GENERAL DECAY FOR A VISCOELASTIC EQUATION OF VARIABLE COEFFICIENTS WITH A TIME-VARYING DELAY IN THE BOUNDARY FEEDBACK AND ACOUSTIC BOUNDARY CONDITIONS

A variable coefficient viscoelastic equation with a time-varying delay in the boundary feedback and acoustic boundary conditions and nonlinear source term is considered.Under suitable assumptions, general decay results of the energy are established via suitable Lyapunov functionals and some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term and the elements of the matrix A and the kernel function g.

BOUNDARY ELEMENT METHOD FOR SOLVING DYNAMICAL RESPONSE OF VISCOELASTIC THIN PLATE(Ⅱ)──THEORETICAL ANALYSIS

In this paper, the necessary theoretical analysis for the approximation boundary element method to solve dynamical response of viscoelastic thin plate presented in [1] is.discussed. The theorem of existence and uniqueness of the approximate solution andthe error estimation are also obtained. Based on these conclusions , the principle forchoosing the mesh size and the number of truncated terms in the fundamental solution are given. It isshown that the theoretical ana analysis in this paper are consistent with thenumerical results in [1].

Modelling and predicting the dynamic response of an axially graded viscoelastic core sandwich beam

The present study explored the influence of axial gradation of viscoelastic materials on the dynamic response of the sandwich beam for structural applications.The finite element(FE)formulations are used to model and investigate dynamic response of the sandwich beam.The classical beam theory is used to develop the FE formulations and Lagrange's approach is considered to obtain the equations of motion(EOM).FE code is developed and validated with the existing literature and also conducted the convergence study for the developed FE method.Further,the influence of different viscoelastic materials and boundary conditions on the dynamic response of the sandwich beam is investigated.Four different axial gradation configurations of viscoelastic materials are considered for the present work to explore the influence on natural frequency,loss factor and frequency response of the sandwich beam.The modeled axial gradation of viscoelastic material has displayed a considerable impact on the peak vibrational amplitude response of the sandwich beam for all the boundary conditions and these configurations improved the damping capabilities at different configurations for the structural applications.

Stress boundary layers in the viscoelastic flow past a cylinder in a channel:limiting solutions

The flow past a cylinder in a channel with the aspect ratio of 2 ： 1 for the upper convected Maxwell （UCM） fluid and the Oldroyd-B fluid with the viscosity ratio of 0.59 is studied by using the Galerkin/Least-square finite element method and a p-adaptive refinement algorithm. A posteriori error estimation indicates that the stress-gradient error dominates the total error. As the Deborah number, De, approaches 0.8 for the UCM fluid and 0.9 for the Oldroyd-B fluid, strong stress boundary layers near the rear stagnation point are forming, which are characterized by jumps of the stress-profiles on the cylinder wall and plane of symmetry, huge stress gradients and rapid decay of the gradients across narrow thicknesses. The origin of the huge stress-gradients can be traced to the purely elongational flow behind the rear stagnation point, where the position at which the elongation rate is of 1/2De approaches the rear stagnation point as the Deborah number approaches the critical values. These observations imply that the cylinder problem for the UCM and Oldroyd-B fluids may have physical limiting Deborah numbers of 0.8 and 0.9, respectively.

GLOBAL NONEXISTENCE FOR A VISCOELASTIC WAVE EQUATION WITH ACOUSTIC BOUNDARY CONDITIONS

This paper deals with a class of nonlinear viscoelastic wave equation with damping and source terms utt-Δu-Δut-Δutt+∫^t0g(t-s)Δu(s)ds+ut|ut|^m2-=u|u|^p-2 with acoustic boundary conditions.Under some appropriate assumption on relaxation function g and the initial data,we prove that the solution blows up in finite time if the positive initial energy satisfies a suitable condition.

