Effect of rotation in magneto-thermoelastic transversely isotropic hollow cylinder with three-phase-lag model

This article deals with the various heat source responses in a transversely isotropic hollow cylinder under the purview of three-phase-lag (TPL) generalized thermoelasticity theory. In presence of magnetic field and due to the rotating behavior of the cylinder, the governing equations are redefined for generalized thermoelasticity with thermal time delay. In order to obtain the stress, displacement and temperature field, the field functions are expressed in terms of modified Bessel functions in Laplace transformed domain. When the outer radius of hollow cylinder tends to infinity, the corresponding results are discussed. Finally an appropriate Laplace transform inversion technique is adopted.     

Characterization of canonical classes for systems of linear ODEs

The equivalence group is determined for systems of linear ordinary differential equations in both the standard form and the normal form. It is then shown that the normal form of linear systems reducible by an invertible point transformation to the canonical form y ⁽ⁿ⁾=0 consists of copies of the same iterative scalar equation. It is also shown that contrary to the scalar case, an iterative vector equation need not be reducible to the canonical form by an invertible point transformation. Other properties of iterative linear systems are also derived, as well as a simple algebraic formula for their general solution. Copyright © 2017 John Wiley & Sons, Ltd.     

Bonding,Aromaticity and Isomerization of Furfuraldehyde through Off-Nucleus Isotropic Magnetic Shielding

Off-nucleus isotropic magnetic shielding (σ_iso(r)) and multi-points nucleus independent chemical shift (NICS(0-2 Å)) index were utilized to find the impacts of the isomerization of gas-phase furfuraldehyde (FD) on bonding and aromaticity of FD. Multidimensional (1D to 3D) grids of ghost atoms (bqs) were used as local magnetic probes to evaluate σ_iso(r) through gauge-including atomic orbitals (GIAO) at density functional theory (DFT) and B3LYP functional/6-311+G(d,p) basis set level of theory. 1D σ_iso(r) responses along each bond of FD were examined. Also, a σ_iso(r) 2D-scan was performed to obtain σ_iso(r) behavior at vertical heights of 0–1 Å above the FD plane in its cis, transition state (TS) and trans forms. New techniques for evaluating 2D σ_iso(r) cross-sections are also included. Our findings showed that bonds in cyclic and acyclic parts of FD are dissimilar. Unlike the C−O bond of furanyl, the C=O bond of the formyl group is magnetically different. C−C and C−H bonds in furanyl are found similar to those in aromatic rings. A unique σ_iso(r) trend was observed for the C₂−C₆ bond during FD isomerization. Based on NICS(0-2 Å) values, the degree of aromaticity follows the order of cis FD<trans FD<furan<TS FD.     

功能梯度压电材料圆环位移和电势边值问题的精确解

圆环形的压电材料器件在智能结构中得到了广泛的应用。本文推导了横观各向同性功能梯度压电材料圆环在内、外边界上给定位移和电势情况下的一般解。极化方向在圆环的半径方向，材料常数的梯度方向也设定在半径方向，并可表示为半径r的幂，本构关系为线性。然后推导了压电圆环外壁固定、接地，内壁沿垂向有一微小位移、电势分别为余弦分布和均匀分布的问题的精确解，并计算了该问题在这两种电势情况下产生的无量纲形式的径向和环向位移、电势、应力及电位移沿径向分布的数值结果。计算中考虑了不同的材料梯度，以及内壁的位移与电势的不同比例。     

DYNAMIC INTERACTION BETWEEN ELASTIC THICK CIRCULAR PLATE AND TRANSVERSELY ISOTROPIC SATURATED SOIL GROUND

IntroductionThe vibration of the plate on the porous saturated building foundation is a complicateddynamic contact problem.Its consideration is very important in both earthquake and geo-technical engineering.Lots of research works have been done in recent…     

横观各向同性层状场地对入射SH波的响应分析

本文采用横观各向同性层状弹性模型模拟半空间之上的层状了，推导了在ＳＨ波入射时这种场地土的动力刚度矩阵及基岩输入运动时场地呼应的计算公式，算例表明，横观各向同性层状场地与各向同性层状了频谱特性有明显的区别，应当引起重视。     

