血液-血管耦合特性与脉搏波传播特性的关系

脉搏波既不可简单地理解为可压缩血液流体中的压力纵波,也不可简单地理解为沿固体血管传播的涨缩位移横波,而是超乎普通想象的流-固耦合和纵波-横波耦合的复杂波。从分析耦合本构关系的新途径出发,本文中提出了一个流-固耦合/纵波-横波耦合的串联模型,可为解读“位数形势”中医脉诊提供更丰富的信息。结果表明,脉搏波耦合系统的等效体积压缩模量K_s以及相应的耦合系统脉搏波传播速度c_s主要依赖于两个无量纲参数:血液-血管模量比K_b(p)/E(p)和薄壁血管径厚比D(p)/h₀,它们因人而异、因人的不同脉搏位置而异。文中定量分析了它们对c_s的影响,显示人体的K_b/E值在103数量级,从而c_s值在100～101 m/s数量级,以适应人体生理生化反应。由临床有创测量,证实脉搏体积横波与脉搏压力纵波是相耦合地以相同速度传播;还显示脉搏波是在其波阵面上具有氧合生化反应的“生物波”。此外,还讨论了“脉压放大”现象与非线性本构关系和与血管分叉处加载增强反射之间的关系,并讨论了Lewis关于重搏波形成的假设。     

脉搏波本构关系实验研究的探索

脉搏波本构关系决定着脉搏波的传播特征。如何通过实验研究来确定脉搏波本构关系，以及如何通过这些方法从现有文献数据来获得脉搏波本构关系，是当前研究的核心之一。本文中探索了3个可行途径:(1)由实测脉搏波波速对压力的关系C(p)进行反分析（无创法）；(2)直接对脉搏波p-V本构关系进行实测（有创法）；(3)由一系列实测脉搏波波形进行Lagrange反分析（无创法）。采用上述方法，根据现有文献数据，发现由C(p)关系的Rogers-Huang简化式可推得指数型p(V)本构关系；由MK-Hughes式可推得对数型p(V)本构关系。脉搏波传播特性随非线性本构参数发生显著变化。按中医体质分类观点，相应的脉搏波本构关系原则上也有不同类型，因人而定。在这个意义上，脉搏波的Lagrange反分析具有广阔发展前景，但它对正确选择测点和提高测量敏感性和精度等方面提出了更高要求。     

固体的动力学性质与非线性波动问题的研究

一、前言非线性介质是指描述物体的应力和变形(包括变形速率和变形历史)的本构关系是非线性的。这种非线性性质往往和物体的有限变形联系在一起。在高速变形条件下,金属、岩石、高分子聚合物、复合材料、土壤等表现出不同的力学性质,应力波的传播规律也各不相同。研究非线性介质中波动的一般理论;应力波在各种介质中发生、发展、相互作用和转化的规律以及通过各种测试手段,尤其是对各种波动讯号的测量来确定材料的动态力学性质,构作本构方程成为近代力学发展 ...     

论心脏功能的“泵说”与“波说”

分析了心脏功能的“泵说”和“波说”。研究表明,心脏扮演的角色实际上不是泵,而是脉搏波发生器,产生一系列携带能量的脉搏波。每个脉搏波由升支和降支组成。前者对应于加载过程:压力、粒子速度、能量和血氧饱和度均随时间升高。而后者则对应于卸载过程:压力、粒子速度、能量以及血氧饱和度都下降,直至为零。因此,“泵说”中诸如Windkessel效应、一机二泵和舒张泵等概念都难以成立。所谓约1.5 W的心脏功率实质上表征了每个脉搏波的功率。针对脉搏波是流-固耦合和纵波-横波耦合的复杂波之特征,研究表明,能量的主要部分(99.99%)由横波携带,它沿固体血管传播,损耗低,效率高。研究还表明,血管分支处广义波阻抗的增大有助于抵消脉搏波传播中的衰减耗散,升高传入血管分支的脉搏波脉压,可视为人体的一种自我调节机制。     

弯曲动脉壁非线性弹性力学性质的理论分析

血管壁非线性力学特性是探索心血管中的血液流动规律及脉搏波传播现象的一个重要前提．在血管力学研究中,直管动脉壁的本构方程已有相当深人的研究,唯独象主动脉弓那样的弯管动脉壁本构方程;至今还没有建立一个理论模型．文中在已有的直管动脉壁本构方程研究基础上,提出一个理论方法来分析弯曲动脉壁的非线性弹性力学性质,在弯曲动脉壁被模拟为均质、正交各向异性、不可压缩材料的前提下,作者从理论上建立了一个表达弯管动脉壁非线性弹性性质的三维ｅ指数型本构方程文中还探讨了弯曲动脉壁内的残余应变分析．     

