垂直入射弹性波在一般各向异性压电材料单侧接触界面上的传播

弹性波垂直于压电材料摩擦接触界面入射会引起界面局部滑移或分离,导致问题具有边界非线性。应用傅里叶分析技术将问题的求解转化为一组代数方程,通过迭代-修正的方法确定粘着、滑移、分离区的分布位置,给出了各种状态产生的条件及规律。由于边界非线性导致波形畸变并诱发高频谐波,对某些各向异性压电材料,在某些条件下单一入射波遇到界面产生再极化,导致耦合P波及SV波产生,文中给出了高频谐波解及波形极化的产生条件。外加荷载和外加电场通过机电耦合效应对界面产生影响,通过实例分析,给出了外加作用力和电场对一般各向异性材料的影响规律,并分析了因为材料常数不同而引起的影响规律的不同。     

弹性波作用下压电体摩擦接触界面滑移特性分析

弹性波与压电体摩擦接触界面相互作用会引起界面滑移或分离,滑移和分离位置的分布与外加压力、剪力、电场及入射波的条件有关。应用Fourier分析及matlab软件给出了滑移范围的解,给出了粘着、滑移或分离的判定条件,通过算例分析了滑移和分离出现的影响因素和条件,为工程应用提供了理论依据。     

一般各向异性单侧接触界面上波的反射和折射

研究简谐弹性波在一般各向异性介质单侧接触界面上的反射和折射问题．利用Fouier分析方法将非线性Coulomb摩擦接触边界波动问题化为一组代数方程．给出了确定局部分离、滑移和粘着区的思路和方法及各区域的解；讨论了出现界面局部分离和滑移的条件．对特定材料组合情况进行了详细数值计算，给出了界面力、相对滑移速度、张开位移、高频谐波的反射折射系数等特征参量；考察了平面和反平面波动的耦合及整体滑移等．其中关于高频谐波的结果可对已有实验结果给出很好的定性解释．在大多数情况下，即使对摩擦系数无穷大的粘滞接触界面，分离区端部也总是存在一个很小的滑移区。     

单侧摩擦接触约束夹杂物与平面波的动力相互作用--时域边界元分析

应用时域边界元法研究了瞬态平面波对单侧摩擦约束夹杂物的散射问题，假设界面摩擦遵守库仑定理，当入射波足够强时界面会出现局部分离和滑移，由于边界上的区域(分离区、滑移区和粘着区)是未知的，所以该问题实际上是个复杂的边界非线性问题，为了确定未知区域，该文发展了一种有效的迭代技术，作为算例，计算了一个无限域中圆柱埋置夹杂物对瞬态平面波的散射问题。     

平移断层的倾角对地震产生的影响

利用边界单元法和滑移弱化摩擦本构关系分析了平移断层上地震的产生。从依赖于速率和状态的摩擦本构关系出发,通过忽略速度的影响得到了滑移弱化摩擦本构关系。建立了两种本构关系之间的联系,使得在两种模型中可以使用共同的参数。通过将地球表面模拟成一个包含在无穷大弹性介质中的无穷大裂纹,已有的边界积分方法可以直接用来分析断层的滑移。由于断层上的摩擦本构关系的非线性,得到的方程也是非线性的,采用牛顿迭代法进行求解。通过数值计算得到了平移断层上滑移位移、速度及摩擦力的分布规律。考察了平移断层的倾角对地震产生的影响,计算结果表明断层的倾角越小,地震产生的位置离地球表面越近且地震产生所需滑移的时间越短。     

弹性半空间中含粘性滑移界面圆形衬砌洞室对平面SH波的散射

为揭示粘性滑移界面对衬砌洞室地震响应规律的影响,采用一种高精度的间接边界积分方程法,基于粘性滑移界面模型,求解了弹性半空间中浅埋圆形衬砌洞室对入射平面SH波的散射。结果表明:中低频波入射时,随着界面滑移刚度系数的增加,衬砌洞室上方地表位移幅值减小,而界面粘性系数对地表位移反应不明显;衬砌内壁应力幅值随界面滑移刚度系数的增加而增大。高频波入射下,较小的界面粘性系数对地表位移放大效应更为显著;当界面滑移刚度系数较小时,部分频段由于体系共振效应会造成显著的应力集中;高频特别是共振频率段,粘性系数对应力幅值有明显的降幅效应。研究结论可为实际地下工程结构的抗震设计提供部分理论依据。     

