轴向冲击载荷作用下锥壳中弹性应力波传播的计算和实验研究

本文利用有限元分析和模型实验研究了在轴向冲击载荷作用下,锥壳中弹性应力波的传播、计算和实验结果表明,结构中存在着弹性纵波和弹性弯曲波的传播,它们传播的速度各不相同,使壳面承受不同的应力状态;讨论了纵波和弯曲波随壳面的衰减;实验指出,由于边界的影响,即使纵波的反射也会产生新的反射弯曲波沿锥面传播。     

高度非线性孤立波与弹性大板的耦合作用研究

一维颗粒链的一端受到一个有初速度颗粒的撞击,导致颗粒连中产生稳定传播的应力波——高度非线性孤立波,该应力波的波长、波速以及幅值都能保持很好的稳定性,且遇到边界才会反射. 孤立波是一种良好的信息载体,广泛应用于无损检测技术中. 基于孤立波的特性,研究高度非线性孤立波与弹性大板耦合作用,基于赫兹定律和板的内在非弹性理论,推导出晶体链与大板的耦合微分方程组. 用龙格库塔法求解该微分方程组,得到颗粒链中各颗粒的位移、速度曲线. 通过分析回弹波出现的时间、回弹波所携带的能量以及模量、厚度、重力等对孤立波的影响,发现反射孤立波对大板的弹性模量和厚度尤为敏感,此外,颗粒链的摆放对整个耦合过程也有影响. 研究的结果为孤立波对结构体的无损探伤提供了理论依据,该技术可实现对结构体的快速检查和可控性研究.     

基于微形态模型的颗粒材料中波的频散现象研究

基于颗粒材料冲击与波动响应特性的调控波传播行为的超材料设计受到广泛关注,设计这类材料需要对颗粒材料的波传播机制及调控机理有深入认识. 波在颗粒材料中传播的频散现象及频率带隙等行为与材料的非均匀性密切相关,通常讨论频散现象是基于弹性理论框架建立微结构连续体或高阶梯度连续体等广义连续体模型来进行. 本研究基于细观力学给出了一个颗粒材料的微形态连续体模型. 在该模型中,考虑了颗粒的平动和转动,且颗粒间的相对运动分解为两部分:即宏观平均运动和细观真实运动. 基于此分解,提出了一个完备的变形模式,得到了对应于不同应变及颗粒间运动的宏细观本构关系. 结合宏观变形能的细观变形能求和表达式,获得了基于细观量表示的宏观本构模量. 应用所建议模型考察了波在弹性颗粒介质的传播行为,给出了不同形式的波的频散曲线,结果显示此模型具有预测频率带隙的能力.      

应力波传播与屈曲耦合情况下结构动力屈曲控制方程及波前边界条件的探讨

从应力波作用下结构动力屈曲的特点出发,指出应力波作用下结构屈曲与应力波传播的耦合导致时间成为结构屈曲的参变量,从而应力波作用下结构屈曲的真实运动与邻近运动是不同时刻、不同扰动区域的比较,这使得其控制方程的建立不宜采用传统的等时积分变分原理;以压应力波作用下弹性直杆为例,应用能量守恒原理,根据屈曲时刻结构能量的转换关系,建立了其屈曲控制方程,并实际推导得到了波前边界条件为横向位移,转角和曲率为零;其中,波前边界第三个条件出现的原因是轴向应力波的传播与屈曲的耦合.     

爆炸载荷下板条边界斜裂纹的动态扩展行为

为了研究爆炸应力波作用下板条边界斜裂纹的动态扩展行为,首先分析了爆炸应力波在含边界斜裂纹板条中的传播,其次采用动态焦散线实验方法,进行了爆炸载荷下板条边界斜裂纹扩展规律的实验研究.研究结果表明,爆炸应力波作用下,板条试件边界斜裂纹的扩展过程中,裂纹扩展速度、扩展加速度和裂尖动态应力强度因子随时间波动变化,扩展速度最大值...     

