Reflection of plane micropolar viscoelastic waves at a loosely bonded solid-solid interface

A solution of the field equations governing small motions of a micropolar viscoelastic solid half-space is employed to study the reflection and transmission of plane waves at a loosely bonded interface between two dissimilar micropolar viscoelastic solid half-spaces. The amplitude ratios for various reflected and refracted waves are computed for a particular model for different values of bonding parameter. The variations of these amplitude ratios with the angle of incidence are shown graphically. Effects of bonding parameter and viscosity on the amplitude ratios are shown.     

Reflection and Refraction of Micropolar Magneto-thermoviscoelastic Waves at the Interface between Two Micropolar Viscoelastic Media

Using micropolar generalized thermoviscoelastic theories, problems of reflection and refraction of magneto-thermoeviscoelastic waves at the interface between two viscoelastic media are studied when a uniform magnetic field permeates the media. Coefficient ratios of reflection and refraction are obtained using continuous boundary conditions. Some special cases are considered, i.e., the absence of micropolar and viscous effects. By numerical calculations, variations of the amplitude ratios of reflection and refraction coefficients with the angle of incidence are shown graphically for incident rotational and dilatational waves at the interface between two media (one medium is aluminium-epoxy micropolar iscoelastic material, and the other is magnesium crystal micropolar viscoelastic material). Comparing the generalized thermoelastic theories developed by Lord and Shulman (LS) and by Green and Lindsay (GL) in this paper to conventional dynamics (CD) theory the effects of a magnetic field and viscosity are shown numerically in this paper.     

Linear theory of memory-dependent micropolar viscoelastic materials with stretch

A linear theory of memory-dependent micropolar viscoelastic materials with stretch has bean developed. Linear constitutive functionals have been considered to depend on the continuous past history of the strain measures, micro-rotation gradient, stretch and stretch gradients. The constitutive equations of isotronic linear micronolar viscoelastic materials with stretch have been obtained as a particular case by neglecting the past history of the motion.     

Two-dimensional wave propagation in a micropolar thermo-elastic layer with stretch

This paper deals with the propagation of 2-dimensional waves in a thermo-elastic micropolar solid layer which can stretch and contract. Thermo-elastic Rayleigh wave velocity equation in the micropolar medium with stretch has been deduced from the above theory. The wave velocity equation obtained is in agreement with the classical result of Rayleigh when the layer is unstretched and thermal and micropolar effects are negligibly small.     

Wave propagation in micropolar mixture of porous media

This paper is concerned with the possible propagation of waves in an infinite porous continuum consisting of a micropolar elastic solid and a micropolar viscous fluid. Micropolar mixture theory of porous media developed by Eringen [A.C. Eringen, Micropolar mixture theory of porous media, J. Appl. Phys. 94 (2003) 4184–4190] is employed. It is found that there exist four coupled longitudinal waves (two coupled longitudinal displacement waves and two coupled longitudinal microrotational waves) and six coupled transverse waves in a continuum of this micropolar mixture. All the waves are found to attenuate and dispersive in nature. A problem of reflection of coupled longitudinal waves from a free boundary surface of a half-space consisting the mixture of a micropolar elastic solid and Newtonian liquid, is investigated. The expressions of various amplitude ratios and surface responses are derived. Numerical computations are performed to find out the phase velocity and attenuation of the waves. The variation of amplitude ratios, energy ratios and surface responses are also computed for a specific model. All the numerical results are depicted graphically. Some limiting cases have also been discussed.     

Shear wave propagation in vertically heterogeneous viscoelastic layer over a micropolar elastic half-space

This article deals with the propagation of SH-wave in a vertically heterogeneous viscoelastic layer lying over a micropolar elastic half-space. Dispersion and damping equations are obtained analytically in closed form. Phase and damped velocities are computed numerically and depicted by means of a graph to exhibit the substantial effect of heterogeneity, viscoelasticity (internal friction), and micropolar parameter. As a special case of the problem, it is found that deduced dispersion relation is well in agreement to the classical-Love wave equation and damping equation vanishes identically for the isotropic case. Influence of micropolarity present in the medium of half-space is highlighted through comparative study.     

