波能耗散的结构阻尼损耗因子度量方法

根据波动理论,用Timoshenko梁理论在高频范围内分析能量的耗散,通过重建作为频率函数的色散关系曲线,得到动力粘弹性模量及材料的损失因子。根据动力系统的固有特征方程与材料弹性特性的关系,研究利用阻尼损耗因子定量描述在高频情况下,波在结构中传播时的能量耗散效应以及结构阻尼损耗因子的表示方法,并通过实验利用波的色散关系估计结构的动力粘弹性模量,理论分析和实验结果表明了这种方法的可行性。     

无黏流体与固体界面的漏瑞利波

漏瑞利波存在于半无限无黏性流体和半无限固体媒质的界面处. 首先推导流固无限各向同性介质界面处漏瑞利波的特征方程和位移及应力的解析计算公式. 然后结合典型结构通过数值计算研究了漏瑞利波特性以及位移和应力在流体和固体中的分布规律. 数值计算结果表明漏瑞利波的相速度和衰减随流固密度比的增大而增大, 在流固界面上法向位移连续而切向位移不连续. 流固密度比对固体媒质中沿垂直于漏瑞利波的传播方向的位移、正应力和剪应力有比较大的影响,而对沿漏瑞利波的传播方向的正应力几乎没影响. 为利用漏瑞利波的无损检测与评价提供了理论基础.      

微结构固体中钟型与扭结孤立波的演化

根据Mindlin理论和Murnaghan模型,首先建立了描述耗散、频散及非线性微结构固体中一维纵波传播的一种简单模型.然后利用有限差分方法,数值模拟了微结构效应对钟型与扭结孤立波演化的影响. 结果表明,随着微结构效应的减弱,钟型孤立波的幅度衰减以及非对称特征变得越来越明显;随着微结构效应的增强,扭结孤立波顶部出现的“帽子”状变化以及由此产生的非对称特征变得越来越明显.      

改进时域间断Galerkin有限元方法在弹塑性波传播数值模拟中的应用

对于高频、强脉动荷载作用下的结构动力学波传播分析,对比于传统的时域算法,时域间断Galerkin方法能捕捉到波阵面的间断,有效得避免了由于间断引起的数值振荡。但时域间断方法却带来了波前面的虚假数值振荡。本文针对上述波前数值振荡的现象进行研究,通过引入人工阻尼的方法对时域间断Galerkin有限元方法进行进一步改进。数值结果表明,所发展的方法能够有效的滤掉强动荷载产生的波前数值振荡现象,同时降低了时域间断Galerkin方法的网格依赖性。     

应用于计算气动声学的优化有限紧致格式

对于含间断的计算气动声学问题,数值计算的格式不仅要求低耗散低色散的设计,对短波具有较高的分辨率,还要求能捕捉激波.中心紧致格式具有高精度,具有无耗散和低色散特征,但不能捕捉间断和激波;WENO格式处理间断较为成功,而耗散和色散误差相对较大.有限紧致格式可以将紧致格式与WENO格式相结合构造成混合格式,利用光滑因子之间的关系对激波区域进行自动判断,将传统的全域求解的紧致格式划分为有限的局部紧致求解,间断点上的激波捕捉铜梁自动作为局部紧致求解的边界通量,在在光滑区域具有紧致格式的高精度低耗散性质,在激波附近不产生非物理振荡.本文利用有限紧致格式思想,构造了新的适合于气动声学问题的优化有限紧致格式,将其应用于计算气动声学一维标准测试问题,对相关格式的模拟性能进行了评估,显示该格式在宽频声波传播和含有间断的声波传播模拟方面具有优势.     

细观结构固体层中孤立波的传播及相互作用特性

利用直接微扰方法.确定了孤立波的放大或衰减与孤立波的初始幅度以及介质的结构参数之间的关系.然后利用线性化技术构造出一种二阶精度的稳定差分格式,并对孤立波在细观结构固体层中传播特性进行了数值模拟,特别对细观结构固体层中传播的不同幅度的孤立波的相互作用进行了详细的数值模拟,从而得到在适当条件下细观结构固体层中孤立波传播时即可以衰减、放大又可以稳定传播,且相互作用不影响这种传播特性.     