锚固洞室中不同方向爆炸应力波传播规律及裂纹形成机理研究

基于抗爆模型试验结果,利用数值分析软件研究锚固洞室中不同方向爆炸应力波传播规律及裂纹形成机理。通过分析锚固洞室爆炸压应力时程曲线规律,发现压应力时程曲线特征符合应力波的一般传播作用规律,这说明数值分析的结果比较合理。集中装药爆炸后,应力波以球面向四周扩散传播,随着时间推移,快速衰减。当应力波向上传播到地表时,会在地表附近发生多次“层裂”形成大面积裂纹,爆源从拱顶至侧墙,地表面附近受拉破坏越来越轻,其中直墙侧爆不发生受拉破坏;当应力波向下传播至地下洞室时,由于反射拉伸,会在锚固区及其末端发生“层裂”。随着应力波继续传播,经由上地表反射的拉伸波会与由洞室表面反射的拉伸波发生相遇,形成加载波,一旦加载波的强度大于围岩的动态抗拉强度,会在相应的位置形成裂纹。     

考虑应力波透反射作用的分层颗粒材料细观动力响应分析

为探究应力波界面透反射行为对分层黏弹性颗粒材料细观动力响应的影响规律，推导了界面透反射系数的理论表达，并建立了单频应力波入射和多频应力波入射两类条件下分层黏弹性颗粒材料的细观动力响应模型．典型算例分析结果表明：单频应力波入射时，上层颗粒动力响应形成“驻波”现象；双频应力波入射时，上下层颗粒动力响应均形成“行波”现象；两类条件下，分层界面处相邻颗粒的位移振幅均出现明显突变．以高速铁路无砟轨道路基基床为应用场景，分析基床填料刚度、阻尼系数及密度等参数对界面透反射特性的影响规律，探讨分层颗粒材料动力变形的调控思路，即增加基床表层填料的刚度、阻尼系数及密度，或减小基床底层填料的密度等措施可实现增益透射、抑制反射目标．此外，动力变形调控时还需控制路基颗粒材料固有频率远离动载激振特征频率．     

椭圆柱壳链的波形弥散特性研究

椭圆柱壳链可以引起波形弥散，从而可以调控应力波的传播.本文通过3D打印、冲击测试、细观有限元模拟和理论分析，研究了在质量块冲击加载下，单胞纵横比、冲击质量和速度对椭圆柱壳链中弹性波传播弥散行为的影响.结果表明，冲击过程中，椭圆柱壳链结构中的速度峰值随着波传播逐渐减小，纵横比越大或冲击质量越小，速度峰值衰减越剧烈，而冲击速度对椭圆柱壳链的波形弥散行为几乎无影响.相关研究对新型波形控制器的设计和精确有效地调控弹性波传播具有重要意义.     

直角平面区域内固定圆形刚性夹杂问题的Green函数解

利用复变函数法、多极坐标移动技术研究了直角平面区域内含有固定圆形夹杂时的反平面问题Green函数解.首先构造出不含夹杂的完整直角平面区域内满足边界应力条件的入射位移场;其次,建立直角平面区域内固定圆形夹杂对该入射场产生的满足直角边界应力自由条件的散射波解,并由叠加原理得到介质内的总波场.最后利用夹杂边界处的位移条件确定出散射波解中的未知系数,最终得到问题的Green函数解,还通过算例讨论了夹杂边界处的径向应力和环向应力随不同波数、角度和不同夹杂位置及不同点源位置的变化情况.算例结果表明了该文方法的有效实用性.     

