纵向磁场中导电薄板的亚谐共振

基于麦克斯韦方程和弹性动力学理论,导出了纵向磁场中导电薄板的非线性磁弹性耦合振动方程和电动力学方程,运用伽辽金法推得了两对边简支导电条形板的达芬型振动方程.针对亚谐波共振问题,应用多尺度法进行求解,得到了相应的近似解析解和幅频响应方程以及非平凡解存在条件.应用李雅普诺夫稳定性理论,对解的稳定性进行了分析,得到了稳态解稳...     

聚合物多相分层流动黏弹性包围机制的数值模拟

针对黏弹性包围引起的复合共挤制品层厚均匀性控制的技术难题,通过数值模拟,研究了黏弹性流变性能参数对黏弹性包围的影响规律和机制.研究结果表明,黏弹性包围是由多相分层流动的第二法向应力差驱动的二次流动诱发,主要取决于成型流动过程中二次流动的方向与强度.熔体二次流动的方向与第二法向应力差的正负号有关,而熔体二次流动强度则与第二法向应力差大小成正比.黏弹性包围随着熔体松弛时间的增加而增大.消除黏弹性包围的理论前提是消除其二次流动,而通过使其流动的第二法向应力差趋于零方可消除其二次流动.第二法向应力差趋于零的前提条件是使无滑移黏着共挤多相分层剪切流动转化为气垫非黏着完全滑移共挤多相分层柱塞流动,而气辅共挤成型工艺的气垫壁面滑移是实现这一转变的有效技术.     

天然胶原的稳态流变性能和数学模拟

用旋转流变仪研究胶原溶液的稳态流变性能,讨论了浓度和温度的变化对胶原溶液流动曲线的影响。实验数据显示胶原溶液的剪切粘度随着剪切速率的增大而降低,表明胶原溶液具有明显的假塑性。同一剪切速率下,温度升高,胶原溶液的剪切粘度降低;浓度增大,剪切粘度增大。用幂律方程、Carreau方程和Cross方程对胶原溶液的流动曲线进行数学拟合,结果表明幂律方程,Carreau方程和Cross方程都能准确地描述胶原的流动曲线,其中幂律方程的粘度指数K和非牛顿指数n的变化能准确反映胶原假塑性的变化;Carreau方程和Cross方程的参数比幂律方程多,其拟合得到的曲线和实验数据吻合得更好。但在本实验条件下,Carreau方程和Cross方程预测的零剪切粘度η0和无穷剪切粘度η∞不准确。     

一类平带驱动系统非线性振动的幅频特性

采用解析和数值方法得到了一类平带驱动系统非线性振动的幅频特性。考虑由主动轮、从动轮、张紧轮和张紧臂构成的平带驱动系统基本力学模型,建立了系统的振动方程。推广平均法的基本思想到多自由度系统,导出了平均化方程,进而可得到了系统响应的幅频特性。针对具体算例,通过用数值方法直接积分系统振动方程,得到了系统的幅频特性。解析结果与数值结果定性一致,但也存在定量方面的误差。     

一维变系数对流扩散方程第三边值问题的紧有限体积方法

对流扩散方程在工程计算中具有广泛应用.本文研究一维变系数对流扩散方程第三边值问题的高精度有限体积方法.通过在控制体积上积分导出了方程的积分守恒形式,然后对积分守恒形式利用泰勒公式和二次埃尔米特插值进行离散得到了紧有限体积格式.该格式导出的线性代数方程组具有三对角性质,因此可使用追赶法求解.进而,通过分析截断误差,采用能量方法证明了格式按照几种标准的离散范数四阶收敛.最后,数值算例验证了格式的正确性和有效性,这与理论分析结果是一致的.     

圆柱壳体的非线性磁弹性振动问题

导出了纵向磁场中圆柱薄壳体的非线性轴对称振动基本方程。利用多尺度法和摄动法求出了两端简支壳体振动的近似解析解,并对振动幅值和频率进行了讨论。     

弹性悬臂微梁谐振系统挤压膜阻尼新解析模型

正确预测挤压膜阻尼对于MEMS器件设计是至关重要的.过去,弹性悬臂微梁挤压膜阻尼的解析计算一般采用Darling等提出的模型.但基于格林函数法的Darling模型简化了流-固耦合关系.从弹性微梁振动方程和雷诺方程的耦合关系出发,提出了新的弹性悬臂微梁挤压膜阻尼解析计算模型,导出了解析形式的等效阻尼系数和等效刚度系数.这两个系数完全由梁和挤压膜气体的物理性质决定.最后,通过与Vignola实验结果、Darling模型计算结果、ANSYS/FLOTRAN计算结果相比表明,所提出模型的计算精度有较明显的提高.     

