Direct and inverse problems of oscillations of an elastoliquid layered medium

A plane problem of forced oscillations of an ideal compressible liquid bounded from above by an elastic layer with a rough lower surface and an inverse geometric problem of determining the shape of the rough lower surface of an elastic layer from the wave characteristics on the upper surface are considered. Three methods are used to solve the direct problem: the small parameter method, the boundary element method, and the Born approximation. Solving the inverse problem is reduced to solving the integral Fredholm equation of the first kind. Results of a numerical experiment are presented.     

Generalized Born scattering in anisotropic media

The Born scattering approximation has been widely used in seismology to study scattered waves, and to linearize the propagation problem for inversion. The standard Born theory requires the model be separated into a smooth, reference model and a perturbation. Scattering occurs from the pertubation. In the distorted Born approximation, when the reference model is inhomogeneous, the reference Green's functions are normally not known exactly, but the error in these Green's functions is rarely quantified. In this paper, we generalize Born scattering theory to include the errors in the Green's functions explicitly, and obtain scattering integrals from these errors. For forward modelling, there is no need to separate the model into a reference and perturbation part - approximate Green's functions in the true model can be used to calculate the scattered signals.

The theory is developed for inhomogeneous, anisotropic media. Asymptotic ray theory results are suitable approximate Green's functions for the generalized Born scattering theory. The error terms are simple, easily calculated and included in the scattering integrals. Various applications of generalized Born scattering theory have already appeared in the literature, e.g. quasi-shear ray coupling, and this paper is restricted to an improved and more complete theoretical development. Further applications will appear elsewhere.     

粗糙颗粒的随机离散元模拟——随机法向接触定律

真实颗粒的力学性质会受到其随机粗糙表面的影响,然而在传统离散元模拟中通常假设颗粒具有光滑表面,因此有必要在定量考虑颗粒表面粗糙度的基础上改进离散元的接触模型。本文基于经典 Greenwood-Williamson(GW)模型通过理论分析和数值模拟提出了一种可以考虑颗粒表面粗糙度的法向接触定律;开发了基于 Newton-Raphson迭代的数值计算方法,通过输入颗粒重叠量和一系列表面粗糙系数计算总接触力;讨论了改进计算方法效率和准确性的相关问题。相对于 GW模型中接触关系的复杂积分表示,拟合得到新随机接触定律的表达式具有类似 Hertz定律的简单结构,只包含一个表征颗粒表面粗糙度标准偏差的新增参数,σ,可以方便的引入当前离散元模拟程序中进行计算。     

摩擦过程中真实接触面积的灰色分析

灰色系统理论是近几年以随机过程为研究对象而形成和发展起来的，在农业和自动控制等方面的研究与应用发展较快．为了使这种理论应用于摩擦学研究领域，从光全反射测量和计算机数值计算两方面，考察了粗糙表面接触时真实接触面积的随机特性，指出摩擦过程中的真实接触面积是一种含有随机成分的变化量，研究目标应当侧重于真实接触面积的变化趋势和范围，而不是它的精确解．在此基础上，首次利用灰色系统理论，分别对静态和动态接触条件下真实接触面积的变化规律进行了灰色分析，建立了精度比较高的预测真实接触面积的灰色模型ＣＭ（１，１）．这种模型对动、静接触面积的计算值与实测值具有良好的一致性，可以用于动态跟踪描述摩擦过程中真实接触面积的变化规律     

点、线接触真实粗糙表面的弹流润滑研究

本文给出了点、线接触的真实粗糙表面的微弹流数值解。在给定随机粗糙表面样本后,求解大小不同的载荷和粗糙的弹流问题。从计算结果可以看出,由于Reynolds方程中速度项的作用,在表面对应粗糙的位置处引起了压力变化,从而因其产生的弹性变形使粗糙变得平滑。对此光滑表面解可以看出,因粗糙引起的压力和膜厚的变化在光滑解附近波动。载荷较大时,压力分节接近固体接触情况。     