粘弹性阻尼器温频影响效应的计算模型及结构分析

本文根据粘弹性阻尼器的力学性能，提出了一种能够体现温度和频率影响的新计算模型-等效标准固体模型，然后通过对9050A材料和一加有粘弹性阻尼器的建筑结构进行实例分析，得出有关结论。     

A layerwise finite element formulation for vibration and damping analysis of sandwich plate with moderately thick viscoelastic core

Abstract

Most previous studies of viscoelastic sandwich plates were based on the assumption that damping was only resulting from shear deformation in the viscoelastic core. However, extensive and compressive deformations in the viscoelastic core should also be considered especially for sandwich plates with moderately thick viscoelastic core. This paper presents a finite element formulation for vibration and damping analysis of sandwich plates with moderately thick viscoelastic core based on a mixed layerwise theory. The face layers satisfy the Kirchhoff theory while the viscoelastic core meets a general high-order deformation theory. The viscoelastic core is modeled as a quasi-three-dimensional solid where other types of deformation such as longitudinal extension and transverse compression are also considered. To better describe the distribution of the displacement fields, auxiliary points located across the depth of the sandwich plate are introduced. And based on the auxiliary points, the longitudinal and transverse displacements of the viscoelastic core are interpolated independently by Lagrange interpolation functions. Quadrilateral finite elements are developed and dynamic equations are derived by Hamilton’s principle in the variation form. Allowing for the frequency-dependent characteristics of the viscoelastic material, an iterative procedure is introduced to solve the nonlinear eigenvalue problem. The comparison with results in the open literature validates the remarkable accuracy of the present model for sandwich plates with moderately thick viscoelastic core, and demonstrates the importance of the higher-order variation of the transverse displacement along the thickness of the viscoelastic core for the improvement of the analysis accuracy. Moreover, the influence of the thickness and stiffness ratios of the viscoelastic core to the face layers on the damping characteristics of the viscoelastic sandwich plate is discussed.     

高阻尼黏弹性阻尼器性能与力学模型研究

对2个高阻尼黏弹性阻尼器进行不同应变幅值、加载频率下的力学性能试验和疲劳性能试验,研究试件在不同工况下的最大剪应力、存储剪切模量、损耗剪切模量和等效黏滞阻尼比等力学性能及其变化规律,提出五单元模型模拟黏弹性阻尼器的滞回性能。研究结果表明：黏弹性阻尼器滞回曲线饱满、稳定,具有较高的等效黏滞阻尼比,表现出良好的变形性能和耗能能力;黏弹性阻尼器力学性能与应变幅值的相关性明显,与加载频率相关性较小,抗疲劳性能较好;五单元模型模拟的滞回曲线与试验滞回曲线吻合良好。     

On the bending of micropolar viscoelastic plates

The theory of micropolar elastic plates has been established by [A.C. Eringen, Linear theory of micropolar viscoelasticity, Int. J. Engng. Sci. 5 (1967) 191–204]. The present paper is concerned with the bending of micropolar viscoelastic plates within the dynamic theory. First, the basic equations of the bending theory of viscoelastic thin plates are presented. Then, a variational characterization of solutions and a minimum principle of Reiss type are established.     

粘弹性材料本构模型的研究

介绍了近年来建立粘弹性材料本构模型的方法。目前主要有两种方法:利用现有本构模型;对粘弹性材料进行试验研究,拟合实验曲线。     

Viscoelastic winding and unwinding mechanics

Abstract

In this paper a viscoelastic analysis of tape systems in winding/ unwinding process is presented. An analytical model is developed to predict stress and displacement fields in the tape system for any winding speed. A three‐parameter solid is used as an illustrated example. Results show that tape velocity is greater than 762 or less than 0.0762 cm/sec, the elastic solutions are applicaple. If the tape velocity is between 0.0762 and 762 cm/sec, the viscoelastic results are applicable.     

Noncentrosymmetry in micropolar elasticity

Consequences of noncentrosymmetry in a micropolar elastic solid are considered. A solid which is isotropic with respect to coordinate rotations but not with respect to inversions, has three new elastic constants in addition to the six considered in the fully isotropic micropolar solid. The acentric micropolar solid is predicted to undergo torsional deformation when subjected to tensile load.     

