Semi-analytical buckling analysis of heterogeneous variable thickness viscoelastic circular plates on elastic foundations

Buckling analysis of the functionally graded viscoelastic circular plates has not been carried out so far. In the present paper, a series solution is developed for buckling analysis of radially graded FG viscoelastic circular plates with variable thickness resting on two-parameter elastic foundations, based on Mindlin's plate theory. The complex modulus approach in combination with the elastic–viscoelastic correspondence principle is employed to obtain the solution for various edge conditions. A comprehensive sensitivity analysis is carried out to evaluate effects of various parameters on the buckling load. Results reveal that the viscoelastic behavior of the materials may postpone the buckling occurrence and the stiffness reduction due to the section variations may be compensated by the graded material properties.     

Semi-analytical buckling analysis of heterogeneous variable thickness viscoelastic circular plates on elastic foundations

Buckling analysis of the functionally graded viscoelastic circular plates has not been carried out so far. In the present paper, a series solution is developed for buckling analysis of radially graded FG viscoelastic circular plates with variable thickness resting on two-parameter elastic foundations, based on Mindlin's plate theory. The complex modulus approach in combination with the elastic-viscoelastic correspondence principle is employed to obtain the solution for various edge conditions. A comprehensive sensitivity analysis is carried out to evaluate effects of various parameters on the buckling load. Results reveal that the viscoelastic behavior of the materials may postpone the buckling occurrence and the stiffness reduction due to the section variations may be compensated by the graded material properties.     

Stresses in rotating heterogeneous viscoelastic composite cylinders with variable thickness

An analytical solution is presented for the rotation problem of a two-layer composite elastic cylinder under a plane strain assumption. The external cylinder has variable-thickness formulation, and is made of a heterogeneous orthotropic material. It contains a fiber-reinforced viscoelastic homogeneous isotropic solid core of uniform thickness. The thickness and elastic properties of the external cylinder are taken as power functions of the radial direction. By the boundary and continuity conditions, the radial displacement and stresses for the rotating composite cylinder are determined. The effective moduli and Illyushin’s approximation methods are used to obtain the viscoelastic solution to the problem. The effects of heterogeneity, thickness variation, constitutive, time parameters on the radial displacement, and stresses are investigated.     

开孔粘弹性薄板的非线性数学模型

应力函数的多值性和位移单值性要求，是开孔薄板大挠度问题中必须注意的两个方面。本文利用线粘性力学中的Ｂｏｌｔｚｍａｎｎ蠕变律，把开孔弹性薄板大挠度问题的一般数学理论推广到开孔弹性薄板。在考察应力函数的多值性和位移单值性条件的基础上，提出了开孔粘弹性薄板的控制方程和初、边值条件，系统地建立了开也粘弹性薄板非线性分析的三类初一边值问题。     

PREDICTION OF THE VISCOELASTIC PROPERTIES OF THE EQUIVALENT PARTICLE FOR THE INTERCALATED MULTI-LAYER STACK OF NANOPLASTICS

The aim of this paper is to apply the asymptotic homogenization method to deter- mining analytically and numerically the transversely isotropic viscoelastic relaxation moduli of the equivalent particle for the intercalated multi-layer stack of intercalated type nanoplastics.A two-phase multilayered material containing n layers is considered.The matrix is assumed to be an isotropic viscoelastic standard linear body and the reinforcement is assumed to be an isotropic elastic body.Final explicit analytical formulae for the effective elastic moduli of the multilay- ered material are derived first;and then the correspondence principle is employed to obtain the homogenized relaxation moduli of the equivalent intercalated particle.A numerical example is given.Final explicit analytical formulae in the time domain derived here make it convenient to estimate the influence of all the particle parameters of micro-structural details on the effective properties of the equivalent intercalated particle.The results of this paper can also be applied to multi-layer composites.     

