Delayed Fracture of a Laminated Viscoelastic Plate with a Through Crack under a Time-Dependent Load

The delayed fracture of a viscoelastic plate with a rectilinear mode I crack under a time-dependent load is studied. The plate is made of a laminated composite with an isotropic elastic reinforcing component and a viscoelastic matrix. The composite is modeled by an orthotropic homogeneous linearly viscoelastic medium with some averaged characteristics. To determine the viscoelastic characteristics of the composite, the Volterra principle and the method of continued fractions are used. The study is made within the framework of the theory of delayed fracture for viscoelastic bodies.     

粘弹性Timoshenko梁的变分原理和静动力学行为分析

从线性，各向同性，均匀粘弹性材料的Boltzmann本构定律出发，通过Laplace变换及其反变换，由三维积分型本构关系给出了Timoshenko梁的本构关系，并由此建立了小挠度情况下粘弹性Timoshenko梁的静动力学行为分析的数学模型，一个积分－偏微分方程组的初边值问题。同时，采用卷积，建立了相应的简化Gurtin型变分原理。给出了两个算例，考查了梁的厚度h与梁的长度l之比β对梁的力学行为的影响。     

分数阶粘弹性地基上薄板波动和振动特性分析

本文研究了粘弹性地基上薄板的波动和振动问题.主要讨论了基于分数导数理论的粘弹性地基模型上薄板弯曲波的传播特性以及固有频率对地基的依赖特性.推导了三种经典粘弹性地基模型的复模量.并利用分数导数的性质得到分数阶粘弹性地基上Kirchhoff板中弯曲波的传播速度、衰减系数以及自由振动的复固有频率.数值算例表明粘弹性地基对弯曲波传播特性存在显著影响,不同粘弹性模型所对应的色散和衰减特性也存在较大差别.分数阶导数可以实现相邻整数阶导数之间的光滑过渡.利用分数导数的本构关系可以更加真实地描述粘弹性地基的历史依赖行为,更准确地表现出粘弹性地基板中弯曲波的色散和衰减特性.     

微振激励下黏弹性阻尼器微观链结构力学模型

减小微振动对高精密仪器至关重要,利用黏弹性阻尼器进行微振动抑制是一个新兴而又具有挑战性的课题.本文采用分子链网络模型方法分析了黏弹性材料的微观分子链结构,综合考虑材料分子链结构中的网络链和自由链对黏弹性材料力学性能的影响,提出一种基于材料微观分子链结构的微振激励下黏弹性阻尼器力学模型.模型分别采用标准线性固体模型和Maxwell模型来描述网络链和自由链中单个链的力学性能,并分别采用8链网络模型和3链网络模型考虑两种类型分子链的综合效应,引入温频等效原理描述温度对微振激励下黏弹性阻尼器力学性能的影响.该模型能够描述温度和频率对黏弹性阻尼器动态力学性能的影响,并能够反映黏弹性材料的微观结构与材料力学性能的关系.为验证所提模型的有效性及考察黏弹性阻尼器在微振激励下的耗能能力和动态力学性能,在微振条件下对黏弹性阻尼器进行了动态力学性能试验.研究结果表明黏弹性阻尼器具有较好的微振耗能能力,其动态力学性能受温度和频率影响较大,所提的力学模型能够精确地描述微振激励下黏弹性阻尼器动态力学性能随温度和频率的变化关系.      

Analysis of frequency-domain vibration response of thin plate attached with viscoelastic free layer damping

To predict the vibration response of viscoelastic composite structure, two key issues need to be conducted, one is introducing the constitutive model of viscoelastic material into the analysis model and the other is describing the real damping behavior of viscoelastic composite structure. The emphasis of this study is to obtain the effects of frequency dependence on the vibration response of viscoelastic composite structure and the method of introducing two kinds of damping (viscoelastic material damping and remaining equivalent viscous damping). Vibration response analysis in frequency domain was investigated for viscoelastically damped plate. A cantilever plate attached with the ZN_1 viscoelastic free layer damping (FLD) was chosen to demonstrate the developed method. Frequency-domain response of the composite plate were solved and the obtained results were compared with the experimental values for the purpose of assessing the rationality of the proposed method. In addition, in order to obtain the effects of viscoelastic material parameters on vibration response of viscoelastic composite structure, a detailed parametric analysis was performed. This study shows that the frequency dependent characteristic of viscoelastic material has significant influence on the vibration response in the resonant region and acceptable results can be achieved in the non-resonant region if frequency dependent parameters are substituted by average values of the viscoelastic parameters reasonably in the analysis process.     