Effective elastic moduli of periodic granular composite with transversely isotropic phases

We find a rigorous solution describing the macroscopically uniform stress state of a periodic granular composite with transversely isotropic phases. The structure of the composite is modeled by a cube containing a finite number of arbitrarily arranged and oriented, transversely isotropic spherical inclusions. This provides the model with a flexible means of describing the microstructure. Applying periodic vector solutions and local expansion formulas reduces the initial boundary-value problem to a system of linear algebraic equations. By averaging the solution over the unit cell, we derived exact finite expressions for the components of the effective stiffness tensor. The numerical data presented help to evaluate the efficiency of the method and the limits of applicability of available approximate theories.Translated from Prikladnaya Mekhanika, Vol. 40, No. 9, pp. 123–130, September 2004.     

Exact solutions for radial deformations of a functionally graded isotropic and incompressible second-order elastic cylinder

We find closed-form solutions for axisymmetric plane strain deformations of a functionally graded circular cylinder comprised of an isotropic and incompressible second-order elastic material with moduli varying only in the radial direction. Cylinder's inner and outer surfaces are loaded by hydrostatic pressures. These solutions are specialized to cases where only one of the two surfaces is loaded. It is found that for a linear through-the-thickness variation of the elastic moduli, the hoop stress for the first-order solution (or in a cylinder comprised of a linear elastic material) is a constant but that for the second-order solution varies through the thickness. The radial displacement, the radial stress and the hoop stress do not depend upon the second-order elastic constant but the hydrostatic pressure and hence the axial stress depends upon it. When the two elastic moduli vary as the radius raised to the power two or four, the radial and the hoop stresses in an infinite space with a pressurized cylindrical cavity equal the pressure in the cavity. For an affine variation of the elastic moduli, the hoop stress in an internally loaded cylinder made of a linear elastic isotropic and incompressible material at the point is the same as that in a homogeneous cylinder. Here R_in and R_ou equal, respectively, the inner and the outer radius of the undeformed cylinder and R the radial coordinate of a point in the unstressed reference configuration.     

The Stress Response of Functionally Graded Isotropic Linearly Elastic Rotating Disks

The purpose of this research is to investigate the effects of material inhomogeneity on the response of linearly elastic isotropic solid circular disks or cylinders, rotating at constant angular velocity about a central axis. The work is motivated by the recent research activity on functionally graded materials (FGMs), i.e., materials with spatially varying properties tailored to satisfy particular engineering applications. The analog of the classic problem for a homogeneous isotropic rotating solid disk or cylinder is considered. The special case of a body with Young"s modulus depending on the radial coordinate only, and with constant Poisson"s ratio, is examined. For the case when the Young"s modulus has a power-law dependence on the radial coordinate, explicit exact solutions are obtained. It is shown that the stress response of the inhomogeneous disk (or cylinder) is significantly different from that of the homogeneous body. For example, the maximum radial and hoop stresses do not, in general, occur at the center as in the case for the homogeneous material. Furthermore, for the case where the Young"s modulus increases with radial distance from the center, it is shown that radially symmetric solutions exist provided the rate of growth of the Young"s modulus is, at most, cubic in the radial variable. It is also shown for the general inhomogeneous isotropic case how the material inhomogeneity may be tailored so that the radial and hoop stress are identical throughout the disk. This revised version was published online in August 2006 with corrections to the Cover Date.     

Investigation of Alternative Length Scale Substitutions in Detached-Eddy Simulation

The objective of this work is the comparison of three different DES-style hybrid RANS/LES implementations based on the Wilcox k– model. The three variants are designed to investigate alternative methods of substitution of the DES length scale within the background Reynolds Averaged Navier-Stokes (RANS) model. Basis for comparison is provided by both the idealised case of the decay of isotropic turbulence (DIT) as well as the practical case of the massively separated, turbulent flow around an airfoil at high angle of attack. The results of the investigations are discussed in detail, the outcome of which is an emphasis of the importance of DIT as a method for calibration, as well as of the relative freedom with which alternative DES-inspired approaches can be implemented for flows of practical relevance.