粘塑性流体的界面滑移对润滑性能的影响研究

首先指出经典润滑理论中的边界无滑移条件已不再适用于具有极限剪应力的粘塑性流体润滑．而后,通过确定最大剪应力位置和加入剪应力边界条件,建立了界面滑移后的润滑方程．在联立求解不同区域的润滑方程基础上,对界面滑移的开始位置及扩展方式进行了分析．最后,讨论了不同膜厚比下滑移对润滑性能的影响．     

钢板夹芯混凝土组合板界面滑移计算分析

在钢板夹芯混凝土组合板中,界面滑移是影响组合板力学性能的一个重要因素。通过对界面滑移的理论分析,建立了其微分方程;根据截面剪力分布和边界条件求出了任意集中载荷和均布载荷作用下界面滑移的计算公式。采用实验结果对本文公式的合理性进行了验证,最大误差为22.22%。根据计算结果及其比较分析可知:界面滑移沿组合板纵向呈非线性变化,组合板端部界面滑移最大,沿组合板纵向向跨中逐渐减小,跨中界面滑移为零;剪力连接程度、含钢率对界面滑移影响较大,混凝土强度等级对其影响较小;界面滑移随着剪力连接程度的提高、含钢率的降低、混凝土强度等级的提高而减小。     

动压载荷下受限纳米水膜流动特性的分子动力学仿真研究

利用分子动力学模拟方法探究了外加载荷作用下纳米尺度受限水膜的流动特性.仿真结果表明:受限空间内的水膜随着载荷的增加,其出现分层现象和黏度增加,当黏度超过一个临界值后,在分层和黏度增加共同作用下,水膜的流动状态将由层流和湍流的混合状态过渡到单一的层流状态.同时,随着受限空间壁面的切向运动,受限水膜均会出现边界滑移现象,且随着载荷的增加,滑移现象越发显著.但当水膜单一层流状态形成后,受限空间壁面的滑移速度,对水膜的边界滑移长度影响并不显著.     

非周期波浪与直墙作用的非线性数值研究

基于时域高阶边界元方法,建立了完全非线性二维数值波浪水槽,对非周期波浪与直墙的相互作用问题进行了模拟和研究.自由表面满足完全非线性自由水面运动学和动力学边界条件,采用混合欧拉-拉格朗日方法追踪瞬时自由面流体质点,采用四阶Runge-Kutta法对下一时间步的波面和自由面速度势进行更新.采用加速度式法求解直墙表面速度势的时间导数,对瞬时物体湿表面上的水动力压强积分,得到作用在物体上的瞬时波浪力.首先,将全非线性与Serre-Green-Naghdi(SGN)模型的结果进行了对比分析,发现对于大幅值双入射波问题,仅满足弱色散关系的SGN模型大大低估了最大波浪爬高;其次,研究了双入射波与直墙的非线性作用问题,发现线性预报对波浪最大爬高有较大低估,而波浪的非线性成分不只导致了自由面爬高的异常增大,也引起了局部自由面的高频振荡,该物理过程中,直墙所受的波浪载荷,也展示出了与波浪爬高相似的非线性特性;最后,对波浪爬升和波浪力的时间历程进行了频谱分析,发现入射主频波的部分能量传递给了更高频的波浪成分,反映出该问题具有典型的非线性特性.     

Propagation of harmonic waves through micro gap with consideration of frictional contact

Transmission of elastic waves through a micro gap between two solids with consideration of frictional contact is investigated.By using the Fourier analysis technique and the corrective solution method,the nonlinear boundary problem is reduced to a set of algebraic equations.Numerical results exhibit the locations and extents of separation, slip,and stick zones,the interface tractions,and the energy partition.The effects of gap width,frictional coefficients,and the incident angle on the wave transmission ...     