分数阶黏弹性Pasternak地基上两端固支Timoshenko梁的动力响应

本文研究了放置在黏弹性Pasternak地基上的Timoshenko梁在移动载荷作用下的动力响应行为．首先，引入分数阶导数，将整数阶标准固体黏弹性地基模型推广为分数阶标准固体黏弹性模型．对于Pasternak地基，考虑压缩层是黏弹性的而剪切层仍是弹性的情况，给出了地基反作用力．然后，求解了Timoshenko梁的自由振动解，获得含黏性耗散信息的复固有频率及振型函数．在此基础上用振型叠加法分析了在移动简谐荷载作用下梁的位移响应．在数值算例中，给出了不同分数阶导数、地基黏性系数以及载荷移动速度下梁的动态响应，讨论了黏弹性地基对梁的动态响应的影响规律．     

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.     

一种面向激波噪声计算的加权优化紧致格式及非线性效应分析

在超声速流动中, 激波与湍流结构的相互作用会产生高强度的激波噪声. 激波噪声的高保真计算要求激波捕捉格式具有高阶精度、低耗散和低色散特性, 同时还要尽可能地减弱格式的非线性效应. 现有的六阶精度迎风/对称混合型加权非线性紧致格式CCSSR-HW-6在基于对称模板构造网格中心处的数值通量时引入了两级加权, 且两级加权都需要构造非线性的权系数, 因而非线性效应较强. 本文以修正波数的误差积分函数为优化目标函数, 优化了CCSSR-HW-6格式的非线性特性, 建立了加权优化紧致格式WOCS. 精度验证表明WOCS格式的精度高于5阶. 谱特性分析表明, 与原方法相比, WOCS格式的耗散误差和非线性效应显著降低. 典型激波噪声问题数值实验表明: WOCS格式不仅提高了对高频波的分辨能力, 而且显著地消除了数值解中因格式的非线性效应所导致的非物理振荡.      

基于VPM-THINC/QQ模型的波浪高保真模拟

为实现波浪传播的高保真数值模拟,采用包含单元均值和点值(volume-average/point-value method,VPM)的有限体积法求解纳维-斯托克斯方程和具有二次曲面性质和高斯积分的双曲正切函数(THINC method with quadratic surface representation and Gaussian quadrature,THINC/QQ)方法来重构自由面,建立以开源求解库OpenFOAM底层函数库为基础的VPM-THINC/QQ模型. 在本模型中添加推板造波法实现波浪的产生功能,采用松弛法实现消波功能,构建高精度黏性流数值波浪水槽. 分别采用VPM-THINC/QQ模型和InterFoam求解器(OpenFOAM软件包中广泛使用的多相流求解器)开展规则波的数值模拟,重点探究网格大小和时间步长等因素对波浪传播过程的影响,定量地分析波高衰减程度;为验证本模型的适应性,对长短波进行模拟. 结果表明,在相同网格大小或时间步长条件下,VPM-THINC/QQ模型的预测结果与参考值吻合较好,波高衰减较少,且无相位差,在波浪传播过程的模拟中呈现出良好的保真性. 本文工作 为波浪传播的模拟研究提供了一种高精度的黏性数值波浪水槽模型.      

Stationary discontinuity and flutter instability of wave propagation in elasto-plastic saturated porous media

In the present work a model based on the Biot theory for simulating coupled hydrodynamic behavior in saturated porous media is utilized with integration of the inertial coupling effect between the solid-fluid phases of the media into the model. The non-associated Drucker-Prager criterion to describe nonlinear constitutive behavior of pressure dependent elasto-plasticity for the media is particularly considered. With no consideration of compressibility of solid grains and the pore fluid, the discontinuity and instability of the wave propagation in saturated porous media are analyzed for the plane strain problems in detail. The critical conditions of stationary discontinuity and flutter instability in the wave propagation are given. The results and conclusions obtained by the present work will provide some bases or clues for overcoming the difficulties in numerical modeling of wave propagation in the media subjected to dynamic loading. The project supported by the National Natural Science Foundation of China (19832010)     