梁中复合应力波的传播

采用有限差分法讨论了梁中复合应力波的传播．给出了粘塑性悬臂梁当自由端受突加弯矩载荷作用时梁内复合应力波传播的基本图象。指出，在冲击早期响应阶段．截面横向转动惯性效应起着重要作用，是不可忽视的。标志弹塑性边界的塑性效，一开始由自由端向固定端运动，但在反射卸载波的迎面作用下，会出现回退现象。在波动早期阶段，固定端主要处于弹性变形状态。此外，还对弹塑性梁中复合应力波的控制方程进行了必要的讨论。     

黏弹性固体中地下爆炸辐射地震波能量的演化

地下爆炸与介质的能量耦合和介质中的波传播机制是理解地下爆炸源物理的重要基础。为研究地下爆炸辐射地震波能量的传播衰减规律,分析了黏弹性介质中地下爆炸地震波能量的组成。基于无限介质中黏弹性球面波理论,给出了速度、位移、应力、应变等物理量Laplace域的理论解。利用Laplace数值逆求解方法,建立了黏弹性介质中地下爆炸辐射地震波场的计算方法。以干黄土作为典型黏弹性材料,计算给出了地震波能量的传播特征,分析了地下爆炸辐射能量的传播衰减规律。结果表明:（1）在黏弹性介质中,某球面处流入的能量随半径增加而逐渐降低。在理想弹性介质中,某球面处流入的能量在几倍弹性半径外即可稳定到某一定值;（2）在某一固定的有限观测区域内,当观测时间足够长时,势能和耗散能均趋于某一定值,辐射动能趋于零;（3）当有限的观测区域能容纳一个完整波长的地震波时,地震波辐射动能的稳态值随波传播距离的增大而减小,总体上可以用指数函数和幂函数进行分段拟合。     

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.     

Elastic waves in an electro-microelastic solid

The present study is concerned with the wave propagation in an electro-microelastic solid. The reflection phenomenon of plane elastic waves from a stress free plane boundary of an electro-microelastic solid half-space is studied. The condition and the range of frequency for the existence of elastic waves in an infinite electro-microelastic body are investigated. The constitutive relations and the field equations for an electro-microelastic solid are stemmed from the Eringen’s theory of microstretch elasticity with electromagnetic interactions. Amplitude ratios and energy ratios of various reflected waves are presented when an elastic wave is made incident obliquely at the stress free plane boundary of an electro-microelastic solid half-space. It has been verified that there is no dissipation of energy at the boundary surface during reflection. Numerical computations are performed for a specific model to calculate the phase speeds, amplitude ratios and energy ratios, and the results obtained are depicted graphically. The effect of elastic parameter corresponding to micro-stretch is noticed on reflection coefficients, in particular. Results of Parfitt and Eringen [Parfitt, V.R., Eringen, A.C., 1969. Reflection of plane waves from a flat boundary of a micropolar elastic half-space. J. Acoust. Soc. Am. 45, 1258–1272] have also been reduced as a special case from the present formulation.     

基于修正光滑粒子流体动力学算法的低能量耗散数值波浪水池开发

目前, 无网格光滑粒子流体动力学SPH粒子法在波浪与结构物相互作用研究方面得到广泛应用, 但该方法模拟波浪远距离传播时, 常常面临严重的能量耗散问题, 导致波高非物理性降低, 给大范围海域、长时间作用下的波-物耦合作用研究带来一定困难. 对此, 本文采用一种核函数修正算法, 在确保粒子间相互作用对称性的同时, 改进压力梯度离散项的计算精度, 设法解决SPH方法中能量非物理性耗散的难题. 相较于前人减缓能量非物理性衰减的方法, 本文的修正SPH算法避免了自由液面搜索等复杂处理过程, 并能保证动量守恒特性. 数值结果中, 采用振荡液滴、规则波、不规则波等算例, 验证本修正SPH算法的准确性和有效性. 结果表明, 该修正SPH算法能准确模拟振荡液滴形态变化, 且动能保持较好守恒性. 通过数值水池与物理水池两者规则波与不规则波结果的对比分析表明, 基于本文修正SPH算法建立的数值波浪水池具有较好的抗能量衰减效果, 能实现长时间、远距离波浪传播的准确模拟. 此外, 本算法能在低光滑长度系数条件下, 实现精确模拟, 将极大缩减三维SPH模拟的时间, 从而节约计算成本.      