Acoustic viscoelastic modeling by frequency-domain boundary element method

Earth medium is not completely elastic, with its viscosity resulting in attenuation and dispersion of seismic waves. Most viscoelastic numerical simulations are based on the finite-difference and finite-element methods. Targeted at viscoelastic numerical modeling for multilayered media, the constant-Q acoustic wave equation is transformed into the corresponding wave integral representation with its Green＇s function accounting for viscoelastic coefficients. An efficient alternative for full-waveform solution to the integral equation is proposed in this article by extending conventional frequency-domain boundary element methods to viscoelastic media. The viscoelastic boundary element method enjoys a distinct characteristic of the explicit use of boundary continuity conditions of displacement and traction, leading to a semi-analytical solution with sufficient accuracy for simulating the viscoelastic effect across irregular interfaces. Numerical experiments to study the viscoelastic absorption of different Q values demonstrate the accuracy and applicability of the method.

Decay Rate for a Viscoelastic Equation with Strong Damping and Acoustic Boundary Conditions

This paper is concerned with a nonlinear viscoelastic equation with strong damping: . The objective of the present paper is to provide some results on the long-time behavior to this equation with acoustic boundary conditions. By using the assumptions on the relaxation function due to Tatar [1], we show an arbitrary rate of decay with not necessary of an exponential or polynomial one and without the assumption condition. The result extends and improves some results given in Cavalcanti [2].

Analysis of one-dimensional consolidation of fractional viscoelastic saturated soils under continuous drainage boundary conditions

This paper presents the one-dimensional(1D)viscoelastic consolidation system of saturated clayey soil under continuous drainage boundaries.The fractional-derivative Merchant(FDM)model has been introduced into the consolidation system to simulate the viscoelasticity.Swartzendruber’s flow law is also introduced to describe the non-Darcian flow characteristics simultaneously.The generalized numerical solution of the 1D consolidation under continuous boundaries is given by the finite difference scheme.Furthermore,to illustrate the effectiveness of the numerical method,two simplified cases are compared against the current analytical and numerical results.Finally,the effects of boundary parameters and model parameters on the viscoelastic consolidation were illustrated and discussed.The results indicated that the boundary parameters have a significant influence on consolidation.The larger the values of boundary parameters,the faster the whole dissipation of the excess pore-water pressure and soils’settlement rate.Fractional-order and viscosity parameter have little effect on consolidation,which are primarily significant in the middle and late consolidation phases.With the increase of the modulus ratio,the whole consolidation process becomes faster.Moreover,considering Swartzendruber’s flow delays the consolidation rate of the soil layer.

Stability conditions of explicit integration algorithms when using 3D viscoelastic artificial boundaries

Viscoelastic artificial boundaries are widely adopted in numerical simulations of wave propagation problems.When explicit time-domain integration algorithms are used,the stability condition of the boundary domain is stricter than that of the internal region due to the influence of the damping and stiffness of an viscoelastic artificial boundary.The lack of a clear and practical stability criterion for this problem,however,affects the reasonable selection of an integral time step when using viscoelastic artificial boundaries.In this study,we investigate the stability conditions of explicit integration algorithms when using three-dimensional(3D)viscoelastic artificial boundaries through an analysis method based on a local subsystem.Several boundary subsystems that can represent localized characteristics of a complete numerical model are established,and their analytical stability conditions are derived from and further compared to one another.The stability of the complete model is controlled by the corner regions,and thus,the global stability criterion for the numerical model with viscoelastic artificial boundaries is obtained.Next,by analyzing the impact of different factors on stability conditions,we recommend a stability coefficient for practically estimating the maximum stable integral time step in the dynamic analysis when using 3D viscoelastic artificial boundaries.

Mud-Wave Interaction: A Viscoelastic Model

This study is devoted to the interaction between water surface waves and a thin layer of viscoelastie mud on the bottom. On the assumption that the mud layer is comparable in thickness with the wave boundary layer and is much smaller than the wavelength, a two-layer Stokes boundary layer model is adopted to determine the mud motions under the waves. Analytical expressions are derived for the near-bettom water and mud velocity fields, surface wave-damping rate, and interface wave amplitude and phase lag. Examined in particular is how these kinematic quantities may depend on the viscous and elastic properties of the mud.

Stretching surface in rotating viscoelastic fluid

The boundary layer flow over a stretching surface in a rotating viscoelastic fluid is considered. By applying a similarity transformation, the governing partial differ- ential equations are converted into a system of nonlinear ordinary differential equations before being solved numerically by the Keller-box method. The effects of the viscoelastic and rotation parameters on the skin friction coefficients and the velocity profiles are thor- oughly examined. The analysis reveals that the skin friction coefficients and the velocity in the x-direction increase as the viscoelastic parameter and the rotation parameter in- crease. Moreover, the velocity in the y-direction decreases as the viscoelastic parameter and the rotation parameter increase.