Squirt-Flow in Fluid-Saturated Porous Media: Propagation of Rayleigh Waves

Propagation of attenuated waves is studied in a squirt-flow model of porous solid permeated by two different pore regimes saturated with same viscous fluid. Presence of soft compliant microcracks embedded in the grains of stiff porous rock defines the double-porosity formation. Microcracks and pores respond differently to the compressional effect of a propagating wave, which induces the squirt-flow from microcracks to pores. Elastodynamics of constituent particles in porous aggregate is represented through a single-porosity formulation, which involves the frequency-dependent complex moduli. This formulation is deduced as a special case of double-porosity formation allowing the wave-induced flow of pore-fluid. This squirt-flow model of porous solid supports the attenuated propagation of two compressional waves and one shear wave. Superposition of these body waves, subject to stress-free surface, defines the propagation of Rayleigh wave. This wave is governed by a complex irrational dispersion equation, which is solved numerically after rationalising into an algebraic equation. For existence of Rayleigh wave, a complex solution of the dispersion equation should represent a leaky wave, which decays for propagation along any direction in the semi-infinite medium. A numerical example is solved to analyse the effects of squirt-flow on phase velocity, attenuation and polarisation of the Rayleigh waves, for different combinations of parameters. Numerical results suggest the existence of an additional (second) Rayleigh wave in the squirt-flow model of dissipative porous solids.     

INSTABILITY AND DISPERSIVITY OF WAVE PROPAGATION ININELASTIC SATURATED/UNSATURATED POROUS MEDIA

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Wave propagation modeling in cylindrical human long wet bones with cavity

The wave propagation modeling in cylindrical human long wet bones with cavity is studied. The dynamic behavior of a wet long bone that has been modeled as a piezoelectric hollow cylinder of crystal class 6 is investigated. An analytical solutions for the mechanical wave propagation during a long wet bones have been obtained for the flexural vibrations. The average stresses of solid part and fluid part have been obtained. The frequency equations for poroelastic bones are obtained when the medium is subjected to certain boundary conditions. The dimensionless frequencies are calculated for poroelastic wet bones for various values for non-dimensional wave lengths. The dispersion curves of the dry bone and wet bone for the flexural mode n=2 are plotted. The numerical results obtained have been illustrated graphically.     

Attenuated Wave Field in Fluid-Saturated Porous Medium with Excitations of Multiple Sources

This research addresses the investigation of an elastic wave field in a homogeneous and isotropic porous medium which is fully saturated by a Newtonian viscous fluid. A new methodology is developed for describing the wave field in the medium excited by multiple energy sources. To quantify the relative displacements between the fluid and solid of the medium, the governing equations of the elastic wave propagation are derived in the form of displacements specially. The velocities and attenuation of the waves are considered as functions of viscosity and frequency. Making use of the Hankel function and the moving-coordinate method, a model of the wave motion with multiple cylindrical wave sources is built. Making use of the model established in this research, the relative displacement between the fluid and the solid can be quantified, and the wave field in the porous media can then be determined with the given energy sources. Numerical simulations of cylindrical waves from multiple energy sources propagating in the porous medium saturated by viscous fluid are performed for demonstrating the practicability of the model developed.     

Transient wave propagation of isotropic plates using a higher-order plate theory

Transient wave propagation of isotropic thin plates using a higher-order plate theory is presented in this paper. The aim of this investigation is to assess the applicability of the higher-order plate theory in describing wave behavior of isotropic plates at higher frequencies. Both extensional and flexural waves are considered. A complete discussion of dispersion of isotropic plates is first investigated. All the wave modes and wave behavior for each mode in the low and high-frequency ranges are provided in detail. Using the dispersion relation and integral transforms, exact integral solutions for an isotropic plate subjected to pure impulse load and a number of wave excitations based on the higher-order theory are obtained and asymptotic solutions which highlight the physics of waves are also presented. The axisymmetric three-dimensional analytical solutions of linear wave equations are also presented for comparison. Results show that the higher-order theory can predict the wave behavior closely with exact linear wave solutions at higher frequencies.     