粘弹性地基上弹性梁的自由振动分析

本文将文克尔弹性地基梁模型中的弹簧用粘弹性元件来替代,建立了三元件文克尔粘弹性地基止粘弹性梁的静力和动力本构方程,求出了粘弹性地基上弹性梁的自由振动的级数解。并且对不同的振动情况进行讨论,最后给出了算例及结论。     

岩石三轴蠕变试验黏弹性解析及参数识别

基于岩石三轴蠕变试验,推导了相应的黏弹性解析解,并对三参量H-K流变模型给出 了黏弹性解析解的显式以及流变参数的识别方法. 在此基础上,针对花岗岩及片岩两种岩石 的室内蠕变分级加载试验曲线进行了流变参数的识别与反演. 分析表明,同一岩样在不同加 载级别下的弹性及黏弹性参数在量值上均有所不同,其中黏弹性模量和黏滞系数的量值随 载荷的增加出现损伤衰减,基于试验反演所获参数的解析蠕变曲线与试验蠕变曲线吻合较好.     

黏弹性传动带1:3内共振时的周期和混沌运动

研究了参数激励作用下黏弹性传动带在1:3内共振时的周期解分岔和混沌动力学. 同时考虑传动带的线性外阻尼因素和材料内阻尼因素. 首先建立了具有线性外阻尼情况下的黏弹性传动带平面运动时的非线性动力学方程, 黏弹性材料的本构关系用Kelvin模型描述. 然后考虑黏弹性传动带的横向振动问题, 利用多尺度法和Galerkin离散法得到黏弹性传动带系统在1:3内共振时的平均方程. 最后利用数值模拟方法研究了黏弹性传动带系统的周期振动和混沌动力学, 得到了系统在不同参数下的混沌运动. 数值模拟结果说明黏弹性传动带系统存在周期分岔, 概周期运动及混沌运动.     

Generalized variational principles of the viscoelastic body with voids and their applications

From the Boltzmann‘ s constitutive law of viscoelastic materials and the linear theory of elastic materials with voids, a constitutive model of generalized force fields for viscoelastic solids with voids was given. By using the variational integral method, the convolution-type functional was given and the corresponding generalized variational principles and potential energy principle of viscoelastic solids with voids were presented. It can be shown that the variational principles correspond to the differential equations and theinitial and boundary conditions of viscoelastic body with voids. As an application, a generalized variational principle of viscoelastic Timoshenko beams with damage was obtained which corresponds to the differential equations of generalized motion and the initial and boundary conditions of beams. The variational principles provide a way for solving problems of viscoelastic solids with voids.     

Nonlinear random stability of viscoelastic cable with small curvature

The nonlinear planar mean square response and the random stability of a viscoelastic cable that has a small curvature and subjects to planar narrow band random excitation is studied. The Kelvin viscoelastic constitutive model is chosen to describe the viscoelastic property of the cable material. A mathematical model that describes the nonlinear planar response of a viscoelastic cable with small equilibrium curvature is presented first. And then a method of investigating the mean square response and the almost sure asymptotic stability of the response solution is presented and regions of instability are charted. Finally , the almost sure asymptotic stability condition of a viscoelastic cable with small curvature under narrow band excitation is obtained.     

On the separation of geometric and viscoelastic dispersion in composite materials

With the completion of an experimental study of the dispersion characteristics of fiber-reinforced viscoelastic materials, a sufficient body of information has been generated to demonstrate the feasibility of separating viscoelastic dispersion from the total dispersion spectrum of this class of material. The basic procedure for the separation is to construct a homogeneous viscoelastic constitutive equation for the composite and to use cross plots of the viscoelastic characterization with the total dispersion spectrum of the composite to reveal the influence of viscoelastic dispersion on the total spectrum. Two methods of constructing the homogeneous model are discussed and the results are compared with experimental data.     

非线性粘弹性平面问题的数学模型及其失记效应

本文以位移为基本未知量,利用非线性粘弹性力学中的Leaderman本构关系和线性几何假设,建立了非线性粘弹性平面问题的数学模型;在粘弹性泊松比为常数的情况下,利用Titchmarsh定理和Laplace变换法证明了非线性粘弹性平面问题与非线性弹性平面问题之间存在着某些对应关系,对应关系为粘弹性问题的求解提供了一种新的思路,利用这些关系可直接从相应弹性问题获得粘弹性平面问题的部分响应,与传统的时域有限差分法相比,计算时间明显缩短,另外,对应关系也揭示了粘弹性结构的失记效应,即结构的部分响应仅与外部输入的现时值有关,而与其历史无关。     

A simplified viscoelastic constitutive equation applied to a dynamic finite deformation problem

A single integral type of constitutive equation for finite viscoelastic deformation is proposed. A special case, which is a viscoelastic generalization of the constitutive equation for a neo-Hookean elastic solid, is used to consider the finite deformation problem of shock wave propagation resulting from the sudden application of compressive force at the end of a semi-infinite viscoelastic bar. An approximate method is used to determine the shock front path and shock strength when the viscoelastic dissipative effect is small.     

