非线性变形节理中纵波传播特性的理论研究

基于波前动量守恒理论和位移不连续方法所提出的时域分析新方法,引入岩石非线性法向本构关系,对弹性纵波在岩石非线性节理中的传播特性进行了理论分析。采用节理变形的双曲线模型(BB模型),获得纵波P波斜入射非线性节理的传播波动方程,并通过参数研究分析了在岩石节理中节理非线性系数、节理初始刚度、应力波入射角和入射波幅值等因素对纵波传播规律的影响。结果表明:所推导的应力波传播方程在考虑多种非线性问题时,通过迭代计算即可方便求出透射波和反射波的数值解,避免了复杂的数学运算;当波斜入射节理面时,产生了波型转换,节理变形的非线性对透射波和反射波有较大影响,透射系数和反射系数并非随着非线性参数的变化而单调变化。时域内所推导的波传播方程更有益于波斜入射时非线性参数的广泛研究,为开展该方面的理论研究工作提供了借鉴。     

梁中非线性弯曲波传播特性的研究

研究了梁中的非线性弯曲波的传播特性,同时考虑了梁的大挠度引起的几何非线性效应和 梁的转动惯性导致的弥散效应,利用Hamilton变分法建立了梁中非线性弯曲波的波动方程. 对该方程进行了定性分析,在不同的条件下,该方程在相平面上存在同宿轨道或异宿轨道, 分别对应于方程的孤波解或冲击波解. 利用Jacobi椭圆函数展开法,对该非线性方程进行 求解,得到了非线性波动方程的准确周期解及相对应的孤波解和冲击波解,讨论了这些解存 在的必要条件,这与定性分析的结果完全相同. 利用约化摄动法从非线性弯曲波动方程中导 出了非线性Schr\"{o}dinger方程,从理论上证明了考虑梁的大挠度和转动惯性时梁中存在 包络孤立波.     

非圆截面杆中的非线性扭转波及其行波解

研究了非圆截面杆中非线性扭转波的传播特性.由于非圆截面杆的扭转运动会伴随有横截面的翘曲,这种翘曲运动将引起扭转波的弥散.如果同时考虑有限扭转变形和翘曲弥散的共同作用,将会得到非线性扭转波的方程.在相平面上,对非线性扭转波动方程进行定性分析,结果表明,在一定条件下方程存在同宿轨道或异宿轨道,分别相应于方程的孤波解或冲击波解.本文利用Jacobi椭圆函数展开法,对该非线性方程进行求解,得到了非线性波动方程的三类准确周期解及相应的孤波解和冲击波解,讨论了这些解存在的必要条件.这些条件与定性分析的结果相一致.     

多尺度有限差分方法求解波动方程

小波分析是多尺度分析方法，本文利用具有紧支集的正交小波变换对有限差分方程进行空间多尺度近似，提出适合于层状介质波传问题数值计算的多尺度有限差分方法，将波动方程的求解转换到小波域中进行。利用小波基的自适应性与消失矩特性，有效减少了计算量、提高了稳定性，扩大了可求解的速度范围。地球物理勘探中的数值实例显示了算法具有良好效率。     

半空间弹性波双参数强非线性逆散射

半空间弹性波强散射源逆问题是一个实用而又难度很大的强非线性问题,而经典的Born迭代方法只适用于弱非线性问题．基于DBI方法（Distorted-Born Iterative方法）,提出了一种求解弹性波强非线性逆散射问题的迭代方法．在数值模拟运算时利用矩量法进行离散处理,并采用正则化原则避免求解病态矩阵方程。计算结果表明该方法具有较快的收敛速度及较高的精度。     

非圆截面杆中非线性扭转波方程的解析求解

研究了非圆截面杆中非线性扭转波动方程的精确求解问题.利用直接积分与微分变换相结合的方法,得到了该方程的隐式通解.通过对积分常数和方程系数的不同情形的讨论,给出了该方程三角函数、双曲函数、椭圆函数、指数函数以及它们的组合形式的解,分别对应于非线性扭转波的孤立波、周期波以及冲击波等多种传播形式.     

非线性弹性杆中的应变孤波

本文对非线性弹性杆中的应变孤波进行了分析,着重讨论了杆的物理参数和几何参数对于波动的影响,阐明了孤波传播过程的主要特征。     

促进其线性频散特征另一种形式的Bousinesq方程

Ｂｏｕｓｉｎｅｓｑ方程能够用于模拟表面重力波传播过程中的折射、绕射、反射以及浅化，非线性作用等现象．用不同垂直积分方法所得到的二维Ｂｏｕｓｓｉｎｅｓｑ方程形式具有不同的线性频散特征．采用两个不同的水深层的水平速度变量组合，推导出一个新形式的Ｂｏｕｓｉｎｅｓｑ方程．通过对其参数的设置可得到精确的线性频散解Ｐａｄｅ近似４阶精度．其适用范围已由原来的浅水，向深水拓进．相速误差小于２％，其拓展适用范围可达到０８个波长水深．应用所得到的新型Ｂｏｕｓｉｎｅｓｑ方程，采用有限差分法，对经典工况进行了数值模拟，其计算结果表明，计算值与物模实验值吻合较好．这说明本文新形式的Ｂｏｕｓｓｉｎｅｓｑ方程对变水深非线性效应所产生的能量频散有着较为精确的描述     

