wave, and some comments are made on the possibility of coherent bremsstrahlung and distributed feedback lasers in single crystals.