Nonlinearly Viscoelastic Nanoindentation of PMMA Under a Spherical Tip

The Oliver-Pharr method has been well established to measure Young’s modulus and hardness of materials without time-dependent behavior in nanoindentation. The method, however, is not appropriate for measuring the viscoelastic properties of materials with pronounced viscoelastic effects. One well-known phenomenon is the formation of unloading “nose” or negative stiffness during unloading that often occurs during slow loading-unloading in nanoindentation on a viscoelastic material. Most methods in literature have only considered the loading curve for analysis of viscoelastic nanoindentation data while the unloading portion is not analyzed adequately to determine the nonlinearly viscoelastic properties. In this paper, nonlinearly viscoelastic effects are considered and modeled using the nonlinear Burgers model. Nanoindentation was conducted on poly-methylmethacrylate (PMMA) using a spherical indenter tip. An inverse problem solving approach is used to allow the finite element simulation results to agree with the nanoindentation load–displacement curve during the entire loading and unloading stage. This approach has allowed the determination of the nonlinearly viscoelastic behavior of PMMA at submicron scale. In addition, the nanoindentation unloading “nose” has been captured by simulation, indicating that the negative stiffness in the viscoelastic material is the result of memory effect in time-dependent materials.     

Generalized Maxwell model for the viscoelastic behavior of a soda-lime-silica glass under low frequency shear loading

The linear viscoelastic behavior of a soda-lime-silica glass under low frequency shear loading is investigated in the glass transition range. Using the time-temperature superposition technique, the master curves of the shear dynamic relaxation moduli are obtained at a reference temperature of 566°C. A method to determine the viscoelastic constants from dynamic relaxation moduli is proposed. However, some viscoelastic constants cannot be directly measured from the experimental curves and others cannot be precisely obtained due to non-linearity effects at very low frequencies. The generalized Maxwell model is investigated from the experimental dynamic moduli without fixing the viscoelastic constants. A set of parameters is shown to be in good agreement with the experimental dynamic relaxation moduli, but does not give the correct values of the viscoelastic constants of the investigated glass. The soda-lime-silica glass exhibits a non-linear viscoelastic behavior at very low stress level which is usually observed for organic glasses. This non-linear behavior is questioned.     

粘弹性流体的入口收敛流动

本文以聚合物流体为研究对象,对其在入口收敛流动中产生的粘弹效应及机理进行了初步的讨论和分析,并就近10年来国内外有关粘弹性流体入口流动研究及进展作了简要的评述。      

Transient deformation of an inviscid inclusion in a viscoelastic extensional flow

The transient deformation of a bubble in a viscoelastic extentional flow is analyzed by means of a finite element algorithm for viscoelastic moving boundary problems. Using the Oldroyd-B constitutive model, we find that bubbles in a viscoelastic fluid deform to the same steady-state configurations as bubbles in a Newtonian fluid at equal values of the far-field extensional stresses (corresponding to different stretch rates). Vapor bubbles in a developed extensional flow collapse more readily in the viscoelastic liquid than bubbles in Newtonian fluids because of the large compressive stresses associated with the viscoelastic liquid.     

Viscoelastic properties of human cornea

Viscoelastic response of intact human cornea subjected to physiological intraocular pressure was determined from local deformations measured by a flying spot micrometer. One eye of a paired specimen was prepressurized at 15 mmHg for at least 8 hr while the other eye was left unpressurized before testing. Test results of five paired eyes showed that, in prepressurized enucleated eyes, the viscoelastic response was insignificant while significant viscoelastic response existed in the nonpressurized eyes. The latter viscoelastic properties were characterized by a five-element linear viscoelastic model and a nonlinear hereditary integral by Fung.     

Viscoelastic Deformation of a Reinforced Plate with a Crack

The deformation of a viscoelastic reinforced composite is studied. The composite has an axis of elastic symmetry and consists of transversally isotropic fibers and a viscoelastic matrix, which differ by the volume concentration and mechanical characteristics. The material is modeled by a transversely isotropic homogeneous linearly viscoelastic medium with some averaged characteristics. A plate fabricated from the composite in question is weakened by a through mode I crack and is subjected to constant tensile forces. The viscoelastic properties of the matrix material are described by a convolution operator. The Volterra principle is used to derive expressions for the viscoelastic characteristics and crack opening. The irrational function of the integral operator that describes the crack opening is expanded into an operator continued fraction and is represented as the sum of base operators     

Investigation of guided waves propagation in orthotropic viscoelastic carbon–epoxy plate by Legendre polynomial method

The effect of viscoelasticity on the guided waves propagation in viscoelastic plate has been investigated according to multi-aspect. To this purpose, an extension of the Legendre polynomial method is proposed to formulate the guided waves equation in orthotropic viscoelastic plate composed of carbon–epoxy. The validity of the proposed Legendre polynomial method is illustrated by comparison with available data. The convergence of the method is discussed through a numerical example. The hysteretic and Kelvin–Voigt viscoelastic models are used to integrate the imaginary part of the complex stiffness matrix associated with the viscoelastic plate in this study. Accordingly, both viscoelastic models do not affect on the dispersion curves results. However, appreciable effects are seen in the attenuation curves. Also, the sensitivity of the guided waves propagation caused by variations of elastic and viscoelastic modulus has been studied in detail. Finally, the advantages of the Legendre polynomial method are described.