Error Bounds for Approximate Solutions for Bending of Unsymmetrically Laminated Plates

Abstract

Certain types of heterogeneous plates exhibit coupling between membrane and flexural effects in their constitutive relations. Such a situation commonly occurs in unsymmetrically laminated plates and in reinforced concrete slabs after cracking. Approximate solutions, principally the “reduced bending stiffness” approximation, have been proposed in the past. The accuracy of this approximation has been examined for several specific cases, but no general investigations have been reported. This paper presents a method for determining bounds on the relative mean square error of approximate solutions to general coupled plate bending problems.     

Flow-excited acoustic resonances of coaxial side-branches in an annular duct

This paper investigates the aeroacoustic response of an annular duct with closed coaxial side-branches, and examines the effect of several passive countermeasures on the resonance intensity. The investigated geometry is inspired by the design of the Roll-Posts in the Rolls-Royce LiftSystem^® engine, which is currently being developed for the Lockheed Martin Joint Strike Fighter (JSF^®) aircraft. The effects of design parameters, such as diameter ratio, branch length ratio and thickness of the annular flow on the frequency and resonance intensity of the first acoustic mode are studied experimentally. Numerical simulations of the acoustic mode shapes and frequencies are also performed. The annular flow has been found to excite several acoustic modes, the strongest in all cases being the first acoustic mode, which consists of a quarter wavelength along the length of each branch. The ratios of the branch length and diameter, with respect to the main duct diameter, have been found to have strong effects on the frequency of the acoustic modes.     

A Study of Strain Rate Effects for Turbulent Premixed Flames with Application to LES of a Gas Turbine Combustor Model

Large-scale strain rate field, a resolved quantity which is easily computable in large-eddy simulations (LES), could have profound effects on the premixed flame properties by altering the turbulent flame speed and inducing local extinction. The role of the resolved strain rate has been investigated in a posterior LES study of GE lean premixed dry low-NOx emissions LM6000 gas turbine combustor model. A novel approach which is based on the coupling of the linear-eddy model with a one-dimensional counterflow solver has been applied to obtain the parameterizations of the resolved premixed flame properties in terms of the reactive progress variable, the local strain rate measure, and local Reynolds and Karlovitz numbers. The strain rate effects have been analyzed by comparing LES statistics for several models of the turbulent flame speed, i.e, with and without accounting for the local strain rate effects, with available experimental data. The sensitivity of the simulation results to the inflow velocity conditions as well as the grid resolution have been also studied. Overall, the results obtained demonstrate that the effects of the resolved strain rate are not dominant for the considered premixed flame configuration and the unstrained turbulent flame speed model is found to perform as well as the one that allows for the strain rate effects.     

Particle Deposition in Porous Media: Analysis of Hydrodynamic and Weak Inertial Effects

We have studied the transport and capture of non-Brownian particles in porous media, when the particles are mainly submitted to hydrodynamic and weak inertial effects. Visualization experiments have been performed using several models of porous media which consist of transparent etched networks of interconnected channels. Typical particle deposits have been observed at the corners of the grains of the porous medium. Their shape and their orientation were dependent on flow rate and on the anisotropy of the flow field. A trajectory analysis model has been applied to a porous medium made of a doubly periodic array of rectangular grains very close to the experimental model. This numerical model has been used to localize particle deposits and to determine particle capture efficiency on the grains over a range of low Stokes numbers, grain aspect ratios and flow-field anisotropy ratios. The results have been interpreted in terms of shape of particle deposits and compared successfully to experimental observations.     

Visco-elastic flow due to a plate which starts oscillating in the presence of a parallel stationary plate

In this paper, the flow of a visco-elastic liquid between two parallel plates has been studied when one plate is stationary and the other plate suddenly starts oscillating. Both finite Fourier sine transform and Laplace transform technique have been employed to solve the basic differential equations. The flow phenomenon has been characterized by the parameters, and and the effects of these on the flow characteristics have been studied through several graphs.Late professor of the department, who died in an accident on 7th July 1978.     