Action of periodic surface pressure on an ice cover in the vicinity of a vertical wall

This paper presents the solution of the linear hydroelastic problem for steady forced vibrations of a semi-infinite ice cover under the effect of localized external load. The ice cover is simulated by a viscoelastic thin plate, the thickness of the fluid layer is assumed to be small, and the shallow water theory is used. The fluid is limited by a solid vertical wall, and the rectilinear edge of the elastic plate adjacent to the wall can be both free and clamped. The solution is obtained with the help of the Fourier integral transform. The behavior of the ice cover is studied depending on the frequency of the external load and boundary conditions on the edge of the plate. It is shown that, in the case of a free edge of the plate, there are considerable deflections on the edge, which could be comparable with deflections at the center of the pressure impact region. It is established that, due to the existence of wave movements of the type of edge waves, the external load energy is transferred to larger distances along the free edge, and there are significant bending moments on the edge of the clamped plate, which can lead to fracture of the ice cover with sufficiently great intensity of the external load.     

黏弹性体界面裂纹的冲击响应

研究两半无限大黏弹性体界面Griffith裂纹在反平面剪切突出载荷下,裂纹尖端动应力强度因子的时间响应,首先,运用积分变换方法将黏弹性混合黑社会问题化成变换域上的对偶积分方程,通过引入裂纹位错密度函数进一步化成Cauchy型奇异积分方程,运用分片连续函数法数值求解奇异积分方程,得到变换域内的动应力强度因子,再用Laplace积分变换数值反演方法,将变换域的解反演到时间域内,最终求得动应力强度因子的时间响应,并对黏弹性参数的影响进行分析。     

Exact Lévy-Type Solutions for Plate Bending Exist for Transversely Isotropic but Not for General Monoclinic Materials

An exact three-dimensional Lévy-type solution for the bending of an elastic slab is one in which there are edge loads only and the unknown displacement and stresses have very simple polynomial dependence on the thickness coordinate. Lévy obtained such a solution in 1877 for a linearly elastic, isotropic, plate-like body. The most general material that allows bending and stretching to be uncoupled is monoclinic (13 elastic constants). However, it is shown that only transversely isotropic materials (5 elastic constants) admit exact solutions having polynomial dependence in the thickness direction. Such solutions are listed explicitly.     

A wave propagation problem for non-uniform screw dislocation motion in a viscoelastic half-plane

The wave propagation problem for a largely arbitrary anti-plane displacement discontinuity imposed along a line perpendicular to the surface of a stress-free linearly viscoelastic half-plane is considered. The general Laplace transform solution is obtained and then inverted for the case of a screw dislocation moving at an arbitrary speed in a Maxwell material. It is shown that the material viscoelasticity alters the coefficient of the dislocation edge stress singularity and damps the surface displacements from the elastic values. The surface damping increases with time, distance from the dislocation path and dislocation speed, whether sub- or supersonic.     

粘弹性阻尼修改后结构系统动特性的预测

无阻尼或比例阻尼结构系统经粘弹阻尼修改后,可变为粘弹性阻尼系统。要获得其动特性,需求解复特征值问题。但是,随之带来了计算量大、费用高等问题。尤其是粘弹性材料特性随频率而变化,需求解高阶非线性复特征值问题,这对于一个自由度较大的结构,计算量太大,通常较难实现。本文在特征值修改方法的基础上,提出粘弹性阻尼局部动力修改方法,即仅需已知原结构系统的实模态参数,就可求出粘弹阻尼修改后系统的复模态参数。还发展了特征值和修改量同时迭代方法,有效地解决了粘弹材料复模量随频率变化引起的非线性复特征值问题。     

材料黏滞系数与损耗因子的频率相关性研究

针对黏弹性材料KV阻尼模型的黏滞系数与复阻尼模型的损耗因子间的关系,由单自由度体系的结构动力学分析,并基于结构振动响应的一致性,推导建立了黏滞系数与损耗因子在结构线性稳态简谐振动和自由振动时的一般关系式;并利用该关系式,试验研究了纤维混凝土材料黏滞系数和损耗因子的频率相关性.结果表明,黏滞系数与损耗因子间的关系在稳态简谐振动和自由振动时的表达形式相同,只是频率取值不同;纤维混凝土的损耗因子和黏滞系数都随频率增加而降低,且在0.5～1.0Hz频段降幅显著,而后渐趋平缓;相比于素混凝土,纤维混凝土的黏滞系数和损耗因子与激振频率的相关性更强.试验所得纤维混凝土频率相关的黏滞系数、损耗因子及推导所建立的两参数关系式为构建物理意义明确且又便于结构振动反应分析的阻尼系数或阻尼矩阵奠定了基础.      