Shear wave dispersion and attenuation in periodic systems of alternating solid and viscous fluid layers

The attenuation and dispersion of elastic waves in fluid-saturated rocks due to the viscosity of the pore fluid is investigated using an idealized exactly solvable example of a system of alternating solid and viscous fluid layers. Waves in periodic layered systems at low frequencies are studied using an asymptotic analysis of Rytov’s exact dispersion equations. Since the wavelength of shear waves in fluids (viscous skin depth) is much smaller than the wavelength of shear or compressional waves in solids, the presence of viscous fluid layers necessitates the inclusion of higher terms in the long-wavelength asymptotic expansion. This expansion allows for the derivation of explicit analytical expressions for the attenuation and dispersion of shear waves, with the directions of propagation and of particle motion being in the bedding plane. The attenuation (dispersion) is controlled by the parameter which represents the ratio of Biot’s characteristic frequency to the viscoelastic characteristic frequency. If Biot’s characteristic frequency is small compared with the viscoelastic characteristic frequency, the solution is identical to that derived from an anisotropic version of the Frenkel–Biot theory of poroelasticity. In the opposite case when Biot’s characteristic frequency is greater than the viscoelastic characteristic frequency, the attenuation/dispersion is dominated by the classical viscoelastic absorption due to the shear stiffening effect of the viscous fluid layers. The product of these two characteristic frequencies is equal to the squared resonant frequency of the layered system, times a dimensionless proportionality constant of the order 1. This explains why the visco-elastic and poroelastic mechanisms are usually treated separately in the context of macroscopic (effective medium) theories, as these theories imply that frequency is small compared to the resonant (scattering) frequency of individual pores.     

Propagation and Evolution of Wave Fronts in Two-Phase Porous Media

An investigation is made into the propagation and evolution of wave fronts in a porous medium which is intended to contain two phases: the porous solid, referred to as the skeleton, and the fluid within the interconnected pores formed by the skeleton. In particular, the microscopic density of each real material is assumed to be unchangeable, while the macroscopic density of each phase may change, associated with the volume fractions. A two-phase porous medium model is concisely introduced based on the work by de Boer. Propagation conditions and amplitude evolution of the discontinuity waves are presented by use of the idea of surfaces of discontinuity, where the wave front is treated as a surface of discontinuity. It is demonstrated that the saturation condition entails certain restrictions between the amplitudes of the longitudinal waves in the solid and fluid phases. Two propagation velocities are attained upon examining the existence of the discontinuity waves. It is found that a completely coupled longitudinal wave and a pure transverse wave are realizable in the two-phase porous medium. The discontinuity strength of the pore-pressure may be determined by the amplitude of the coupled longitudinal wave. In the case of homogeneous weak discontinuities, explicit evolution equations of the amplitudes for two types of discontinuity waves are derived.     

Reflection and refraction of attenuated waves at boundary of elastic solid and porous solid saturated with two immiscible viscous fluids

The propagation of elastic waves is studied in a porous solid saturated with two immiscible viscous fluids.The propagation of three longitudinal waves is represented through three scalar potential functions.The lone transverse wave is presented by a vector potential function.The displacements of particles in different phases of the aggregate are defined in terms of these potential functions.It is shown that there exist three longitudinal waves and one transverse wave.The phenomena of reflection and refraction due to longitudinal and transverse waves at a plane interface between an elastic solid half-space and a porous solid half-space saturated with two immiscible viscous fluids are investigated.For the presence of viscosity in pore-fluids,the waves refracted to the porous medium attenuate in the direction normal to the interface.The ratios of the amplitudes of the reflected and refracted waves to that of the incident wave are calculated as a nonsingular system of linear algebraic equations.These amplitude ratios are used to further calculate the shares of different scattered waves in the energy of the incident wave.The modulus of the amplitude and the energy ratios with the angle of incidence are computed for a particular numerical model.The conservation of the energy across the interface is verified.The effects of variations in non-wet saturation of pores and frequencies on the energy partition are depicted graphically and discussed.     

Stability of Contact Discontinuities for the 1-D Compressible Navier-Stokes Equations

In this paper, we study the large-time asymptotic behavior of solutions of the one-dimensional compressible Navier-Stokes system toward a contact discontinuity, which is one of the basic wave patterns for the compressible Euler equations. It is proved that such a weak contact discontinuity is a metastable wave pattern, in the sense introduced in [24], for the 1-D compressible Navier-Stokes system for polytropic fluid by showing that a viscous contact wave, which approximates the contact discontinuity on any finite-time interval for small heat conduction and then runs away from it for large time, is nonlinearly stable with a uniform convergence rate provided that the initial excess mass is zero. This result is proved by an elaborate combination of elementary energy estimates with a weighted characteristic energy estimate, which makes full use of the underlying structure of the viscous contact wave.