功能梯度压电空心圆柱中分数阶热弹导波的频散和衰减特性

基于分数阶热电弹性理论和Legendre多项式方法,构建了功能梯度空心圆柱中导波传播的数学模型. 讨论了分数阶次、压电效应、径厚比等对导波传播,特别是对其衰减的影响规律. 数值结果表明,压电效应对衰减的影响主要集中在截止频率和突变频率附近,并使得突变频率发生前移;分数阶对热波模态相速度和衰减的影响较大,且热波相速度存在模态交叉,在交叉频率点附近分数阶对相速度的影响相反;热波衰减随着分数阶增大而逐渐减小;第一阶纵向模态衰减受到了压电效应的抑制,其余模态衰减都显著增大,并且电开路受到的影响要比电短路状态大.     

Guided waves in a stratified elastic and locally perturbed domain: theoretical and numerical aspects

This article presents new results concerning guided waves in a three‐dimensional unbounded stratified and locally perturbed elastic medium. On the one hand, we numerically show non‐monotonic dispersion curves, a phenomenon not yet encountered in fields other than elasticity. On the other hand, we prove that the infimum of the essential spectrum of the studied operator depends on the possible non‐monotonicity of such curves. This link is a new result with respect to equivalent situations coming from acoustics or electromagnetism. The numerical study underlines, besides the non‐monotonic dispersion curves, the appearance of generalized Stoneley waves. Copyright © 2000 John Wiley & Sons, Ltd.     

Propagation of torsional waves in a prestretched compound hollow circular cylinder

The propagation of torsional waves in a prestressed compound (bi-layered) hollow circular cylinder is in vestigated within the frame work of a piecewise homogeneous body model, with the use of a three-dimensional linerized theory of elastic waves in initially stressed bodies. The elasticity relations for components of the compound cylinder are obtained from the Murnaghan potential. Numerical investigations are performed for bronze and steel. According to the results obtained, the effect of variations in the geometric (the ratio between the thickness of the cylinder and its inner radius) and mechanical parameters on the dispersion curves are analyzed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 1, pp. 103–116, January–February, 2008.     

Asymptotic behavior of nonlinear waves in elastic media with dispersion and dissipation

In the case of nonlinear elastic quasitransverse waves in composite media described by nonlinear hyperbolic equations, we study the nonuniqueness problem for solutions of a standard self-similar problem such as the problem of the decay of an arbitrary discontinuity. The system of equations is supplemented with terms describing dissipation and dispersion whose influence is manifested in small-scale processes. We construct solutions numerically and consider self-similar asymptotic approximations of the obtained solution of the equations with the initial data in the form of a “spreading” discontinuity for large times. We find the regularities for realizing various self-similar asymptotic approximations depending on the choice of the initial conditions including the dependence on the form of the functions determining the small-scale smoothing of the original discontinuity. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 2, pp. 240–256, May, 2006.     

Fracture of a piezoelectric fiber/elastic matrix composite

A piezoelectric fiber/elastic matrix system subjected to axially symmetric mechanical and electric loads is considered. The fiber contains a penny-shaped crack located at its center perpendicularly to the fiber. By using the Fourier and Hankel transforms, the problem is reduced to the solution of an integral equation. Numerical solutions for the crack tip fields are obtained for various crack sizes and different fiber volume fractions. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 3, pp. 301–318, May–June, 2006.     

复合材料层合板三维线性理论的完整性

本文针对文献[1]所述复合材料层合板三维模型,在三维线性弹性理论基本方程和经典变分原理的基础上,通过分块矩阵运算和线性Lagrange乘子法,推导出比文献[1]更全面更系统的基本方程和变分原理,使复合材料层合板三维线性理论臻于完整。     

钢-环氧-钢三明治结构胶层缺陷的导波检测方法研究

钢质环氧套筒广泛应用于油气管道的修复. 套筒与管道之间环氧胶层的完整性直接决定了修复质量. 由于套筒、环氧胶层和管道一起构成了特殊的三明治结构,传统的无损检测方法难以实现胶层缺陷的有效识别,迫切需要发展新的无损检测方法. 该文对钢-环氧-钢三明治结构胶层缺陷的导波检测方法展开了研究. 首先通过半解析有限元方法,计算了三明治结构中导波的频散曲线,通过频散特征、波形结构和衰减特性筛选出了可用于胶层缺陷检测的LS₁波. 接着设计了可用于激励LS₁波的压电换能器,并通过数值模拟和实验验证了换能器的有效性. 然后,通过数值模拟和实验研究了LS₁波与胶层空腔缺陷的作用规律,发现缺陷长度尺寸在4倍波长以内时,LS₁波反射波的幅值随缺陷长度变化近似线性变化. 在此基础上提出了一种信号处理的方法,当缺陷尺寸不小于2倍波长时,该方法可以有效辨识出缺陷反射信号.     