曲面曲率对Rayleigh波传播特性的影响

对任意形状的均匀各向同性线弹性曲面物体,用 WKB～（1）方法求解了沿曲面传播的Rayleigh表面波的运动微分方程,同时考虑了波传播方向及其垂直方向曲面曲率对波的穿透性的影, 所获波动方程的势函数解答表明,在一般情况下垂直波传播方向的曲面曲率对波的穿透深度的影响是不容忽视的.进而以同种介质平面表面情况下的Rayleigh面波的传播特性为基准,给出了曲面曲率引起波数或波速变化的解析表达式.通过理论分析和数值算例,描述了曲面上Rayleigh面波传播行为的一些基本特征.     

Directional Wave Propagation in a Highly Nonlinear Square Packing of Spheres

We studied the dynamic response of a two-dimensional square packing of uncompressed stainless steel spheres excited by impulsive loadings. We developed a new experimental measurement technique, employing miniature tri-axial accelerometers, to determine the stress wave properties in the array resulting from both an in-plane and out-of-plane impact. Results from our numerical simulations, based on a discrete particle model, were in good agreement with the experimental results. We observed that the impulsive excitations were resolved into solitary waves traveling only through initially excited chains. The observed solitary waves were determined to have similar (Hertzian) properties to the extensively studied solitary waves supported by an uncompressed, uniform, one-dimensional chain of spheres. The highly directional response of this system could be used as a basis to design granular crystals with predetermined wave propagation paths capable of mitigating stress wave energy.     

Assessment of assembly shape and geometric effects on amplification of shear waves using discrete element method

The discrete element method (DEM) is a capable tool used to simulate shear wave propagation in granular assemblies for many years. Researchers have studied assembly shapes such as rectangles (in 2D simulations) or cylinders and cubes (in 3D simulations). This paper aimed to qualify the effect of assembly shape on the shear wave propagation and maximum amplification in the vertical plane (horizontal and vertical directions) caused by this propagation. To this end, shear wave propagations in different assembly shapes such as rectangle, trapezium, and triangle with rigid boundary conditions were simulated. A sine wave pulse was applied with a point source by moving a particle as the transmitter particle. To evaluate the shear wave velocity of the assemblies, the transmitter and receiver particles were simulated. All the simulations were performed with 2D DEM which is a useful tool to determine the amount and location of the maximum amplification factor of the assembly in both horizontal and vertical directions. An advantage of this study was assessing the effect of parameters such as input wave frequency, assembly height, shape, and aspect ratios on the amplification of the input waves.     

Reflection of longitudinal displacement wave at the viscoelastically supported boundary of micropolar half-space

The reflection of elastic waves at the boundary of micropolar half-space with the viscoelastic support is studied in this paper. The spring-dashpot model is used to model the viscoelastic support. The boundary condition includes the force stress, couple stress, the displacements and the micro-rotation and the contribution from the spring and the dashpot on them. The amplitude ratios and phase shifts of reflection waves with respect to the incident wave are obtained from the visco-elastic boundary conditions. Further, the energy flux ratios of the reflection waves to the incident wave are estimated and the energy flux conservation with consideration of the energy dissipation of visco-elastic boundary is used to validate the numerical results. Based on the numerical results, the influences of spring and dashpot are studied respectively. It is found that the elastically supported boundary and the viscously supported boundary have evident different influences on the amplitude ratio and the phase shift. The causes resulting in these deviations are related with the instantaneous elasticity of elastic boundary and the time-delay effects of viscous boundary.     

单向纤维增强复合材料中剪切波多重散射问题的复变函数法

基于弹性波的多体散射理论和复变函数方法,利用波函数展开法和保角映射方法,研究了任意形纤维增强复合材料中剪切波的传播。根据相应的边界条件确定弹性波模式系数。给出了复合材料中基体区和纤维核区的波场。作为算例,分析了相同入射频率,不同纤维核的尺寸和形状的情况下,弹性波的传播特性。通过分析发现,低频长波区,弹性波以近似正弦函数的形式传播,纤维核的尺寸和形状对波场影响不明显;随着频率的增加,影响变得明显,大于一定的频率,纤维核的形状可明显地辨别出。最后对结果进行了分析讨论。