非牛顿流体雾化力学机理研究

本文用稳定性分析和数值计算方法研究了粘弹性液体射流雾化的力学机理。结果表明,雾化液体的 Ohnesorge 数和 Deborah 数的增大均使波频 ω_i 降低,但前者使空间增长率 k_1上升,而后者的作用相反。本文发现,对于雾化液体应使其表面扰动波的波数大于某一确定波数,并尽量降低液体的 Deborah 数。     

The influence of strong crosswinds on safety of different types of road vehicles

Strong crosswinds have a great influence on the safety of road vehicles. Different vehicle types may have different behavior under strong crosswinds, thereby leading to different dominant accident modes and accident risks. In order to compare the crosswind stability of road vehicles, a probabilistic method based on reliability analysis has been applied in this paper. The crosswind is simulated as a stochastic gust model with nonstationary wind turbulence. The vehicles are classified into several categories. For each vehicle type, a worst case vehicle model and the corresponding aerodynamic coefficients have been identified. Dominant accident modes and failure probabilities have been computed and are compared. The influence of road conditions (dry/wet) and wind directions on the crosswind stability has been taken investigated. The proposed model makes it possible to compare the effect of crosswind on different vehicle types based on a risk analysis.

     

Diamagnetism of conductors moving in a magnetic field

Several theoretical [1–3] and experimental [4] studies have been made of the diamagnetic perturbations during expansion of a conducting material in a magnetic field. These studies have related either to superconducting media [1], or to a strong magnetic field which has a considerable effect on the motion of the medium [2], or to a weakly ionized media, in which the effects of field variation in the medium can be neglected [3]. In the following we examine the expansion of a substance with finite conductivity in a weak (having no effect on the motion of the medium) magnetic field with account for the effects of field attenuation within the expanding matter. This occurs in the diagnostics of the state of the matter of a spark at a laser focus on the basis of diamagnetic induction signals [4]. The relations obtained in the following appear to be applicable for estimating the diamagnetic properties of meteor trails.The method of solution of this problem may be of some interest; therefore, in the following the solution is obtained by several techniques for different basic geometries.     

Transition mechanisms in laminar separation bubbles with and without incoming wakes and synthetic jet effects

Laminar separation and transition processes of the boundary layer developing under a strong adverse pressure gradient, typical of Ultra-High-Lift turbine profiles, have been experimentally investigated for a low Reynolds number case. The boundary layer development has been surveyed for different conditions: with steady inflow, with incoming wakes and with the synchronized forcing effects due to both incoming wakes and synthetic jet (zero net mass flow rate jet). In this latter case, the jet Strouhal number has been set equal to half the wake-reduced frequency to synchronize the unsteady forcing effects on the boundary layer. Measurements have been taken by means of a single-sensor hot-wire anemometer. For the steady inflow case, particle image velocimetry has been employed to visualize the large-scale vortical structures shed as a consequence of the Kelvin?CHelmholtz instability mechanism. For the unsteady inflow cases, a phase-locked ensemble averaging technique, synchronized with the wake and the synthetic jet frequencies, has been adopted to reconstruct the boundary layer space-time evolution. Results have been represented as color plots, for several time instants of the forcing effect period, in order to provide an overall view of the time-dependent transition and separation processes in terms of ensemble-averaged velocity and unresolved unsteadiness distributions. The phase-locked distributions of the unresolved unsteadiness allowed the identification of the instability mechanisms driving transition as well as the Kelvin?CHelmholtz structures that grow within the separated shear layer during the incoming wake interval and the synthetic jet operating period. Incoming wakes and synthetic jet effects in reducing and/or suppressing flow separation are investigated in depth.     