DYNAMIC INTERACTION OF PLANE WAVES WITH A UNILATERALLY FRICTIONALLY CONSTRAINED INCLUSION-TIME DOMAIN BOUNDARY ELEMENT ANALYSIS

A 2D time domain boundary element method (BEM) is developed to solve the transient scattering of plane waves by a unilaterally frictionally constrained inclusion. Coulomb friction is assumed along the contact interface. The incident wave is assumed strong enough so that localized slip and separation take place along the interface. The present problem is in effect a nonlinear boundary value problem since the mixed boundary conditions involve unknown intervals (slip, separation and stick regions). In order to determine the unknown intervals, an iterative technique is developed. As an example, we consider the scattering of a circular cylinder embeddedin an infinite solid.     

Boundary film shear elastic modulus effect in hydrodynamic contact. Part II: influence of operational parameters

The present paper is the subsequent research of the first part (Theor Comput Fluid Dyn, 2009). It investigates the boundary film shear elastic modulus effect in a hydrodynamic contact in different operating conditions. The hydrodynamic contact is one-dimensional, composed of two parallel plane surfaces, which are respectively rough rigid with rectangular micro projections in profile periodically distributed on the surface and ideally smooth rigid. The whole contact consists of cavitated area and hydrodynamic area. The hydrodynamic area consists of many micro Raleigh bearings which are discontinuously and periodically distributed in the contact. The hydrodynamic contact in a micro Raleigh bearing consists of boundary film area and fluid film area which, respectively, occur in the outlet and inlet zones. In boundary film area, the film slips at the upper contact surface due to the limited shear stress capacity of the film–contact interface, while the film does not slip at the lower contact surface due to the shear stress capacity of the film–contact interface large enough. In boundary film area, the viscosity, density, and shear elastic modulus of the film are varied across the film thickness due to the film–contact interactions, and their effective values are used in modeling which depends on the film thickness. In fluid film area, the film does not slip at either of the contact surfaces, and the shear elastic modulus of the film is neglected. It is found from the simulation results that the boundary film shear elastic modulus influences are normally negligible on the mass flow through the contact, the carried load of the contact and the overall film thickness of the contact, and the boundary film shear elastic modulus would normally influence the local film thickness in an elastic contact when the local film thickness is on the film molecule diameter scale. It is also found that the boundary film shear elastic modulus effect has the tendency of being increased with the reduction of the width of a micro contact. It is increased with the reduction of the boundary film–contact interfacial shear strength or with the increase of the critical boundary film thickness, while it is strongest at certain values of the contact surface roughness, the width ratio of fluid film area to boundary film area, and the lubricant film shear elastic modulus.

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Interesting effects in harmonic generation by plane elastic waves

The harmonics of plane longitudinal and trans-verse waves in nonlinear elastic solids with up to cubic nonlinearity in a one-dimensional setting are investigated in this paper. It is shown that due to quadratic nonlinearity, a transverse wave generates a second longitudinal harmonic. This propagates with the velocity of transverse waves, as well as resonant transverse first and third harmonics due to the cubic and quadratic nonlinearities. A longitudinal wave generates a resonant longitudinal second harmonic, as well as first and third harmonics with amplitudes that increase linearly and quadratically with distance propagated. In a second investigation, incidence from the linear side of a pri-mary wave on an interface between a linear and a nonlinear elastic solid is considered. The incident wave crosses the interface and generates a harmonic with interface conditions that are equilibrated by compensatory waves propagating in two directions away from the interface. The back-propagated compensatory wave provides information on the nonlinear elastic constants of the material behind the interface. It is shown that the amplitudes of the compensatory waves can be increased by mixing two incident longitudinal waves of appropriate frequencies.     

