Attenuation of Solitary Waves and Localization of Breathers in 1D Granular Crystals Visualized via High Speed Photography

We investigate the propagation, attenuation, and localization of nonlinear elastic waves in a 1D granular crystal using high speed photography. We measure temporal displacement profiles of individual particles with a micrometer-scale resolution, and we reconstruct force profiles of propagating solitary waves and localized breathers by synchronizing and analyzing the acquired data. These investigations provide quantitative evidence for the transmission and attenuation trends of travelling solitary waves in a soft polymeric chain, which are significantly different from those in a hard metallic chain. We additionally study energy localization in a chain of hard particles embedded with a soft polymeric impurity. Specifically, we show that the proposed experimental technique is able to visualize the formation of localized breathers and quantify the energy highly concentrated in the vicinity of the impurity site—a phenomenon which can be exploited for harvesting vibrational energy in engineering applications. Finally, we compare, with good agreement, the experimental results with discrete element numerical simulations that account for dissipative effects due to viscoelasticity. The findings reported in this study imply that high speed photography can be an efficient and effective tool for non-contact measurements of nonlinear wave dynamics in granular lattices, despite their short characteristic times and minute displacements.     

Scattering of Nondispersive Waves at Nonlinear Joints in One-Dimensional Structures*

ABSTRACT

Reflection and transmission of nondispersive waves at a nonlinear joint between two elastic rods is considered. Equations that govern the reflected and transmitted waves are derived. These equations can be applied to joints which include nonlinear springs, nonlinear damping, nonlinear friction, and other types of nonlinearity. Analytic and numerical solutions of these equations are given for a joint that contains weakly nonlinear springs. Good agreement is obtained between the analytic and numerical solutions.     

复合弹模光弹模型中粘结约束应力的消除方法

本文对变弹性模量三维光弹地质体模型中的粘结约束应力进行了分析和讨论。同时,提出了两种消除变弹模光弹模型中粘结约束应力的方法。本文对变弹性模量三维光弹性实验的应用和发展具有一定的参考价值。     

应力波的激光产生和检测

应力波的激光产生和检测，是一个受到各领域专家关注的、在无损检测和应用力学等方面有着极大应用潜力和研究兴趣的新兴领域。针对其力学方面、实验技术和应用前景等，本文对有关原理、方法、技术和实用进行了简要的归纳与总结。     

Acoustic Waves in a Liquid with Solid Particles and Gas Bubbles

The mathematical model which determines acoustic wave propagation in a mixture of liquid with gas bubbles and solid particles is proposed. A system of differential equations is written and the dispersion relation is derived. Low- and high-frequency asymptotics of the phase velocity in the mixture considered are found and illustrated. The effect of solid particles and gas bubbles on acoustic wave dispersion and dissipation is indicated. For the mixture of fluid with solid particles considered the speed of sound is compared with available experimental data.     

The Behaviour of Perturbations to Travelling Waves Arising in Nematic Liquid Crystals

The stability of travelling waves which occur when a nematic liquid crystal is subjected to crossed electric and magnetic fields has been studied previously by (Stewart and Faulkner, Cont. Mech. Thermodyn. (1997)) where conditions on a control parameter q for stability to occur have been given. This article is concerned with the behaviour of the stable perturbations as time increases. For each of the three travelling wave solutions we calculate both the essential spectrum and the eigenvalues and use these to determine the long-term monotonic or oscillatory behaviour of the perturbations. The results are also relevant to liquid crystals subjected to a single field. Received January 14, 1998     

Suspended Particles Transport and Deposition in Saturated Granular Porous Medium: Particle Size Effects