测定非牛顿流体第一法向应力差实验装置的研制

本文介绍了测定非牛顿流体第一法向应力差实验装置的设计思想和组成结构 ,并阐述了该装置在实验教学中的应用     

深水矩形空心桥墩在地震作用下附加动水压力分析

基于辐射波浪理论建立了矩形空心桥墩流体控制方程,以自由表面波动条件、水底水质点运动边界条件、结构与水的速度连续条件为边界条件,采用分离变量法推导了矩形空心桥墩内、外域水体速度势一般解,进而导出了矩形空心墩内、外域水体的附加动水压力的解析式,对某桥墩自振特性的计算表明,该附加动水压力解析式具有较高的计算精度.     

混凝土泵车臂架系统振动机理的研究

结合悬臂输液管流固耦合理论,建立泵车臂架结构与混凝土的流固耦合动力学方程,从流固耦合的角度分析混凝土泵车臂架振动问题。通过试验测试获得混凝土脉动流速图以及仿真边界条件。采用Newmark-β法求解动力学方程,仿真分析了混凝土流动为脉动和常速流时臂架振动响应,发现振动位移响应基本吻合,说明脉动流速对臂架结构应力历程影响较小;仿真分析转台振动为零振动时,混凝土脉动和常速流时臂架振动响应,发现泵送油缸导致的车体振动激扰是臂架振动的主要因素,在臂架系统振动研究时应重点考虑。     

Constitutive equation for rubber-like solids

Summary It has been found convenient to refer the deformation to the reference configuration of the body, the resulting constitutive equation being expressed in terms of the right Cauchy-Green deformation tensor, and a stress tensor which is also concerned solely with the reference configuration of the body. This particular measure of stress is referred to as the second referential stress tensor. The ratio, principal Cauchy stresses/principal stretches, identifies the proper numbers of the second referential stress tensor as the components of the force per unit underformed area. Using the Cayley-Hamilton theorem, the proposed constitutive equation is rearranged and expressed in terms of a quantity which is defined to be one quarter of the difference between the right Cauchy-Green deformation tensor and its inverse. In this way the (effective) strain properties of the proposed constitutive equation are formulated by way of the concept of a strain response function. The three response coefficients associated with the strain response function are assumed to be derivable from a strain intensity function. Two types of strain intensity function are considered. One type is characterised by being continuously differentiable, the other being characterised by the existence of vertices, but is piece-wise linear and continuous. The proposed constitutive equation is used to formulate an effective stress-effective strain relation. This effective stress-effective strain relation is used to correlate the individual stress-strain relations characteristic of various simple modes of deformation to give a single stress-strain relation. Correlation between the predictions of the proposed constitutive equation and the results of experiment proceeds by way of the concept of a generalised shear modulus.With 3 Figures     

高分子熔体的各向异性内部结构流变模型EI

提出了一个高分子熔体内部结构流变模型，采用大分子构象张量表述，并结合经典弹性力学与大分子动力学求得自由能各向异性唯象表达式，运用Ｈａｍｉｌｔｏｎｉａｎ／ＰｏｉｓｏｎＢｒａｃｋｅｔ方法从自由能函数和耗散张量推导建立了高分子构象张量动力学方程与相应的应力张量表达式。ＬＤＰＥ和ＰＳ在简单剪切流场中的粘弹特性的模拟结果与实验数据进行了分析对比，两者基本相符。本文还预测和讨论了上述流体大分子构象的变化过程以及各向异性参数的作用。     

Rheology of Superplastic Ceramics

Constitutive equation of rheology describing a phenomenological level of superplastic deformation as functional correlation between tensor components of stress and strain rate has been analyzed for the case of superplastic ceramic flow. Rheological properties of material are taken into account by means of scalar rheological coefficients of shear and volume viscosity, which are functions of temperature, effective stress (or strain rate) and density of material.     

A Lagrangian model for hardening behaviour of materials at finite deformation based on the right plastic stretch tensor

In this paper a modified multiplicative decomposition of the right stretch tensor is proposed and used for finite deformation elastoplastic analysis of hardening materials. The total symmetric right stretch tensor is decomposed into a symmetric elastic stretch tensor and a non-symmetric plastic deformation tensor. The plastic deformation tensor is further decomposed into an orthogonal transformation and a symmetric plastic stretch tensor. This plastic stretch tensor and its corresponding Hencky’s plastic strain measure are then used for the evolution of the plastic internal variables. Furthermore, a new evolution equation for the back stress tensor is introduced based on the Hencky plastic strain. The proposed constitutive model is integrated on the Lagrangian axis of the plastic stretch tensor and does not make reference to any objective rate of stress. The classic problem of simple shear is solved using the proposed model. Results obtained for the problem of simple shear are identical to those of the self-consistent Eulerian rate model based on the logarithmic rate of stress. Furthermore, extension of the proposed model to the mixed nonlinear isotropic/kinematic hardening behaviour is presented. The model is used to predict the nonlinear hardening behaviour of SUS 304 stainless steel under fixed end finite torsional loading. Results obtained are in good agreement with the available experimental results reported for this material under fixed end finite torsional loading.     