Dynamic Analysis of Submarine Pipelines on an Elastic / Viscoelastic Foundation

This paper presents a new finite element method for solving static and dynamic problems in laying operation of pipelines. The effect of the viscoelastic soil behavior is considered by using the Pasternak foundation model. Some examples are also presented.

A Thermal Shock-Chemical Reactive Problem in Flow of Viscoelastic Fluid with Thermal Relaxation

Effects of thermal and species diffusion with one relaxation time on the boundary layer flow of a viscoelastic fluid bounded by a vertical surface in the presence of transverse magnetic field have been studied. The state space approach developed by Ezzat [1] is adopted for the solution of one-dimensional problem for any set of boundary conditions. The resulting formulation together with the Laplace transform techniques are applied to a thermal shock-chemical reactive problem. The inversion of the Laplace transforms is carried out using a numerical approach. The numerical results of dimensionless temperature, concentration, velocity, and induced magnetic and electric fields distributions are given and illustrated graphically for the problem.

斜入射地震波下单层球面网壳土-结构相互作用及其地震响应分析

为分析斜入射地震波下单层球面网壳土-结构相互作用及其地震响应,采用等效节点力实现地震波输入,通过黏弹性人工边界处理无穷远辐射条件,分析了地震波类型、土体参数、入射角度等因素对单层球面网壳结构的土-结构相互作用及其地震响应影响。结果表明:单层球面网壳结构在地震波入射一侧出现翘起,网壳总体沿入射方向发生旋转,当P波斜入射时支座位移差最大达0.514 m,为网壳跨度的1/250。当P波斜入射时,软弱土情况下网壳顶点位移比中硬土和中软土大,顶点位移随入射角增大呈现先增大后减小的趋势;当SV波入射时,中软土情况下网壳顶点位移比中硬土和软弱土大,顶点位移随入射角增大而增大。斜入射地震波下,考虑土-结构相互作用后网壳顶点位移增幅最大达5.5倍,网壳外圈位移增幅大于网壳跨中增幅。

基于改进傅里叶级数的黏弹性夹层板动力问题的数值算法研究

本文提出了一种基于改进傅里叶级数的新型数值算法,用于求解任意边界条件下黏弹性夹层板的自由振动特性。该算法利用一阶剪切理论建立面外位移场,采用改进的傅里叶级数拟合位移容许函数,结合Rayleigh-Ritz法计算动能和势能,并利用Hamilton变分原理得到振动特征矩阵方程。计算结果表明,无论是梁式板结构还是各种边界条件下的夹层板结构,该算法得到的自振频率和损耗因子与解析解、2D有限元解、数值计算法和ABAQUS有限元软件等计算结果相比,误差均不超过1%,计算效率提高了10倍,并且克服了传统方法只能求解特定边界下振动问题的局限性。本文建立的方法具有收敛性好、计算效率高和适应性强等特点。

考虑SSI效应的带地下室RC框架结构抗震性能研究

土-结构相互作用效应(Soil-Structure Interaction,SSI)是带地下室钢筋混凝土(Reinforced Concrete,RC)框架结构抗震性能分析的重要因素。基于模态和动力时程分析,通过有限元分析软件系统探究了地下室顶板嵌固、基础顶面嵌固和考虑SSI效应地下室周围土体嵌固等3种不同嵌固方式的RC框架结构抗震性能。结果表明:考虑SSI效应带地下室RC框架结构的自振周期明显延长,其中心柱剪力、各层加速度和层间位移角均有所减小;基础顶面嵌固模型未考虑SSI效应,其计算结果较为保守;SSI效应对带地下室RC框架结构会产生较大的减震影响。

