Percolation in layered media — A conductivity approach

Long square-lattice and cubic-lattice samples consisting of many layers are simulated. Within each layer, the concentration of permeable bonds is constant whereas each layer has a different concentration chosen randomly from the interval between the percolation threshold and unit concentration. The conductivity of the random resistor network corresponding to this percolation model is calculated, both parallel and perpendicular to the layers, in both two and three dimensions. For the conductivity parallel to the layers, an effective medium calculation comes within 10% of the true conductivity. For the conductivity perpendicular to the layers, percolation theory is necessary.List of Symbols G Total Conductivity in units of the conductivity of one bond - L Length of sample in units of the length of one bond - n Width of sample in units of the length of one bond - N Number of layers - p Probability that a bond conduct - p _c Percolation threshold - R Resistivity in units of the resistivity of one bond - t Percolation conductivity exponent - v Percolation correlation length exponent - Correlation length in units of the length of one bond     

平面波输入下海水−海床−结构动力相互作用分析

海洋工程结构的地震反应分析是保证海洋工程结构地震安全的重要环节.由于其所处的复杂环境,该问题涉及到流固耦合和土-结相互作用.本文基于海水、饱和海床、基岩流固耦合统一计算框架,采用Davidenkov模型和修正的Masing准则考虑饱和海床的非线性,在脉冲SV波垂直入射下,进行了海域场地和海洋工程结构的动力响应分析.首先,对比分析了线性自由场和非线性自由场输入情形的海域场地非线性反应,结果表明线性自由场输入时反应不合理,自由场分析和场地分析应该采用相一致的本构模型.然后,对比分析了海床分别为线性和非线性情形时,海域场地以及海水-海床-结构体系的反应特征.与线性海床情形相比,非线性对海床反应的影响主要由如下两方面因素控制:一方面,非线性导致饱和海床模量减小,饱和海床与基岩间的波阻抗比减小,由基岩到饱和海床间的反射系数和透射系数增加,导致反应增大;另一方面,非线性导致阻尼加大,使海床反应减小.对于本文算例而言,阻尼对非线性海床结果的影响占主导作用.     

Non-axisymmetrical vibration of elastic circular plate on layered transversely isotropic saturated ground

The non-axisymmetrical vibration of elastic circular plate resting on a layered transversely isotropic saturated ground was studied.First,the 3-d dynamic equations in cylindrical coordinate for transversely isotropic saturated soils were transformed into a group of governing differential equations with 1-order by the technique of Fourier ex- panding with respect to azimuth,and the state equation is established by Hankel integral transform method,furthermore the transfer matrixes within layered media are derived based on the solutions of the state equation.Secondly,by the transfer matrixes,the general solutions of dynamic response for layered transversely isotropic saturated ground excited by an arbitrary harmonic force were established under the boundary conditions, drainage conditions on the surface of.ground as well as the contact conditions.Thirdly, the problem was led to a pair of dual integral equations describing the mixed boundary- value problem which can be reduced to the Fredholm integral equations of the second kind solved by numerical procedure easily.At the end of this paper,a numerical result concerning vertical and radical displacements both the surface of saturated ground and plate is evaluated.     

Magnetoelectroelastic shear body waves in periodically layered metalized ferrite–piezoelectric media

A method of deriving the dispersion equations for magnetoelectroelastic shear waves in periodically layered media is proposed. The media are formed by uniting identical metalized laminates, each consisting of two dissimilar piezoelectric layers separated by a layer with the properties of ferrite. A numerical analysis is carried out and the propagation of body waves in different structures consisting of ZnO and GaYtC layers is described within wide ranges of frequencies and wave numbers. The influence of the physical, mechanical, and geometrical parameters of the layers on the structure of the transmission and suppression zones and the effect of the piezoelectric effect of the position of transmission edges are examined     

Bi-directional fluid–structure interaction for large deformation of layered composite propeller blades

Bi-directional fluid–structure interaction becomes important when viscous flow changes the geometry of the domain significantly because of the pressure load. Large deformation in domain causes numerical convergence problems, which are solved by mesh smoothing, re-meshing and a time discrete iterative solver algorithm using industrial computational fluid dynamics and finite element analysis code. In this paper, this approach is used for laminated composite propellers considered as mixers. It experiences heavy thrust, which causes large deformations. Each layer of laminate is modeled as a solid element with anisotropic material data. Comparative study is presented between uni-directional and bi-directional fluid–structure interaction for mixer blades. Change in pressure distribution, stress distribution, thrust, torque and pitch angle of the blade are presented in later parts of the paper.     