Application of the differential quadrature method to free vibration of viscoelastic thin plate with linear thickness variation

The differential quadrature method has been applied to investigate vibrations of viscoelastic thin plate with variable thickness. Firstly, the governing equations are derived in terms of the thin-plate theory and the two-dimensional viscoelastic differential constitutive relation. Then, the convergence of the method is demonstrated based on the differential equation of uniform thickness elastic square plate, which is reduced from the differential equation of viscoelastic plate with varying thickness. Lastly, the effects of aspect ratio, thickness ratio and dimensionless delay time on the vibrations of the linear thickness viscoelastic plate with different boundary conditions have been studied.     

黏弹性材料界面裂纹应力场奇性分析

研究两半无限大黏弹性体间Griffith界面裂纹在简谐载荷作用下裂纹尖端动应力场的奇异特性.通过引入裂纹张开位移和裂纹位错密度函数,相应的混合边值问题归结为一组耦合的奇异积分方程.渐近分析表明裂尖动应力场的奇异特征完全包含在奇异积分方程的基本解中.通过对基本解的深入分析发现黏弹性材料界面裂纹裂尖动应力场具有与材料参数和外载荷频率相关的振荡奇异特性.以标准线性固体黏弹材料为例讨论了材料参数和载荷频率对奇性指数和振荡指数的影响.     

非理想界面弹性层/压电柱结构中SH波的传播特性

研究了各向同性弹性层与压电柱之间非理想连接时沿周向传播的SH波的频散特性.弹性层表面力学自由;弹性层与压电柱之间应力连续、位移间断.通过求解控制方程,将问题的解用Bessel函数表示,利用界面条件和边界条件得到频散方程,然后对其进行数值求解,分析了界面性态、材料常数和几何尺寸对SH波传播特性的影响.     

The motion of long bubbles through viscoelastic fluids in capillary tubes

The penetration of long gas bubble through a viscoelastic fluid in a capillary tube has been studied in order to investigate the influence of viscoelastic material properties on the hydrodynamic coating thickness and local flow kinematics. Experiments are conducted for three tailored ideal elastic (Boger) fluids, designed to exhibit similar steady shear properties but substantially different elastic material functions. This allows for the isolation of elastic and extensional material effects on the bubble penetration process. The shear and extensional rheology of the fluid is characterized using rotational and filament stretching rheometers (FSR). The fluids are designed such that the steady-state extensional viscosity measured by the FSR at a Deborah number (De) greater than 1 differs over three orders of magnitude (Trouton ratio = 10³–10⁶). The experiment set up to measure the hydrodynamic coating thickness is designed to provide accurate data over a wide range of capillary numbers (0.01 < Ca < 100). The results indicate that the coating thickness in this process increases with an increase in the extensionally thickening nature of the fluid. Experiments are also conducted using several different capillary tube diameters (0.1 < D < 1 cm), in order to compare responses at similar Ca but different flow De. Suitable scaling methods and nonlinear viscoelastic constitutive equations are explored to characterize the displacement process for polymeric fluids. Bubble tip shapes at different De are recorded using a CCD camera, and measured using an edge detection algorithm. The influence of the mixed flow field on the bubble tip shape is examined. Particle tracking velocimetry experiments are conducted to compare the influence of viscoelastic properties on the velocity field in the vicinity of the bubble tip. Local shear and extension rates are calculated in the vicinity of the bubble tip from the velocity data. The results provide quantitative information on the influence of elastic and extensional properties on the bubble penetration process in gas-assisted injection molding. The bubble shape and velocity field information provides a basis for evaluating the performance of constitutive equations in mixed flow. Received: 19 January 1999 Accepted: 30 June 1999     

弹性湍流及其对微混合效率影响研究的若干进展

介绍和评述弹性湍流的产生及其对于微混合效率的影响等问题上的若干研究进展. 弹性 湍流和惯性湍流具有类似的流场特征,但引发机理有所不同. 惯性湍流产生的原因 是惯性引起的Reynolds应力,而弹性湍流则是由弹性应力所引起的. 鉴于在微流动 中,惯性力可忽略不计,因此牛顿流体的混合变得十分困难. 此时可在流体中加入 微量高分子聚合物以生成黏弹性流体. 由黏弹性流体所引发的弹性湍流在提高流体 微混合的效率上可发挥重要作用.     