铁路交通荷载作用下的土体移动多源黏弹性边界

黏弹性边界由于可以有效地消除土体边界反射、易与有限元结合等优点,成为结构-土体动力相互作用分析中常用的人工边界。黏弹性边界是基于单源和固体源提出的,然而交通荷载作用下轨枕、路基和桥墩等铁路基础设施振动引发的环境振动属于多源和移动源问题,采用现有的黏弹性边界会产生一定的误差。该研究基于多源及移动源的特点,利用波动方程对既有的黏弹性边界进行修正,提出了移动多源黏弹性边界方程。同时为减小前处理工作量,结合黏弹性本构方程和UMAT子程序构建了移动多源黏弹性边界单元,实现了边界单元材料属性的自动更新,并进行了算例验证。研究结果表明,在多源和移动源作用下,移动多源黏弹性边界和自由边界的计算结果差异基本保持在5%以内,而修正前的黏弹性边界与自由边界的垂向位移最大可相差35%。可以看出,相比于修正前的黏弹性边界,在处理多源和移动源问题时修正后的黏弹性边界具有更高的精度。

考虑土-结构相互作用永祚寺文峰塔地震响应分析

为研究土-结构相互作用对古塔地震响应的影响,借助ABAQUS有限元软件通过对地基土施加黏弹性边界,建立了不考虑土-结构相互作用(soil-structure interaction, SSI)效应、SSI效应下不考虑基础与地基土分离滑移与SSI效应下考虑分离滑移三种模型,通过时程分析法对比分析了SSI效应对山西省永祚寺文峰塔动力特性与破坏形态及损伤的影响。结果表明:考虑SSI效应后古塔高阶自振频率显著降低,其水平位移与层间位移角将总体增大,水平加速度放大系数呈下降趋势,塔下层损伤明显加剧且上层损伤有所降低,基础损伤明显;在设防地震作用下基础与地基土分离滑移现象加剧,有将沿中和轴破坏的风险,底层塔檐为薄弱部分,且基础的损伤不容忽视。分析结果对于预测高层密檐塔损伤破坏具有参考作用。

考虑土体非线性及倾角影响的盆地地震响应研究

基于二维沉积盆地模型,采用D-P弹塑性模型模拟盆地的非线性特征。利用显式有限元与黏弹性边界结合的方法,通过改变盆地边缘倾角,在时域和频域内分析盆地地表的地震动响应,对比线性与非线性盆地地震反应的差异。结果表明:(1)土体非线性对整个盆地范围内地震动的影响都较显著。考虑非线性时地震动放大系数明显降低,降低幅度在30%~50%。同时,考虑非线性和倾角影响时最强烈放大区域的范围和位置变化,且很小倾角下的分布特征显著不同。(2)两分量的放大系数都有随边缘倾角的增大而增强的趋势,但均是盆地边缘区域受非线性的影响最为显著。此外,真实地震波输入下显著放大区域的范围及线性与非线性结果的差异程度相对更大。(3)考虑非线性时,对于不同频率地震波的放大系数差别明显,但都表现出从低频到高频谱比分布越来越复杂的现象,同时盆地倾角的影响程度随频率的增大更加明显。(4)考虑土体非线性并未改变地震波传播的总体特征,但各震相强度相对降低。

塔顶排架结构对进水塔动力响应的影响

进水塔顶部启闭机室通常为排架结构,地震时往往先发生损坏导致水电站无法正常运行。为探索塔顶排架结构对进水塔动力响应的影响,针对某抽水蓄能电站下水库的进水口结构动力响应开展研究。基于双自由度无阻尼简化体系进行理论探索,并采用三维非线性有限元数值模拟方法计算进水塔有、无塔顶排架两种工况的自振特性、位移、加速度、应力、损伤体积比和能量耗散等指标来对比研究。任意时刻的地震反应用时程分析法求解,并引入黏弹性人工边界模拟地基辐射阻尼作用。结果表明,地震时进水塔—排架系统可能会产生鞭梢效应进而减小进水塔的动力响应。塔顶排架使进水塔的自振频率提高约2.10%~3.80%,使塔体关键点最大相对位移的最大值及最大加速度的最大值减小,减幅分别大于23.94%、22.30%。有排架时进水塔的拉应力降低而压应力增大,损伤体积比、塑性耗散能、损伤耗散能最大可减小23.93%以上。塔顶排架结构可以减小进水塔地震动力响应,对进水塔的抗震性能具有积极影响。