脉搏波系统的力学模型及反演兼对若干中医学问题的讨论

对脉搏波进行客观化定量研究,是我们面临的跨中医与西医、跨医学与数理学科的新挑战,是中国传统医学现代化发展的重点研究课题之一.本文遵循中医整体观点的传统思路,把脉搏波系统理解为生命能量以波的形式在血液中传播的整个系统,从连续介质力学的波动理论出发,为脉搏波系统建立一个等价的力学模型,并把力学反演方法推广发展到脉搏波.指出脉搏波是压力波P（X,t）,质点速度波v（X,t）、比容波V（X,t）和内能波E（X,t）这些不同形式波动的总成.脉搏现象包含着血液的流动和在血液中以远快于血液流速之波速传播的携带能量的脉搏波.前者是人眼易见的实体血液的“物质流”,而后者是人眼不易见、以波的形式传播的“能量流”,可分别理解为中医的“血”和“气”.脉搏波的传播特性由反映生命体整体系统的本构方程决定,就其重要性和地位而言,系统本构方程与中医的体质相当,应探索其内在联系.初步讨论了脉搏波系统本构关系非线性效应和黏性效应对脉搏波特性的影响.      

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。     

流体饱和标准线性粘弹性多孔介质中的平面波

研究了流体饱和不可压标准线性粘弹性多孔介质中平面波的传播和反射问题．在固相骨架小变形的假定下,得到了粘弹性多孔介质中波动方程的一般解,讨论了弥散关系和波的衰减特性．结果表明：在流体饱和不可压粘弹性多孔介质中,仅存在一个耦合纵波和一个耦合横波,纵波和横波的波速、衰减率等取决于孔隙流体与固相骨架间的相互作用以及固相骨架本身的粘性．同时,研究了半空间自由边界上入射波(纵波、横波)的反射问题。得到了非均匀反射波的波速、反射系数、衰减率等的表达式及其相关的数值结果．     

饱和黏弹性多孔介质中的平面波及能量耗散

研究了流体饱和不可压黏弹性多孔介质中的非均匀平面波及其能量流和能量耗散规律. 在流 相和固相物质微观不可压、固相骨架宏观服从积分型本构关系和小变形的假定下，利用 Helmholtz分解，得到了饱和黏弹性多孔介质中非均匀平面波的一般解以及纵波、横波相速 度和衰减率等的解析表达式，分析了平面波传播矢量和衰减矢量之间的关系. 数值结果表明 孔隙流体与固相骨架间的相互作用以及固相骨架的黏性对波的相速度、衰减率等有着显著的 影响. 同时，得到了饱和黏弹性多孔介质的能量方程，给出了能量流矢量和能量耗散率. 对 非均匀平面纵波和横波，推导了平均能量流矢量和平均能量耗散率的解析表达式.     

G/E材料动态力学性能的应力波实时测定

线性粘弹性复合材料的动态力学性能测定不同于弹性材料静态力学性能的测定,而应力波方法又是不同于其它测定粘弹性本构的方法.本文用纵波沿 G/E长杆中的传播,测出了它的拉压复模量,同时也引建了一套完善的应力波实时测定系统.     

爆轰波与激波对撞爆轰状态演化机理研究

对当量比氢氧混合气体中爆轰波与激波的正面对撞过程进行了二维数值研究. 采用了二阶精度NND差分格式与改进的两阶段化学反应模型,并以数值x-t纹影图以及烟迹图记录了对撞过程. 数值研究表明,透射爆轰波受到膨胀影响首先会衰减,甚至产生局部解耦现象;然后由于三波点的碰撞又能再次重新耦合. 在爆轰波对撞过程中,由于燃烧不均匀性而产生的弱横波对爆轰胞格的形成起着重要作用.      

压剪联合冲击下K9玻璃中的失效波

对K9玻璃进行了冲击速度为150~400 m/s,倾斜角为10、15的纵剖试样斜撞击实验。结果表明，在加载剪切横波(S+)和卸载纵波(P-)之间有波速超过了纵波波速的波阵面存在，此波的存在对卸载纵波和卸载横波的幅值有一定的影响。由于失效波的产生与材料的表面性质密切相关，为消除纵剖试样中间界面的影响，模拟VISAR的实验条件，进行了冲击速度为70~300 m/s、倾斜角为10的横剖试样斜撞击实验。可以确定在此冲击范围失效波的波速在0.98~1.4 km/s，产生失效波的临界状态为:压应力0.86~1.01 GPa，对应剪应力0.053~0.071 GPa。表明剪应力的存在极大降低了失效波产生的阈值。在此基础上初步分析了撞击面的动摩擦因数和相对滑移速度。     

液饱和多孔介质中三维应力波的传播

为了深入研究液饱和多孔介质中应力波的传播，提出了三维两相细观计算模型．基于此模型。应用Galerkin余量法并计及流-固耦合界面的耦合效应，利用直接耦合的技术，开发了三维流-固混合显式动力有限元计算程序．在此基础上对冲击载荷作用下液饱和多孔介质中三维应力波的传播现象进行了数值模拟，并详细讨论了孔隙率，孔隙形状等因素对应力波传播主导波形的影响．     