Klein-Gordon波动方程多波传播的非线性特性

基于双波初值问题,讨论非线性对多波传播的影响。通过选取合适的多重尺度,对Klein-Gordon波动方程进行变形,得到方程的解的多尺度展式首项近似和三波传播时速度相互影响的定量关系,揭示了多波传播的非线性特性;最后,应用Mathematica对波动方程进行数值仿真。研究结果表明,另外多个波的存在会使波的传播速度（相速）超过独自传播时的速度（相速）。     

夹层圆柱壳中弹性波传播的辛特性分析

论文研究了正交各向异性夹层圆柱壳中轴对称自由简谐波的传播问题.通过对变量合理的组织变换,将结构本构方程化为状态空间形式,采用分段平均假设得到哈密顿矩阵,进而利用哈密顿系统下的辛数学方法,扩展的Wittrick-Williams算法及精细积分方法,得到各种夹层结构波传播问题的频散关系,并将该方法与多项式方法进行对比,验证了该方法在多孔结构波传播问题中的优越性.     

短纤维增强对聚碳酸酯非线性粘弹性性能的影响

本文采用SHP B装置研究了聚碳酸酯和短玻璃纤维增强聚碳酸酯在10-4～103/秒应变率范围和有限应变条件下的非线性粘弹性力学行为。根据Coleman和Noll的材料本构关系理论和本文实验结果,提出聚碳酸酯的本构方程 m（e,（?））=E0e+e2+e3+E1 integral from n=0 to 1（（?）exp（-（t-）/1）d）+E2 integral from n=0 to 1（（?）exp（-（t-）/2）d+（?）） 并进而得到短纤维增强聚碳酸酯的一个相当简单的本构方程 frm=m（e,（?）） 在加卸载全过程,两种本构方程的理论计算值都能满意地与实验结果相一致。     

研究材料动态本构特性中的重要作用

在材料动态本构关系的研究中，不论是由波传播信息反求材料本构关系，即所谓解第二类反问题，还是利用应力波效应和应变率效应解耦的方法（如SHPB技术），应力波传播实际上都起着关键作用。在一般性讨论的基础上，就SHPB试验技术分析了应力波传播如何影响材料动态本构特性的有效确定。对于应力/应变沿试件长度均匀分布假定以及一维应力波假定，着重进行了分析。     

复杂介质中任意阶频率依赖耗散声波的分数阶导数模型

实验现象表明,声波在复杂介质中传播时,其衰减往往呈现频率的任意次幂律依赖现象.鉴于复杂介质的力学和物理性质的记忆性和长程相关性,频率幂律依赖的声波衰减现象难以用经典的声波方程描述,因为经典的阻尼波方程和近似热黏性波方程只能分别描述与频率无关和频率二次方依赖的声衰减.近年来,带有分数阶导数项的声波方程已被成功用于描述这一声衰减现象.基于课题组对声波衰减分数阶导数建模的研究,对已有的分数阶导数声波方程的研究进展及获得的成果做一个系统的综述,重点讨论这些模型的力学本构、统计力学解释等.简述了软物质中声波传播的时间分数阶导数唯象模型和本构模型,空间分数阶导数唯象模型和本构模型,并深入讨论了各种模型之间的联系与区别:介绍了分数阶导数声波模型在多孔介质中的成功应用,该部分内容涉及了均匀和非均匀多孔介质,刚性固体骨架和可变形固体骨架多孔介质等;通过空间分数阶扩散方程与Levy稳定分布之间的联系,给出了频率幂律依赖指数的变化区间为[0,2]的统计力学解释.最后,讨论了声波传播耗散行为的分数阶导数建模领域仍然存在的问题,并对今后的研究方向进行了探讨和展望.     

Wave propagation and dispersion in microstructured wool felt

On the basis of the experimental data of the piano hammers study the one-dimensional constitutive equation of the wool felt material is proposed. This relation enables deriving a nonlinear partial differential equation of motion with third order terms, which takes into account the elastic and hereditary properties of a microstructured felt. This equation of motion is used to study pulse evolution and propagation in the one-dimensional case. Thorough analysis both of the linear and nonlinear problems is presented. The physical dimensionless parameters are established and their importance in describing the dispersion effects is discussed. It is shown that both normal and anomalous dispersion types exist in wool felt material. The dispersion analysis shows also that for the certain ranges of physical parameters negative group velocity will appear. The initial value problem is considered and the analysis of the numerical solution describing the strain wave evolution is provided. The influence of the material parameters on the form of a propagating pulse is demonstrated and explained.     