Three-dimensional free vibration analysis of functionally graded piezoelectric annular plates on elastic foundations

Three-dimensional free vibration analysis of functionally graded piezoelectric (FGPM) annular plates resting on Pasternak foundations with different boundary conditions is presented. The material properties are assumed to have an exponent-law variation along the thickness. A semi-analytical approach which makes use of state-space method in thickness direction and one-dimensional differential quadrature method in radial direction is utilized to obtain the influences of the Winkler and shearing layer elastic coefficients of the foundations on the non-dimensional natural frequencies of functionally graded piezoelectric annular plates. The analytical solution in the thickness direction can be acquired using the state-space method and approximate solution in the radial direction can be obtained using the one-dimensional differential quadrature method. Numerical results are given to demonstrate the convergency and accuracy of the present method. The influences of the material property graded index, circumferential wave number and thickness of the annular plate on the dynamic behavior are also investigated. Since three-dimensional free vibration analysis of FGPM annular plates on elastic foundations has not been implemented before, the new results can be used as benchmark solutions for future researches.     

考虑膜厚影响薄膜磁致伸缩系数、泊松比和杨氏模量的同时测量

基于经典层合板理论,建立了一个能同时测量薄膜-基底系统中薄膜的磁致伸缩系数、杨氏模量和泊松比的板模型.以前的研究计算薄膜磁致伸缩系数时,大多假设薄膜的弹性属性与相应的块材一致,由此导致的磁致伸缩系数计算是不准确的.在目前大多数方法中仅仅在使用一个单一的弹性各向同性基底中能够避免这个问题.该文模型在各向异性基底下同样适用,并且不要求薄膜的厚度远远小于基底厚度,因此也能够用来计算磁致伸缩应变和设计微电机械系统和生物微电机械系统.对已有的铁基非晶薄膜的实验数据,在不同磁场强度下,磁致伸缩系数的计算结果与已有模型进行了比较,它们之间的差异得到了解释.同时,还可以得到薄膜的弹性常数.     

IMPROVEMENT OF EXPLICIT ALGORITHMS STABILITY WITH VISCO-ELASTIC ARTIFICIAL BOUNDARY ELEMENTS 1)

黏弹性人工边界单元是目前常用的处理半无限空间波动问题的数值模拟方法,可有效吸收计算区域内产生的外行波动.黏弹性人工边界单元具有与内部介质不同的质量密度、刚度和阻尼,受其影响,对整体模型进行显式时域逐步积分时,在边界区域易发生失稳现象,影响整体系统显式积分的计算效率. 针对该问题目前尚无行之有效的解决方法.本文针对二维黏弹性人工边界单元,建立可代表整体系统典型特征的侧边子系统和角点子系统,利用传递矩阵谱半径分析方法,基于传统中心差分格式,推导得到局部子系统稳定性条件的解析解.在此基础上通过研究解析解中各物理参数对稳定性条件的影响,给出通过增加人工边界单元的质量密度,以改善采用黏弹性人工边界单元时显式算法稳定性的方法.均匀和成层半空间波动问题算例分析表明,将内部单元质量密度设置为人工边界单元质量密度的上限,可以在保证黏弹性人工边界计算精度的前提下,有效改善整体系统显式时域逐步积分的数值稳定性,大幅提高计算效率.     

界面裂纹问题中的弹性T项和应力强度因子

研究两相材料有限板含单边界面裂纹的断裂力学特性，对不同的材料组合用广义变分法分析了不同尺寸试件和裂纹长度下的应力强度因子和弹性T项，讨论了材料特性对应力强度因子和弹性T项的作用．分析了试件尺寸和裂纹长度对应力强度因子和弹性T项的影响．