A general Struble's technique for solving an nth order weakly non-linear differential system with damping

A general formula (based on the method of variation of parameters) has been presented for determining an approximate solution of an nth order n=2,3,… weakly non-linear differential system with several damping effects. The general solution covers the under-damped, undamped and over-damped cases. The formulation as well as determination of the solution is simple. The method is illustrated by several examples.     

飞机壁板结构的动特性分析与计算

本文以“修正的变分方法”为基础推导了一种新的飞机壁板结构动力分析方法.该法不需要将结构理想化或离散化而直接对复杂的飞机壁板结构进行特征分析或响应分析,方法的实质是将一个复杂结构划分为一个参考结构和一些附加结构,而把这些附加结构视为作用在该参考结构上的广义力,这些广义力由系统能量的变分求得.同时,本文还将有限条法与各向异性壳法相结合,发展了新的有限条分析方法.文中通过固有频率的计算,对这种方法的计算精度和应用场合等问题进行了讨论.     

结构金属材料超高周疲劳破坏行为

受传统试验方法的限制,结构材料的疲劳研究范围常限于107周次以内。然而,过去十年出现了一系列意料之外的破坏事件,尤其是对于认为具有明显疲劳极限的钢铁结构部件。因此,对于不同材料达到1010周次的超高周疲劳行为的研究引起了广泛关注,尤其是近年来成为了热点。本文综述了结构金属材料超高周疲劳的研究现状并介绍了其基本方面。主要内容包括：加速疲劳试验方法的发展与应用、超高周疲劳引起的内部断裂的裂纹萌生机制与扩展特征、S-N曲线的形状特点、疲劳极限存在性及其预测、加载频率和环境及表面状况的影响等。在此基础上提出值得进一步研究的一些方向。     

A CFD comparative study of bubble break-up models in a turbulent multiphase jet

In this paper several bubble break-up models are compared. They have been implemented in the CFX-4.4 fluid dynamic commercial code, which uses the population balance equations for describing liquid/gas multi-phase flows. The models have been assessed against published experimental data, obtained for air bubble break-up within a turbulent water jet. The model of Martínez-Bazán, based on purely kinematics arguments, has shown better agreement with the experimental data. The capabilities of using these models coupled to a CFD code for multiphase flow prediction in industrial applications have been demonstrated.     

Thermal effects of the micropolar fluid parameters on the laminar free convection in spherical annuli with mixed boundary conditions

The effects of micro-rotation and vortex viscosity in micropolar fluids have been investigated numerically to determine heat transfer by natural convection between concentric and vertically eccentric spheres with specified mixed boundary conditions. Calculations were carried out systematically for several different eccentricities and a range of modified Rayleigh numbers to determine the average Nusslet numbers which are affected by the micropolar parameters (F) of the flow and temperature fields. The skin friction stress on the walls has also been studied and discussed. The governing equations, in terms of vorticity, stream function, temperature and angular momentum are expressed in a spherical polar coordinate system. Results were obtained for steady heat-transfer in spherical annuli at a Prandtl number of 0.7, with the modified Rayleigh number ranging from 10³ to 5 × 10⁵, for a radius ratio of 2.0 and eccentricities varying from −0.625 to +0.625. Comparisons are attempted between the Newtonian fluid and micropolar fluid.     

A thermo-hydraulic numerical model to study spot laser welding

The aim of this study is to better understand the basic mechanisms leading to defect occurrence in spot laser welding. For that purpose we have developed a numerical model, which takes into account the key-hole dynamics together with a dedicated energy deposition model featuring the multiple reflection effects. Many experiments have also been achieved enabling us to report several defect classes. The analysis of some of these scenarios have been performed, and favourably compared to experiments. To cite this article: M. Medale et al., C. R. Mecanique 335 (2007).     