Reflection of long waves from a “nonreflecting” bottom profile

The transformation of long surface waves in a zone of variable depth is investigated within the framework of shallow-water theory. In the particular case of a bottom profile containing a so-called “nonreflecting” relief segment adjacent to an even bottom, expressions for the reflected and transmitted pulse waves are obtained in explicit form. It is shown that waves are reflected from such a profile. The role of distributed and concentrated reflection of a wave propagating above an uneven bottom is discussed.     

On the energy conservation and critical velocities for the propagation of a ＂steady-shock＂ wave in a bar made of cellular material

The propagation of shock waves in a cellular bar is systematically studied in the framework of continuum solids by adopting two idealized material models, viz. the dynamic rigid, perfectly plastic, locking （D-R-PP-L） model and the dynamic rigid, linear hardening plastic, locking （D-R-LHP-L） model, both considering the effects of strain-rate on the material properties. The shock wave speed relevant to these two models is derived. Consider the case of a bar made of one of such material with initial length L 0 and initial velocity v i impinging onto a rigid target. The variations of the stress, strain, particle velocity, specific internal energy across the shock wave and the cease distance of shock wave are all determined analytically. In particular the ＂energy conservation condition＂ and the ＂kinematic existence condition＂ as proposed by Tan et al. （2005） is re-examined, showing that the ＂energy conservation condition＂ and the consequent ＂critical velocity＂, i.e. the shock can only be generated and sustained in R-PP-L bars when the impact velocity is above this critical velocity, is incorrect. Instead, with elastic deformation, strain-hardening and strain-rate sensitivity of the cellular materials being considered, it is appropriate to redefine a first and a second critical impact velocity for the existence and propagation of shock waves in cellular solids. Starting from the basic relations for shock wave propagating in D-R-LHP-L cellular materials, a new method for inversely determining the dynamic stress-strain curve for cellular materials is proposed. By using e.g. a combination of Taylor bar and Hopkinson pressure bar impact experimental technique, the dynamic stress-strain curve of aluminum foam could bedetermined. Finally, it is demonstrated that this new formulation of shock theory in this one-dimensional stress state can be generalized to shocks in a one-dimensional strain state, i.e. for the case of plate impact on cellular materials, by simply making proper replacements of the elastic and plastic constants.     

花岗岩体中应力波传播计算的动态本构关系

在花岗岩体的弹性区域,对实测径向质点速度波形运用Lagrangian分析方法,得到了球面应力波传播的加载速率相关的应力应变关系曲线。由速率相关本构关系所作的计算结果表明,它能较正确地描述岩石中球面应力波传播过程中所体现的主要特征,即应力波峰值衰减指数大于1和波形剖面的展宽。     

The growth and decay of acceleration waves of arbitrary form in bkz viscoelastic fluids

The article explores the amplitude behavior of an acceleration wave of arbitrary form propagating into a particular non-linear viscoelastic fluid with memory. The media is assumed to obey the incompressible, isotropic and isothermal BKZ constitutive model. Investigation is restricted to waves propagating into regions which have been at rest in their reference configuration. Specific cases of plane, cylindrical and spherical wave fronts are examined. The results indicate that the acceleration wave amplitude (which is transverse) obeys a similar equation as found by Varley for simple materials, and hence will always decay.     

Mechanical wave momentum from the first principles

Axial momentum carried by waves in a uniform waveguide is considered based on the conservation laws and a kind of the causality principle. Specifically, we examine (without resorting to constitutive data) steady-state waves of an arbitrary shape, periodic waves which speed differs from the speed of its form and binary waves carrying self-equilibrated momentum. The approach allows us to represent momentum as a product of the wave mass and the wave speed. The propagating wave mass, positive or negative, is the excess of that in the wave over its initial value. This general representation is valid for mechanical waves of arbitrary nature and intensity. The finite-amplitude longitudinal and periodic transverse waves are examined in more detail. It is shown in particular, that the transverse excitation of a string or an elastic beam results in the binary wave. The closed-form expressions for the drift in these waves functionally reduce to the Stokes’ drift in surface water waves (a half the latter by the value). Besides, based on the general representation an energy–momentum relation is discussed and the physical meaning of the so-called “wave momentum” is clarified.