基于ZWT方程的线黏弹性球面波分析

针对时间尺度为1~100 s的爆炸冲击加载,忽略低频Maxwell体的松弛效应,同时为简化分析,忽略非线性弹簧效应项,推导了三维应力状态下的线黏弹性ZWT本构关系。基于球面波的基本动力学方程,结合ZWT线黏弹性本构关系,得到了以位移u表征的三阶波动方程。利用该方程分析固体介质中线黏弹性球面波传播过程中的吸收和弥散现象,得知:高频球面波的衰减因子趋于常数,相速趋于高频下的纵波速度;低频球面波的衰减因子和圆频率的平方成正比,其相速趋于低频下的纵波速度;低频球面波的纵波波速低于高频球面波的纵波波速,两者的比值和介质的泊松比、弹性模量及Maxwell体弹性模量相关。     

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.      

The effects of blood viscoelasticity on the pulse wave in arteries

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考虑阻尼的无限长小垂度缆索弹性波的传播

缆索结构被广泛应用于电气、土木、海洋和航空工程等领域,随着缆索在工程中的应用长度越来越长,高阶振动越来越明显,研究时应该考虑扰动沿着缆索的传播.现有对缆索弹性波传播的研究中,通常不考虑阻尼项,然而阻尼对于波的传播有着重要影响.文章考虑阻尼的影响,发展了包含阻尼项的三维弹性缆索运动方程.通过求解上述含阻尼项的运动方程,分别考察了面内面外弹性波的频率关系、相速度和群速度等自由传播特性,进而通过计算无限长弹性缆索在初始余弦型脉冲作用下的位移响应,分析扰动沿着该缆索的传播规律,考察波的色散现象以及阻尼对于缆索弹性波传播的影响.结果表明,考虑阻尼后,面内波和面外波均为色散波,面内波在曲率的作用下,为高度色散波.此外,在阻尼的影响下,波的峰值在传播过程不断减小,且波的后缘端点响应总是高于前缘端点响应.     

Effect of a viscous liquid loading on Love wave propagation

This paper describes a theory of surface Love waves propagating in a layered elastic waveguide loaded on its surface by a viscous (Newtonian) liquid. An analytical expression for the complex dispersion equation of Love waves has been established. The real and imaginary parts of the complex dispersion equation were separated and resulting system of nonlinear algebraic equations was solved numerically. The influence of the viscosity of liquid on the dispersion curves of phase velocity, the wave attenuation and the distribution of the Love wave amplitude is analyzed numerically. The propagation loss is produced only by the viscosity of liquids. Elastic layered waveguide is assumed to be loss-less. The numerical solutions show the dependence of the phase velocity change, the wave attenuation and the wave amplitude distribution in terms of the liquid viscosity and the wave frequency. The results of the investigations are fundamental and can be applied in the design and development of liquid viscosity sensors and biosensors, in Non-Destructive Testing (NDT) of materials, in geophysics and seismology.     

Rayleigh-type wave propagation in incompressible visco-elastic media under initial stress

Propagation of Rayleigh-type surface waves in an incompressible visco-elastic material over incompressible visco-elastic semi-infinite media under the effect of initial stresses is discussed. The dispersion equation is determined to study the effect of different types of parameters such as inhomogeneity, initial stress, wave number, phase velocity, damping factor, visco-elasticity, and incompressibility on the Rayleigh-type wave propagation. It is found that the affecting parameters have a significant effect on the wave propagation. Cardano’s and Ferrari’s methods are deployed to estimate the roots of differential equations associated with layer and semi-infinite media. The MATHEMATICA software is applied to explicate the effect of these parameters graphically.     

Determination of correlation functions of turbulent velocity and sound speed fluctuations by means of ultrasonic technique

An experimental study of the propagation of high-frequency acoustic waves through grid-generated turbulence by means of an ultrasound technique is discussed. Experimental data were obtained for ultrasonic wave propagation downstream of heated and non-heated grids in a wind tunnel. A semi-analytical acoustic propagation model that allows the determination of the spatial correlation functions of the flow field is developed based on the classical flowmeter equation and the statistics of the travel time of acoustic waves traveling through the kinematic and thermal turbulence. The basic flowmeter equation is reconsidered in order to take into account sound speed fluctuations and turbulent velocity fluctuations. It allows deriving an integral equation that relates the correlation functions of travel time, sound speed fluctuations and turbulent velocity fluctuations. Experimentally measured travel time statistics of data with and without grid heating are approximated by an exponential function and used to analytically solve the integral equation. The reconstructed correlation functions of the turbulent velocity and sound speed fluctuations are presented. The power spectral density of the turbulent velocity and sound speed fluctuations are calculated.     