A newly developed interatomic potential of Nb−Al−Ti ternary systems for high-temperature applications

The application of hard/soft composite structure in personnel armor for blast mitigation is relatively practical and effective in realistic protection engineering, such as the shell/liner system of the helmet. However, there is still lacking a reliable experimental methodology to effectively evaluate the blast mitigation performance when the structure directly contacts the protected target, which limits the development of protection structures. In this paper, we proposed a new method to evaluate experimentally and numerically the blast mitigation performance of hard/soft composite structures. The blast mitigation mechanism is analyzed. The hard/soft structures were composed of ultra-high molecular weight polyethylene (UHMWPE) composite and expanded polyethylene (EPE) foam. In field explosion experiment, a 7.0 kg trinitrotoluene (TNT) spherical charge is used to generate blast waves at a 3.8 m stand-off distance. A pressure test device is designed to support the tested structure and measure the transmitted blast pressure pulses after passing through the structure. Experimental results indicate that the hard/soft structures can mitigate the blast pressure pulse into the triangular pressure pulse, through making the pulse profile flatter, reducing the pressure amplitude, and delaying the pulse arrival time. Specifically, the combination of 7 mm UHMWPE composite and 20 mm EPE foam can reduce the blast pressure amplitude by 40%. Correspondingly, the finite element simulation is also carried out to understand the blast mitigation mechanism. The numerical results indicate that the regulation for blast pressure pulses mainly complete at the hard/soft interface, which is attributed to the reflection of pressure waves at the interface and the deformation of the soft layer compressed by the hard layer possessing kinetic energy. Furthermore, based on these analyses, the corresponding theoretical model is proposed, and it can well explain the experimental and numerical results. This study is meaningful for evaluating and designing high-performance blast mitigation structures.

     

Filtration characteristics of granular bed with layered drawers for removing dust from gas streams

Filtration tests were conducted on a granular bed filter with layered drawers filled with corundum particles with sizes between either 1 mm and 1.5 mm or 2 mm and 3 mm or with quartz sand particles with sizes between 0.125 mm and 1.5 mm.Filtration velocity,filter particle thickness,and filter particle size were all found to influence the filtration efficiency and the pressure drop of both the fixed granular bed and the layered-drawer granular bed.Granular strata with different thickness ratios also strongly influenced the filtration efficiency and pressure drop.For a granular bed with two sizes of filter particles,the coarse granules in the upper layer capture dust with large particle sizes,while the fine granules in the lower layer capture dust with smaller particle sizes that passes through the filter cake and upper layer.Optimal operating conditions were determined at which the filtration efficiency was found to be 99.42%with a bed pressure drop of 320 Pa.     

A robust formulation of the v2−f model

The elliptic relaxation approach of Durbin (Durbin, P.A., J. Theor. Comput. Fluid. Dyn. 3 (1991) 1–13), which accounts for wall blocking effects on the Reynolds stresses, is analysed herein from the numerical stability point of view, in the form of the $\bar v^2 - f$ . This model has been shown to perform very well on many challenging test cases such as separated, impinging and bluff-body flows, and including heat transfer. However, numerical convergence of the original model suggested by Durbin is quite difficult due to the boundary conditions requiring a coupling of variables at walls. A ‘code-friendly’ version of the model was suggested by Lien and Durbin (Lien, F.S. and Durbin, P.A., Non linear κ ? ε ? υ ² modelling with application to high-lift. In: Proceedings of the Summer Program 1996, Stanford University (1996), pp. 5–22) which removes the need of this coupling to allow a segregated numerical procedure, but with somewhat less accurate predictions. A robust modification of the model is developed to obtain homogeneous boundary conditions at a wall for both $\bar v^2 $ and f. The modification is based on both a change of variables and alteration of the governing equations. The new version is tested on a channel, a diffuser flow and flow over periodic hills and shown to reproduce the better results of the original model, while retaining the easier convergence properties of the ‘code-friendly’ version.     

Über die Bestimmung des dynamischen Elastizitätsmoduls und des dynamischen Schubmoduls im Frequenzbereich von 10−5 bis 10−1 Hz

Zusammenfassung Eine einfache Meßanordnung wird beschrieben, mit der sowohl die dynamische wie auch die statische Bestimmung des Elastizitätsmoduls und des Schubmoduls hochpolymerer Stoffe durchgeführt werden kann. Meßergebnisse werden mitgeteilt und diskutiert. SchrifttumHerrn Prof. Dr.Grützmacher bin ich für die Förderung dieser Arbeit zu besonderem Dank verpflichtet. Ebenso danke ich HerrnEggelsmann für die sorgfältige Durchführung der Messungen. Die Polyvinylchloridproben wurden freundlicherweise von Herrn Prof. Dr.K. Wolf, BASF Ludwigshafen, zur Verfügung gestellt.     

Torsional split Hopkinson bar tests at strain rates above 104s−1

The torsional split Hopkinson bar is used for testing materials at strain rates above 10⁴s⁻¹. This strain rate, which is an order of magnitude higher than is typical with this technique, is obtained by using very short specimens. Strain rates of 6.4×10⁴s⁻¹ have been achieved with specimens having a gage length of 0.1524 mm. Results from tests on 1100 aluminum show an increase in rate sensitivity as the strain rate increases.     