Torsional wave dispersion relations in a pre-stressed bi-material compounded cylinder with an imperfect interface

This paper studies the influence of the imperfectness of the contact condition on the torsional wave propagation in the initially stressed (stretched) bi-material compounded circular cylinder. The investigation is carried out within the scope of the piecewise homogeneous body model with the use of the Three-dimensional Linearized Theory of Elastic Waves in Initially Stresses Bodies. The mathematical formulation of the corresponding eigen-value problem is formulated and the solution method for that is developed. The two cases considered are the bi-material compounded cylinder consists of the solid inner and surrounding hollow outer cylinders (Case 1); the bi-material compounded cylinder consists of the hollow inner and surrounding hollow outer cylinders (Case 2). The mechanical relations of the cylinders’ materials are written through the Murnaghan potential. It is proven that the imperfectness of the contact condition does not influence the asymptotic-limit values of the wave propagation velocity. Moreover, the numerical results on the effects of the imperfectness of the boundary condition on the influence of the initial stresses on the wave propagation velocity are presented and discussed.     

变厚度非均匀粘弹性复合圆柱体的旋转应力

在平面应变的假设下,给出了两个复合弹性圆柱体旋转时的解析解．外柱是由厚度按公式变化的正交各向异性材料所组成,它包裹着一个等厚度纤维增强粘弹性均匀各向同性的实心圆柱体．外圆柱体的厚度和弹性性质按半径方向的幂函数变化．应用边界和连续条件,确定复合圆柱体旋转时的径向位移和应力,应用等效模量和Illyushin逼近法,得到问题的粘弹性解．讨论了各向异性、厚度变化、本构参数以及时间参数,对径向位移和应力的影响．     

Scattering by a perfect conductor in a waveguide: energy-preserving schemes for integral equations

^** Email: darkovolkov{at}yahoo.ca, darko{at}wpi.edu The scattering matrix for a perfectly conducting electricalcylinder (or a sound hard obstacle) in a waveguide is unitary.This is a well-known result which is a consequence of the conservationof power. When a numerical method is employed to approximatethe reflection and transmission coefficients of the cylinder,an approximate scattering matrix can be constructed. An integralequation of the second kind for an unknown density can be solved,and the density can then be used for computing the entries ofthe approximate scattering matrix. We show that this approximatematrix is unitary for cylinders of symmetric cross-section,regardless of the order of the approximation. In the nonsymmetriccase, the approximate scattering matrix still satisfies a conservationof energy condition, albeit in an unfamiliar form. As the orderof the approximation is increased, conservation of energy isalso satisfied in the more familiar form to machine accuracy.     

Elastic wave propagation in a cylindrical bore situated in a micropolar elastic medium with stretch

Propagation of surface elastic waves in a cylindrical bore through a micropolar elastic medium with stretch is analysed in two cases. In the first case, the cylindrical bore is considered empty while in the second case, the bore is filled with homogeneous inviscid liquid. In both the problems, period equations are obtained in closed form. The problem of Banerji and Sengupta [2,3] has been reduced as a special case. Numerical calculations have been performed for a particular model and results obtained are presented graphically. It is noticed that the effect of micropolarity on dispersion curve is significant while the effect of micro-stretch on dispersion curve is not appreciable.     

On the propagation of Lamb waves in a sandwich plate made of compressible materials with finite initial strains

The propagation of flexural Lamb waves in a prestrained sandwich plate made from compressible highly elastic materials is investigated within the scope of a piecewise homogeneous body model by utilizing TLTEWISB. The mechanical relations of layer materials are described by a harmonic-type potential, and numerical results are obtained for the first and second vibration modes. According to the results, the influence of problem parameters and of the initial stretching strain along the layers on the wave propagation speed is examined. The asymptotic values of the speed are considered in the cases of short and long wavelengths, and the influence of the initial strains on these asymptotic (limit) values are also analyzed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 2, pp. 231–244, March–April, 2008.     