Boundary film shear elastic modulus effect in hydrodynamic contact. Part I: theoretical analysis and typical solution

Boundary film shear elastic modulus effect is analyzed in a hydrodynamic contact. The contact is one-dimensional composed of two parallel plane surfaces, which are, respectively, rough rigid with rectangular micro projections in profile periodically distributed on the surface and ideally smooth rigid. The whole contact is consisted of cavitated area and hydrodynamic area. The hydrodynamic area consists of many micro Raleigh bearings which are discontinuously and periodically distributed in the contact. Analysis is thus carried out for a micro Raleigh bearing in this contact. The hydrodynamic contact in this micro Raleigh bearing consists of boundary film area and fluid film area which, respectively, occur in the outlet and inlet zones. In boundary film area, the film slips at the upper contact surface due to the limited shear stress capacity of the film–contact interface, while the film does not slip at the lower contact surface due to the shear stress capacity large enough at the film–contact interface. In boundary film area, the viscosity, density and shear elastic modulus of the film are varied across the film thickness due to the film–contact interactions, and their effective values are used in modeling, which depend on the film thickness. The analytical approach proposed by Zhang (J Mol Liq 128:60–64, 2006) and Zhang et al. (Int J Fluid Mech Res 30:542–557, 2003) is used for boundary film area. In fluid film area, the film does not slip at either of the contact surfaces, and the shear elastic modulus of the film is neglected. Conventional hydrodynamic analysis is used for fluid film area. The present paper presents the theoretical analysis and a typical solution. It is found that for the simulated case the boundary film shear elastic modulus effects on the mass flow through the contact, the overall film thickness of the contact and the carried load of the contact are negligible but the boundary film shear elastic modulus effect on the local film thickness of the contact may be significant when the boundary film thickness is on the 1 nm scale and the contact surfaces are elastic. In Part II will be presented detailed results showing boundary film shear elastic modulus effects in different operating conditions.

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Hertzian fracture at unloading

Hertzian fracture through indentation of flat float glass specimens by steel balls has been examined experimentally. Initiation of cone cracks has been observed and failure loads together with contact and fracture radii determined at monotonically increasing load but also during unloading phases. Contact of dissimilar elastic solids under decreasing load may cause crack inception triggered by finite interface friction and accordingly the coefficient of friction was determined by two different methods. In order to make relevant predictions of experimental findings, a robust computational procedure has been developed to determine global and local field values in particular at unloading at finite friction. It was found that at continued loading it is possible to specify in advance how the contact domain divides into invariant regions of stick and slip. The maximum tensile stress was found to occur at the free surface just outside the contact contour, the relative distance depending on the different elastic compliance properties and the coefficient of friction. In contrast, at unloading invariance properties are lost and stick/slip regions proved to be severely history dependant and in particular with an opposed frictional shear stress at the contact boundary region. This causes an increase of the maximum tensile stress at the contour under progressive unloading. Predictions of loads to cause crack initiation during full cycles were made based on a critical stress fracture criterion and proved to be favourable as compared to the experimental results.     

Analysis of electric boundary condition effects on crack propagation in piezoelectric ceramics

There are three types of cracks: impermeable crack, permeable crack and conducting crack, with different electric boundary conditions on faces of cracks in piezoelectric ceramics, which poses difficulties in the analysis of piezoelectric fracture problems. In this paper, in contrast to our previous FEM formulation, the numerical analysis is based on the used of exact electric boundary conditions at the crack faces, thus the common assumption of electric impermeability in the FEM analysis is avoided. The crack behavior and elasto-electric fields near a crack tip in a PZT-5 piezoelectric ceramic under mechanical, electrical and coupled mechanical-electrical loads with different electric boundary conditions on crack faces are investigated. It is found that the dielectric medium between the crack faces will reduce the singularity of stress and electric displacement. Furthermore, when the permittivity of the dielectric medium in the crack gap is of the same order as that of the piezoelectric ceramic, the crack becomes a conducting crack, the applied electric field has no effect on the crack propagation. The project supported by the National Natural Science Foundation of China (19672026, 19891180)