Double-Diffusive Convection in a Saturated Anisotropic Porous Layer with Internal Heat Source

In the present study, double-diffusive convection in an anisotropic porous layer with an internal heat source, heated and salted from below, has been investigated. The generalized Darcy model is employed for the momentum equation. The fluid and solid phases are considered to be in equilibrium. Linear and nonlinear stability analyses have been performed. For linear theory normal mode technique has been used, while nonlinear analysis is based on a minimal representation of truncated Fourier series. Heat and mass transfers across the porous layer have been obtained in terms of Nusselt number Nu and Sherwood number Sh, respectively. The effects of internal Rayleigh number, anisotropy parameters, concentration Rayleigh number, and Vadasz number on stationary, oscillatory, and weak nonlinear convection are shown graphically. The transient behaviors of Nusselt number and Sherwood number have been investigated by solving the finite amplitude equations using a numerical method. Streamlines, isotherms, and isohalines are drawn for both steady and unsteady (time-dependent) cases. The results obtained, during the above analyses, have been presented graphically, and the effects of various parameters on heat and mass transfers have been discussed.     

Material selection for high temperature applications

In this paper several materials have been evaluated in order to select the best suitable alloy for the production of a gas turbine transition piece. These components are exposed to complex thermal stresses and different damages, each of them requiring particular characteristics of the material. The procedure described takes into account the variability of requirements with some parameters, in particular temperature and service time. Due to the high value of temperature and the constraint of ductility, the choice of material has been limited to superalloys and stainless steels. A comparison between several alloys has been carried out on the basis of constraints and requirements previously determined. Using a suitable objective function, the method allows ranking materials in order to find the alloy which maximize component’s performance.     

Free Convection of Non-Newtonian Nanofluids in Porous media with Gyrotactic Microorganisms

The free convection of non-Newtonian nanofluids along a vertical plate in porous medium is investigated numerically. It is assumed that the medium contains gyrotactic microorganisms along with nanoparticles and the plate is subjected to prescribed temperature, concentration of nanoparticles and density of motile microorganisms. It is further assumed that the plate is impermeable. The governing partial differential equations are reduced to nonlinear ordinary differential equations using similarity transformations. The nonlinear ordinary differential equations are then solved by a finite difference numerical method. The effects of controlling parameters on several dimensionless quantities and numbers of our interest are investigated. The numerical results are compared with the published data and an excellent agreement has been found. It is found that nanofluid and bioconvection parameters have strong effects on local Nusselt, Sherwood and density numbers.     

Numerical simulation of shock wave intersections

A large number of papers, generalized and classified in [1, 2], have been devoted to unsteady gas flows arising in shock wave interaction. Experimental results [3–5] and theoretical analysis [6–9] indicate that the most interesting and least studied types of interaction arise in cases when there are several shock waves. At the same time, nonlinear effects, which depend largely on the nature of the shock wave intersections, become appreciable. Regions of existence of different types, of plane shock wave intersections have been analyzed in [10–13]. It has been shown that in a number of cases the simultaneous existence of different types of intersections is possible. The aim of the present paper is to study unsteady shock wave intersections in the framework of a numerical solution of the axisymmetric boundary-value problem that arises in the diffraction of a plane shock wave on a cone in a supersonic gas flow. Flow regimes that augment the experimental data of [3–5] and the theoretical analysis of [9] are considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 134–140, September–October, 1986.     

Elastic behavior of composites containing multi-layer coated particles with imperfect interface bonding conditions and application to size effects and mismatch in these composites

This paper proposes a procedure to deal with n-layered inclusion based composites with imperfect interfaces (which conditions consist of displacement or stress vector jumps) respecting spherical symmetry. For that purpose, “discontinuity matrices” have been introduced. These matrices have been derived for several classical interface-models and an asymptotic method has been used to determine some of them. A self-consistent condition based on a strain-energy equivalence in the case of inclusion-matrix type composite materials is restated for n-layered inclusions with imperfect interfaces and applied to get estimates of such composites materials. The remarkable feature of the presently self consistent approach is that it does not need any tedious algebra providing the attached interface models respect the spherical symmetry. The present Generalized Self Consistent Model (GSCM) is then used to study size effects and mismatch in composites reinforced by coated inclusions.