非局部广义热弹性理论下半导体微结构中波的反射研究

论文基于非局部热弹性理论,研究了纳米半导体介质中波的反射问题.首先建立了在耦合的非局部弹性理论,波型热传导理论和等离子扩散理论下问题的控制方程;然后运用谐波法,得到耗散方程的解以及反射系数率的解析表达式;最后通过数值计算给出了硅纳米结构中相速度、群速度随非局部参数的变化,讨论了非局部参数、热电耦合参数以及热弹性耦合参数对反射系数率的影响.     

Propagation of Rayleigh waves on curved surfaces

The propagation and properties of Rayleigh waves on curved surfaces are investigated theoretically. The Rayleigh wave dispersion equation for propagation on a curved surface is derived as a parabolic equation, and its penetration depth is analyzed using the curved surface boundary. Reciprocity is introduced to model the diffracted Rayleigh wave beams. Simulations of Rayleigh waves on some canonical curved surfaces are carried out, and the results are used to quantify the influence of curvature. It is found that the velocity of the surface wave increases with greater concave surface curvature, and a Rayleigh wave no longer exists once the surface wave velocity exceeds the bulk shear wave velocity. Moreover, the predicted wave penetration depth indicates that the energy in the Rayleigh wave is transferred to other modes and cannot propagate on convex surfaces with large curvature. A strong directional dependence is observed for the propagation of Rayleigh waves in different directions on surfaces with complex curvatures. Thus, it is important to include dispersion effects when considering Rayleigh wave propagation on curved surfaces.     

SH-type waves dispersion in an isotropic medium sandwiched between an initially stressed orthotropic and heterogeneous semi-infinite media

The present paper studies the propagation of shear waves (SH-type waves) in an homogeneous isotropic medium sandwiched between two semi infinite media. The upper half-space is considered as orthotropic medium under initial stress and lower half-space considered as heterogeneous medium. We have obtained the dispersion equation of phase velocity for SH-type waves. The propagation of SH-type waves are influenced by inhomogeneity parameters and initial stress parameter. The velocity of SH-type wave has been computed for different cases. We have also obtained the dispersion equation of phase velocity in homogeneous media in the absence of initial stress. The velocities of SH-type waves are calculated numerically as a function of kH (non-dimensional wave number) and presented in a number of graphs. To study the effect of inhomogeneity parameters and initial stress parameter we have plotted the velocity of SH-type wave in several figure. We have observed that the velocity of wave increases with the increase inhomogeneity parameters. We found that in both homogeneous and inhomogeneous media the velocity of SH-type wave increases with the increase of initial stress parameter. The results may be useful for the study of seismic waves propagation during any earthquake and artificial explosions.     

川藏公路地质环境与整治改建方案的思考

川藏公路由于地质环境复杂、建设标准低、后遗病害多,抗灾能力差,泥石流、滑坡、山崩、雪害、水毁等自然灾害频繁发生,公路阻车断道严重。国家投入巨资进行整治改建,并取得了明显的效果,但由于自然环境特殊、影响因素复杂,许多特大型、大型工程地质病害问题还没有可行、可靠的解决方案。本文通过分析川藏公路沿线的地质环境和灾害特点,总结历年整治改建和经验的教训,提出川藏公路建设的途径、可能达到的目标和应采用的原则。     

Wave propagation in transversely isotropic porous piezoelectric materials

Wave propagation in porous piezoelectric material (PPM), having crystal symmetry 6 mm, is studied analytically. Christoffel equation is derived for the propagation of plane harmonic waves in such a medium. The roots of this equation give four complex wave velocities which can propagate in such materials. The phase velocities of propagation and the attenuation quality factors of all these waves are described in terms of complex wave velocities. Phase velocities and attenuation of the waves in PPM depend on the phase direction. Numerical results are computed for the PPM BaTiO₃. The variation of phase velocity and attenuation quality factor with phase direction, porosity and the wave frequency is studied. The effects of anisotropy and piezoelectric coupling are also studied. The phase velocities of two quasi dilatational waves and one quasi shear waves get affected due to piezoelectric coupling while that of type 2 quasi shear wave remain unaffected. The phase velocities of all the four waves show non-dispersive behavior after certain critical high frequency. The phase velocity of all waves decreases with porosity while attenuation of respective waves increases with porosity of the medium. The characteristic curves, including slowness curves, velocity curves, and the attenuation curves, are also studied in this paper.