Thermo-poroacoustic acceleration waves in elastic materials with voids

A model for coupled elasto-acoustic waves, thermal waves, and waves associated with the voids, in a porous medium is investigated. Due to the use of lighter materials in modern buildings and noise concerns in the environment such models for thermo-poroacoustic waves are of much interest to the building industry. Analysis of such waves is also of interest in acoustic microscopy where the identification of material defects is of paramount importance to industry and medicine. We present a model for acoustic wave propagation in a porous material which also allows for propagation of a thermal wave. The thermodynamics is based on an entropy inequality of A.E. Green, F.R.S. and N. Laws and is presented for a modification of the theory of elastic materials with voids due to J.W. Nunziato and S.C. Cowin. A fully nonlinear acceleration wave analysis is initiated.     

Optimization of Periodic Composite Structures for Sub-Wavelength Focusing

Recently, there has been plenty of work in designing and fabricating materials with an effective negative refractive index. Veselago realized that a slab of material with a refractive index of −1 would act as a lens. Pendry suggested that the Veselago lens would act as a superlens, providing a perfect image of an object in contrast to conventional lenses which are only able to focus a point source to an image having a diameter of the order of the wavelength of the incident field. Recent work has shown that similar focusing effects can be obtained with certain slabs of “conventional” periodic composite materials: photonic crystals. The present work seeks to answer the question of what periodic dielectric composite medium (described by dielectric coefficient with positive real part) gives an optimal image of a point source. An optimization problem is formulated and it is shown that a solution exists provided the medium has small absorption. Solutions are characterized by an adjoint-state gradient condition, and several numerical examples illustrate both the plausibility of this design approach, and the possibility of obtaining smaller image spot sizes than with typical photonic crystals. This work was partially supported by NSF grant DMS-0537015.     

Nondestructive Evaluation of Graphite-Epoxy Composites by the Laser Ultrasonic Method

A laser ultrasonic method for nondestructive evaluation of the structure of composite materials is proposed. Specimens of graphite-epoxy composites with compaction-type defects and air cavities are investigated. The method is based on the laser thermooptical generation of wide-band acoustic pulses - optoacoustic (OA) signals - in the material investigated. The acoustic pulses backscattered by structural ingomogeneities and defects are registered by a wide-band piezotransducer, which makes it possible to detect acoustic pulses in the frequency range from 0.1 to 30 MHz. Since the generation and detection of acoustic pulses takes place on the front surface of the specimen, this method allows us to carry out nondestructive evaluation with one-sided access to the object under study. The spectral and correlation analyses of backscattered OA signals are used for mathematical processing of the experimental data. The method developed makes it possible to determine the type of defects and the depth of their location.     

薄壁内胆碳纤维全缠绕复合材料气瓶轴向残余变形及屈曲分析

针对钛合金薄壁内胆碳纤维全缠绕复合材料气瓶水压试验后轴向缩短及内胆局部发生屈曲失稳现象,开展了试验研究及有限元分析. 结果表明：自紧加卸载后,封头靠近极孔区域沿轴向向内凹陷,封头靠近赤道区域沿径向向外扩张,封头整体沿轴向变短,试验和有限元计算的轴向缩短量为6.15 mm和6.363 mm,误差为3.46%,有限元计算结果与试验结果具有很好的一致性. 最后,采用多极孔法优化封头纤维层厚度分布,封头厚度极值降低32.6%,过渡更加均匀,优化后的气瓶沿轴向略有伸长,平均伸长为0.6 mm,采用CT和内窥镜检测,内胆均未出现屈曲失稳,有效地解决了水压试验后轴向缩短及内胆屈曲问题.     

压电螺型位错与含非理想界面层圆形夹杂的干涉效应

研究了位于压电材料基体或夹杂中任意点的压电螺型位错与含非理想界面层圆形夹杂的电弹性干涉问题．运用复变函数方法,获得了复势函数的精确解．由广义Peach-Koehler公式,导出了作用在螺型位错上的像力的精确表达式．讨论了不同参数对压电螺型位错的运动和平衡位置的影响规律．研究结果表明,对某些材料组合,当界面层的内界面是非理想界面且界面的非理想度达到一定值时,在基体中靠近界面处会出现两个位错的平衡位置,此现象未在以往研究(不考虑非理想界面)中观察到．     

用界面单元法分析复合材料界面力学性能

本文利用界面单元的固有特性，将其用来模拟复合材料中纤维与基体之间的界面特征，计算了一个沿Ｘ轴方向纤维周期排列的单尾板，在横向载荷作用下的应力分布问题．给出了三相（纤维、基体和界面）特性各种配比时应力分布等高线图以及通过界面时径向应力σｒ的变化情况，反映了界面特性对应力分布的影响．