An experimental study on the transport and deposition of suspended particles (SP) in a saturated porous medium (calibrated sand) was undertaken. The influence of the size distribution of the SP under different flow rates is explored. To achieve this objective, three populations with different particles size distributions were selected. The median diameter $d_{50}$ of these populations was 3.5, 9.5, and $18.3~\upmu \hbox {m}$ . To study the effect of polydispersivity, a fourth population noted “Mixture” ( $d_{50} = 17.4\; \upmu \hbox {m}$ ) obtained by mixing in equal proportion (volume) the populations 3.5 and $18.3\;\upmu \hbox {m}$ was also used. The SP transfer was compared to the dissolved tracer (DT) one. Short pulse was the technique used to perform the SP and the DT injection in a column filled with the porous medium. The breakthrough curves were competently described with the analytical solution of a convection–dispersion equation with first-order deposition kinetics. The results showed that the transport of the SP was less rapid than the transport of the DT whatever the flow velocity and the size distribution of the injected SP. The mean diameter of the recovered particles increases with flow rate. The longitudinal dispersion increases, respectively, with the increasing of the flow rates and the SP size distribution. The SP were more dispersive in the porous medium than the DT. The results further showed that the deposition kinetics depends strongly on the size of the particle transported and their distribution.     

硅晶体纳米压痕试验与应力场分析

采用纳米压入法测量了4种硅晶体的微压痕特性,讨论了加载过程与卸载过程的特征,分析了硅晶体的纳米压入测量结果,同时计算了硅晶体中的应力分布,计算结果表明,剪应力为硅晶体微薄片剥落失效的原因。     

大直径SHPB弥散效应的二维数值分析

采用轴对称动态有限元HONDO程序对大直径SHPB装置中压杆横向泊松效应引起的应力波弥散进行二维数值分析,并从以下三个方面讨论波形弥散的影响：（1）SHPB装置中压杆直径和杆长对弥散结果（主要是升时）的影响;（2）压杆中的波形弥散对试件应力-应变曲线的影响;（3）弥散对试件应变率的影响。分析表明,在直径SHPB弥散效应对实验结果的影响很大,必须考虑。     

Phase-Multiplied Photoelastic and Series Interferometer Arrangement for Full-Field Stress Measurement in Single Crystals

A compact, phase-multiplied, circular polariscope and series interferometer arrangement is developed for high-resolution, full-field stress measurement in single crystals with weak piezo-optical coefficients. We present a general stress-optic law, derived from anisotropic piezo-optical constitutive relations, which provides the theoretical framework for obtaining stress field components from measured optical isoclinic, isochromatic and isopachic phase maps. A new phase image processing technique is also developed, which combines data obtained from different interference configurations for the successful removal of low-modulation zones within isoclinic and isopachic phase maps. The validity and accuracy of the proposed interferometer arrangement and stress measurement methodology are demonstrated through a compression test of a c-cut single crystal sapphire plate loaded by a cylindrical indenter.     

非均质变截面杆中弹性波的反射和透射

基于一维弹性波理论，本文对应力波在非均质变截面杆中传播问题进行了一维简单波分析，并把分析结果与二维轴对称有限元分析结果进行了比较，表明一维简单波分析是非常有效和实用的。利用一维简单波分析方法，本文还揭示了应力波在非均质变截面杆中的传播规律，特别对含有内部交界面的非均质变截面杆（带有连接段）进行了一维等效简化分析，研究了连接段对应力波传播的影响。     

Stress Distribution in a Slip Trace of Deformed Ni3Ge Single Crystals

The shearstress distribution produced by distortion of Ni₃Ge single crystals under compression is studied. The evolution of the dislocation structure during deformation of Ni₃Ge single crystals of various orientations ([2¯34], [1¯11]$, [1¯39], and [001]) at T = 77, 293, 523, 673, and 873 K is analyzed. It was found that, up to failure strains, the dislocation structure is characterized by a uniform dislocation distribution. Regardless of the strainaxis orientation, the linear relation = f(^0.5) is valid for all the test temperatures except for T = 77 K. The deviation from the linear relation at T = 77 K is due to the suppressed thermally activated slip of dislocations in nonuniformstrain fragments at the specimen edges. In these fragments, the shear stresses are substantially reduced, and hence, the stresses produced by the dislocation cluster retard the development of slip in this trace.     