Damage-induced stress-softening and viscoelasticity of limited elastic materials

The rate-dependent behavior of filled natural rubber (NR) is investigated in tensile regime. In order to describe the viscosity-induced rate-dependent effects, a constitutive model of finite strain viscoelasticity is proposed on the basis of the multiplicative decomposition of the deformation gradient tensor into elastic and viscous parts. The total stress is decomposed into an equilibrium stress and a viscosity-induced overstress by following the rheological models of Poynting–Thomson and Zener types. To incorporate the Mullins stress-softening phenomenon into a viscoelastic material, an invariant-based stress-softening function is also proposed. To identify the constitutive equation for the viscosity from direct experimental observations, an analytical scheme is proposed that ascertains the fundamental relation between the viscous strain rate and the overstress tensor with limited elastic parent material model. Evaluation of the experimental results using the proposed analytical scheme confirms the necessity of considering both the current overstress and the current deformation as variables to describe the evolution of the rate-dependent phenomena. Based on this, an evolution equation is proposed to represent the effects of internal variables on viscosity phenomena. The proposed evolution equation has been incorporated into the finite-strain viscoelasticity model in a thermodynamically consistent way.     

各向同性弹性介质非线性本构方程

从张量函数出发,围绕共轭应力、应变变量,研究了各向同性非线性弹性介质各种形式的本构方程以及各种形式方程之间的关系。推导出用张量不变量,标量不变量表示的两种形式非线性Green弹性介质本构方程。证明了方程是完备的,不可约的。作为应用举例,研究了橡胶材料的工程应用问题。     

Flow of electro-rheological materials

Summary An electro-rheological fluid is a material in which a particulate solid is suspended in an electrically non-conducting fluid such as oil. On the application of an electric field, the viscosity and other material properties undergo dramatic and significant changes. In this paper, the particulate imbedded fluid is considered as a homogeneous continuum. It is assumed that the Cauchy stress depends on the velocity gradient and the electric field vector. A representation for the constitutive equation is developed using standard methods of continuum mechanics. The stress components are calculated for a shear flow in which the electric field vector, is normal to the velocity vector. The model predicts (i) a viscosity which depends on the shear rate and electric field and (ii) normal stresses due to the interaction between the shear flow and the electric field. These expressions are used to study several fundamental shear flows: the flow between parallel plates, Couette flow, and flow in an eccentric rotating disc device. Detailed solutions are presented when the shear response is that of a Bingham fluid whose yield stress and viscosity depends on the electric field.     

Constitutive equation for a class of isotropic, perfectly elastic solids using a new measure of finite strain and corresponding stress

The definition of a measure of strain, referred to as the bi-configuration strain tensor, centres on the difference between the left Cauchy-Green deformation tensor and its inverse. A new measure of stress, coined the bi-configuration stress tensor, has been defined. This measure of stress refers the traction in the current configuration jointly to the referential and spatial configurations, that is, to an effective element of area identified as an element of bi-configuration area. The stress and strain tensors are assumed to be constitutively related by a finite strain form of a generalised Hooke's law. The predictions obtained from the proposed constitutive equation are compared with the observed mechanical behaviour of various test materials. Comparison with experiment centres on biaxial stress measurements in various simple modes of deformation identified by way of a generalised stress-strain relation. The predictions from the proposed constitutive theory are in good accord with the results of experiment.     

Tensor representations and solutions of constitutive equations for viscoelastic fluids

An approach is developed using tensor representations to assess and characterize both the transient behavior and equilibrium states of viscoelastic fluid constitutive equations in viscometric flows. The methodology is based on the replacement of the differential constitutive equation for the deviatoric part of the viscoelastic stress tensor by an equivalent and more tractable set of differential equations for the characteristic scalar invariants. In the case of planar flows, this equivalence leads to an explicit, closed-form analytic solution for the time evolution of the extra-stress tensor that is formally expressed as a second-order fluid relation, with time-dependent coefficients. As a validation of the approach, an analysis of the transient and equilibrium system characteristics of fluid flows described by the corotational Jeffreys model and general Oldroyd-type constitutive equations is presented.     

Analysis of viscoelastic behaviour of transversely isotropic materials

In this paper a constitutive equation to describe the mechanical behaviour of materials, reinforced with unidirectional fibres, is presented. The material behaviour of both matrix and fibres may be viscoelastic. The constitutive equation is a linear relation between the second Piola–Kirchhoff stress tensor and the Green–Lagrange strain tensor. The effective relaxation functions in the constitutive equation are composed of component relaxation functions employing the structural model of Hashin and Rosen. A two-dimensional membrane element incorporating this constitutive equation is implemented in a finite element program. The results of several calculations are presented in order to demonstrate the possibilities of the numerical tool. One calculation concerns a square membrane with a circular hole in its centre. The effect of fibre orientation on deformation and stresses will be displayed for this structure as well as for another membrane structure.