Analysis of scattering waves in an elastic layered medium by means of the complete eigenfunction expansion form of the Green’s function

A scattering problem due to an object and a plane incident wave in an elastic layered half space is presented in this paper. The complete eigenfunction expansion form of the Green’s function developed by the author and the boundary integral equation method are introduced into the analysis. First, the complete eigenfunction expansion form of the Green’s function is investigated for its application to the scattering problem. A comprehensive explanation is also given for the fact that the complex Rayleigh wave modes exhibit standing waves. Next, a method for the analysis of scattering waves by means of the Green’s function is presented. The advantage of the present method is that the formulation itself is independent of the number of layers and the scattering waves can be decomposed into the modes for the spectra defined for the layered medium. Several numerical calculations are performed to examine the efficiency of the present method as well as the properties of the scattering waves. According to the numerical results, the complete eigenfunction expansion form of the Green’s function provides accurate values for application to a boundary element analysis. The spectral structure and radiation patterns of the scattering wave are presented and investigated. The differences in directionality can be found from the radiation patterns of the scattering waves decomposed into the modes for the spectra.     

Uniqueness of positive solutions of Δu−u+up=0 in Rn

We establish the uniqueness of the positive, radially symmetric solution to the differential equation u–u+u^p=0 (with p>1) in a bounded or unbounded annular region in R ⁿ for all n1, with the Neumann boundary condition on the inner ball and the Dirichlet boundary condition on the outer ball (to be interpreted as decaying to zero in the case of an unbounded region). The regions we are interested in include, in particular, the cases of a ball, the exterior of a ball, and the whole space. For p=3 and n=3, this a well-known result of Coffman, which was later extended by McLeod & Serrin to general n and all values of p below a certain bound depending on n. Our result shows that such a bound on p is not needed. The basic approach used in this work is that of Coffman, but several of the principal steps in the proof are carried out with the help of Sturm's oscillation theory for linear second-order differential equations. Elementary topological arguments are widely used in the study.     

A Class of Large BMO −1 Non-Oscillatory Data for the Navier–Stokes Equations

We address the global regularity of solutions of the Navier–Stokes equations in a domain ${Q = \mathbb{R}^2 \times [-1/2, 1/2]}$ with periodic boundary conditions. We prove that the solutions are smooth under some structural conditions and some natural conditions on the horizontal derivatives of the horizontal components of the velocity and the derivative in the vertical direction. The obtained conditions admit data whose vertical average is large in BMO ^?1. We emphasize that unlike previously known results, our data do not need to oscillate in any direction. Also, the results allow non-zero force and lead to solutions which do not decay in time.     

Effects of cerium incorporation on the catalytic oxidation of benzene over flame-made perovskite La1−xCexMnO3 catalysts

Perovskite-type La_1−xCe_xMnO₃ (x = 0–10%) catalysts were prepared by flame spray pyrolysis and their activities during the catalytic oxidation of benzene were examined over the temperature range of 100–450 °C. The structural properties and reducibility of these materials were also characterized by X-ray diffraction (XRD), N₂ adsorption/desorption, H₂ temperature-programmed reduction (H₂-TPR) and X-ray photoelectron spectroscopy (XPS). The incorporation of Ce was found to improve the benzene oxidation activity, and the perovskite in which x was 0.1 exhibited the highest activity. Phase composition and surface elemental analyses indicated that non-stoichiometric compounds were present. The incorporation of Ce had a negligible effect on the specific surface area of the perovskites and hence this factor has little impact on the catalytic activity. Introduction of Ce⁴⁺ resulted in modification of the chemical states of both B-site ions and oxygen species and facilitated the reducibility of the perovskite. The surface Mn⁴⁺/Mn³⁺ ratio was increased as a result of Ce⁴⁺ substitution, while a decrease in the surface-adsorbed O/lattice O (O_ads/O_latt) ratio was observed. The relationship between the surface elemental ratios and catalytic activity was established to allow a better understanding of the process by which benzene is oxidized over perovskites.     

Axial damping in metal-matrix composites. I: A new technique for measuring phase difference to 10−4 radians

A majority of the current experimental techniques for measuring damping employ either flexural or torsional vibrations.In either case the strain field is nonhomogeneous. If the material damping is linear, i.e., strain independent, then the measured quantity equals the intrinsic material damping. if, on the other hand, the material damping is nonlinear, i.e., strain dependent, then the measured quantity also reflects the nonhomogeneity of the strain field and, therefore, is not equal to the intrinsic material damping. In this work we describe a new experimental technique in which the foregoing problem is circumvented by employing a homogeneous strain field, namely, uniform uniaxial tension. Damping is viewed as the phase angle by which the stress leads the strain. The finiteduration, time-harmonic stress and strain signals are transformed to the frequency domain via the use of Fourier transforms. It is shown that if one confines attention to the immediate neighborhood of the excitation frequency then, for all practical purposes, the phase difference between the two sinusoids is equal to the phase difference between their Fourier transforms. We will demonstrate that this phase difference can be measured to an accuracy of 2/2¹⁶ or 9.587×10^–5 radians.Paper was presented at the 1990 SEM Spring Conference on Experimental Mechanics held in Albuquerque, NM on June 3–6.