生物芯片压电微流体泵液-固耦合系统模态分析

对压电微流体泵粘性流体周期流动进行厚度积分平均近似,得到包含粘性的,非线性浅水波动方程,并采用有限元法得到微泵液体压强矩阵方程．液体压强矩阵方程和压电硅片振动有限元方程耦合,得到一个包含微泵进出口扩散管的液-固耦合系统振动方程．液-固耦合系统的模态分析结果表明,做泵液-固耦合系统的自然频率比不耦合的硅片振动自然频率低很多．随着微泵厚度的减少,液体附加质量和粘性阻尼对耦合系统自然频率的影响更加明显．同时发现,对应的压电片振型函数在液-固耦合前后没有明显变化,还给出硅片-阶模态的振幅-频率特征曲线,对薄型无阀压电微流体泵,浅水波模型合理地表达了微泵液体流动和压电硅片振动的相互作用,以及液体附加质量和粘性阻尼对微泵液-固耦合系统动力特征的影响。     

高温下混凝土的本构模拟及破坏分析

针对已建立的高温下混凝土中化学-热-水力-力学耦合过程分析的分级数学模型,发展了混凝土的化学-热-水力-力学(CTHM)耦合本构模型。在已有的Willam-Warnke弹塑性屈服准则基础上发展了考虑脱水和脱盐引起的材料损伤及化学塑性软化、塑性应变硬化/软化和吸力硬化的广义Willam-Warnke本构模型,模拟高温下混凝土的材料非线性行为。为保证全局守恒方程的Newton迭代过程的二阶收敛率,导出了非线性化学-热-水力-力学(CTHM)耦合本构模型的一致性切线模量矩阵。数值结果显示了本文所发展的化学-热-水力-力学(CTHM)耦合本构模型在模拟高温下混凝土中复杂破坏过程的能力和有效性。     

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.     

The mathematical model of the radial artery blood pressure waveform through monitoring of the age-related changes

Age-related changes in blood vessels affect the pulse wave propagation. These changes may cause an increase in wave reflection which leads to amplification of pulse pressure. The pulse pressure changes are associated with certain vascular diseases. Here we present a mathematical model of blood pressure for different age groups. The model is based on one-dimensional wave propagation theory and assumes that the pressure waveform is a superposition of forward propagating wave and backward waves from many reflection sites. The model is based on experimental data obtained by direct measurement of radial artery blood flow. The model clearly shows age-related changes in blood pressure waveform. The results of mathematical model correlate with the radial pressure waveform data. The model can be used in cases where it is not possible to measure the pressure due to movement of subject. Application of model to the direct blood flow measurements data allows the real-time pressure waveform monitoring. Furthermore, this approach enables monitoring of changes in pressure waveform due to the effects of medications.     

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.     

Wave-based defect detection and interwire friction modeling for overhead transmission lines

In this study, the feasibility of continuous, online monitoring of power lines using ultrasonic waves is considered. Local and global wave-based approaches for wire break detection in overhead transmission lines are presented. Both methods use a sending/receiving transducer to generate an ultrasonic, longitudinal, elastic wave in the cable. Defects in the cable cause a portion of the incident ultrasonic wave to be reflected back to the transducer, which when received, can be used to identify the presence of the defect. Although the transducers can only be attached to the surface of the cable, subsurface wires can also be interrogated since elastic energy spreads to these wires through friction contact. This study also explores how the elastic energy of a propagating wave becomes distributed among contacting rods via friction contact. This work focuses specifically on a two-rod system in which the wave energy from an excited “active” rod is transmitted to a neighboring “passive” rod through friction contact. An energy-based model is used to approximate the time average elastic wave power in the two rods as a function of propagation distance. Power predictions from the energy-based model compare well with experimental measurements and finite element simulations.     

The propagation of elastic stress waves in a conical shell under axial impulsive loading

The propagation of elastic stress waves in a conical shell subjected to axial impulsive loading is studied in this paper by means of the finite element calculation and model experiments. It is shown that there are two axisymmetrical elastic stress waves propagating with different velocities, i.e., the longitudinal wave and the bending wave. The attenuation of these waves while propagating along the shell surface is discussed. It is found in experiments that the bending wave is also generated when a longitudinal wave reflects from the fixed end of the shell, and both reflected waves will separate during the propagation due to their different velocities. Southwest Institute of Structural Mechanics     

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。     

On interacting longitudinal-shear waves in large elastic deformation of a composite cylindrical laminate

We consider a large deformation of a cylindrical layer. Through the process of homogenization and the theory of effective moduli this heterogeneous medium is converted to a homogeneous but anisotropic medium. On the basis of John’s semilinear material, an energy function is identified and equations of motion obtained. Using the method of characteristics the speeds of propagating linear longitudinal and non-linear shear cylindrical waves are obtained: these “p-wave” and “s-wave” do interact, contrary to the known view, of the small deformation theory.     

The displacement wave theory of blood vessel

On the basis of the medical and mechanical analysis and explanations in this paper the visco-elastic simply supported beam model is proposed to treat the displacement wave of the blood vessels. The relationships between the displacement wave and blood vessel elasticity as well as the viscous dissipation of the blood and blood vessel are obtained. The corresponding relations of such kinds of pulses in the traditional Chinese medicine as smooth pulse, surface pulse and deep pulse to the displacement waves of blood vessels are also found. The computational results are in good agreement with those acquired in the experiments with ultrasonic wave.The Projects Supported by National Science Fundation of China.