Acceleration waves in simple and linear viscoelastic micropolar materials

In this work the conditions of propagation of acceleration waves are studied in different types of micropolar media: (a) in simple media whose constitutive equations are given in functional form, (b) in linear viscoelastic media of which the constitutive equations are obtained in the limit of small deformations from a simple micropolar medium obeying the axiom of fading memory. In contrast to the first case, two kinds of acceleration waves can propagate independently in the second case.     

基于Herrmann变分原理的三维粘弹性增量有限元法及其应用

发展了一种不可压和近似不可压粘弹性增量有限元法,并对固体火箭发动机药柱进行了三维分析。首先从Herrmann泛函出发并结合对应原理导出了适用于不可压和近似不可压粘弹性材料的本构关系,然后根据虚功原理建立了三维粘弹性增量有限元列式,最后对弹性约束的圆柱形中孔药柱进行了不可压和近似不可压分析。结果表明该方法可用于泊松比接近甚至等于0.5的粘弹性问题计算,尤其适用于固体推进剂药柱的结构分析。     

基于混合分层理论的粘弹层合圆柱壳的阻尼振动和层间应力研究

应用混合分层理论,并在壳厚方向采用位移和应力插值函数推导出粘弹层合圆柱壳的动力学方程。计算了两层粘弹层合圆柱壳的振动频率和结构损耗因子,与Okazaki A的结果吻合良好。针对不同模量和厚度的粘弹性材料,计算出层合圆柱壳的层间横向应力的幅值。结果表明:过大的层间法向正应力是导致自由阻尼层合壳脱层破坏的主要因素,采用环向加强的粘弹性材料将有效地降低层间法向正应力的幅值。     

三维粘弹壁板颤振分析

基于Kelvin粘弹模型,根据Von Karman大变形应变-位移关系和一阶活塞气动力理论,运用伽辽金方法建立了三维粘弹壁板颤振方程,并采用Rouge-Kutta法进行数值积分,分析粘弹阻尼,面内压力及壁板几何尺寸对粘弹壁板颤振的影响,进而取动压为分叉参数,研究粘弹壁板颤振时的分叉及混沌等特性。结果表明：随着粘弹性阻尼的增大, 系统的静态稳定区域先减小后增大,而静态屈曲解几乎不受影响,同时发现混沌运动区域随着粘弹阻尼的增大而快速减小。当取动压为分叉参数时发现粘弹壁板分叉特性很复杂,系统由屈曲状态进入混沌振动,再经历一系列的分叉进入简谐极限环振动状态;而较大面内压力和较小的长宽比不利于粘弹壁板的稳定。     

Some uniqueness and continuous dependence results in the micropolar mixture theory of porous media

The present paper studies the uniqueness and continuous data dependence of solutions of the initial-boundary value problem associated with the micropolar mixture linear theory of porous media. For a binary homogeneous mixture of an isotropic micropolar elastic solid with an incompressible micropolar viscous fluid, an uniqueness result is established. Then we deduce some estimates for describing the continuous dependence of solution with respect to the changes in the body force and body couple and in the initial-boundary given data. Thus, it is shown that the general approach of a binary homogeneous mixture of an isotropic micropolar elastic solid with an incompressible micropolar viscous fluid is well posed.     

Axi-symmetric problem in micropolar elastic half-space with stretch

The present investigation is concerned with axisymmetric problem in micropolar elastic half-space with stretch. The displacement, force stress, couple stress and vector first moment are obtained for a half-space subjected to an arbitrary normal load and a particular case of impulsive force is studied in detail. The graphs for various quantities have been drawn to illustrate the effect of stretch in each particular case.     

计算粘弹结构动力学参数的新模态应变能方法

粘弹结构在噪声与振动控制领域已得到广泛应用,然而准确地计算粘弹结构的动力学参数一直存在困难,模态应变能法及其修正方法常用作近似计算。在分析模态应变能方法和已有修正方法的原理及其相互关系的基础上,提出一种基于损耗因子幅值的新模态应变能方法,用于计算粘弹结构的损耗因子与固有频率。新方法的修正因子随粘弹结构对应模态阶次损耗因子幅值变化。取可等价为粘弹性夹层梁/板的四参数原型系统和新型高阻尼航天载荷隔振器为算例,通过与已有方法的对比分析了新方法的准确性。