Reflection and Transmission of Elastic Waves at the Interface Between Water and a Double Porosity Solid

The reflection and transmission of an incident plane wave at an interface between water and a fluid-saturated double porosity solid are investigated. The properties of the three compressional waves and one shear wave in double porosity media are discussed in detail. The effect of the viscosity, permeability, and porosity on the phase velocity and attenuation of four bulk waves is presented. Comparison between the double porosity theory and the Biot theory reveals that there exists obvious difference in the phase velocity, attenuation and the reflection and transmission coefficients. Two cases of boundary conditions, i.e., the sealed-pore and the open-pore boundaries, are introduced in the numerical calculation. At last, the effect of the fracture permeability and porosity on the reflection and transmission coefficients considered. It is revealed that the amplitudes of the reflected and transmitted waves strongly depend the boundary condition, fracture permeability, and porosity.     

Stress Intensity Factor for the Interaction between a Straight Crack and a Curved Crack in Plane Elasticity

Formulation in terms of hypersingular integral equations for the interaction between straight and curved cracks in plane elasticity is obtained using the complex variable functions method. The curved length coordinate method and a suitable numerical scheme are used to solve such integrals numerically for the unknown function, which are later used to find the stress intensity factor, SIF.     

球壳中球形夹杂对SV波的三维散射与动应力集中研究

夹杂将导致结构应力集中,是降低结构承载能力重要影响因素,尤其是动载作用情况下,弹性波衍射和叠加将加剧应力集中程度.弹性波衍射方程建立和求解非常复杂,目前主要研究对象集中在二维模型情况,三维有限域内夹杂引起的动应力集中现象在大型结构中比较常见,有界域边界不仅作为边界条件,同时也是散射波波源,提高了求解难度.一般通过近似方法,将三维模型简化为二维情况,往往导致求解结果过于保守不能解释实际问题.论文针对三维球壳包含夹杂一般情况,分别以球壳和夹杂中心建立球坐标以描述球壳内、外壁和夹杂表面散射波势函数,并引入一种球波函数加法公式实现不同坐标下势函数转换,以求解应力集中状态.最后针对三维情况,给出多个动应力集中因子分布状态以描述动应力集中程度.文中研究为一般情况下含夹杂球壳结构的强度分析提供了理论支撑.     

组合超弹性材料中的空穴生成与增长

本文研究了一种组合不可压超弹性材料圆柱体中空穴的生成与增长问题，得到了这种材料受表面均布拉伸死荷载和轴向拉压共同作用下空穴生成问题的解析解，得到了不同组合情况下圆柱体中空穴生成时的临界载荷及分叉曲线，发现组合材料可以发生右分叉，也可以发生左分叉；给出了空穴生成后的应力分布，并讨论了所存在的应力间断和应力集中问题；通过能量比较分析了解的稳定性，讨论了发生右分叉或左分叉的条件，并分析了材料中预存微孔的增长情况。     

Reflection and Transmission of Elastic Waves from the Interface of a Fluid-saturated Porous Solid and a Double Porosity Solid

The reflection and transmission characteristics of an incident plane P1 wave from the interface of a fluid-saturated single porous solid and a fluid-saturated double porosity solid are investigated. The fluid-saturated porous solid is modeled with the classic Biot’s theory and the double porosity medium is described by an extended Biot’s theory. In a double-porosity model with dual-permeability there exist three compressional waves and a shear wave. The effects of the incident angle and frequency on amplitude ratios of the reflected and transmitted waves to the incident wave are discussed. Two boundary conditions are discussed in detail: (a) Open-pore boundary and (b) Sealed-pore boundary. Numerical results reveal that the characteristics of the reflection and transmission coefficients to the incident angle and the frequency are quite different for the two cases of boundary conditions. Properties of the bulk waves existing in the fluid-saturated porous solid and the double porosity medium are also studied.