一种新型转捩技术在跨音速风洞中的应用

针对传统金刚砂粗糙带在跨音速增压风洞实验中易脱落、随机误差大等问题,设计一种新型斑点型粗糙带,解决了大动压条件下,在模型表面实现固定转捩的问题。应用萘升华流动显示技术,分析了固定转捩和自由转捩条件下边界层变化情况;由测力实验得到GBM-01(AGARD-B)标准模型不同Ma数下的气动特性, 并与国外大风洞实验数据进行了比较。实验结果表明：新型斑点型粗糙带能够将层流边界层转变为湍流边界层,可以获得具有高雷诺数特点的数据,且强度高,是一种具有广阔应用前景的新型转捩技术。     

基于共轭梯度法和快速傅立叶变换的粗糙表面微动接触数值研究

实际工程表面多为粗糙表面,研究粗糙表面的表面形貌对微动接触中压力和应力的影响具有重要意义。本文研究接触过程中法向载荷保持不变,切向载荷为周期性的交变载荷。首先,建立接触算法和模型,算法核心是利用共轭梯度法CGM(Conjugate gradient method)计算微动接触中的表面压力及切向应力并利用快速傅里叶变换FFT(Fast Fourier transform)加快计算速度。然后,对单峰表面、正弦表面和随机粗糙表面的接触进行数值研究。结果表明,表面幅值对切向载荷-位移曲线以及接触过程中的能量耗散有影响,表面幅值越大,相同切向载荷作用下产生的切向位移越大,能量耗散也越大。     

连接结构接触界面非线性力学建模研究

连接界面上存在的跨尺度、多物理场和非线性行为是引起结构复杂非线性动力学的主要原因。由于连接界面力学行为的复杂性,以及对连接界面进行直接试验观测的困难,连接界面的力学建模一直是非常具有挑战性的科学问题。本文首先从分析结合面的跨尺度物理机理入手,将名义的光滑平面视作凹凸不平的粗糙面,考虑单个微凸体的黏滑摩擦行为,建立接触载荷与变形的非线性关系,然后采用GW(Greenwood和Williamson, GW)模型数理统计方法建立整个粗糙界面的跨尺度力学模型,并与公开文献中试验结果进行对比。然后考虑连接界面典型非线性特征,提出一种改进的Iwan唯象模型,利用精细有限元方法获得非线性特征结果,采用系统辨识理论建立连接结构的降阶力学模型,并利用有限元结果进行模型验证。结果表明,本文提出的粗糙界面跨尺度模型在法向载荷较小时与试验结果吻合较好,改进的Iwan模型能够较好描述连接界面非线性特征,并与有限元结果吻合较好。      

粗糙薄层弹性体接触刚度分析

薄层弹性体功能结构表面在工程领域有着广泛的应用前景,薄层弹性体的接触特性分析对功能结构表面设计与应用非常重要.采用随机粗糙表面模拟生成技术和有限元分析技术建立了粗糙薄层弹性体表面的接触刚度确定性分析模型,研究了薄层弹性体的接触特性,对基于半数值确定性分析方法的粗糙层-基体层串联模型用于粗糙薄层弹性体接触刚度计算的适用性进行了讨论,进一步分析了粗糙薄层弹性体串联模型接触刚度的误差来源.研究结果表明:当薄层弹性体的基体层厚度小于10倍表面均方根粗糙度时,由传统粗糙层-基体层串联模型分析获得的粗糙薄层弹性体刚度误差将超过15%,误差主要来源于粗糙峰的大变形和基体层的局部变形不均匀的共同作用.     

粗糙表面接触研究进展

工程中的任何接触表面都不会是绝对光滑的,对于某些特殊接触问题必须考虑表面形貌的接触效应.粗糙表面接触研究是一门年轻的交叉学科.它主要研究粗糙表面接触力学,接触导电和导热,接触密封,接触振动和噪声,接触刚度,骨关节接触等问题,涉及固体力学,流体力学,随机过程及概率统计,计量学,电学和传热学,振动理论以及生物学等学科知识.本文综述了粗糙表面接触的研究进展.      

A roll stability performance measure for off-road vehicles

The roll stability is significant for both road and off-road commercial vehicles, while the majority of reported studies focus on road vehicles neglecting the contributions of uneven off-road terrains. The limited studies on roll stability of off-road vehicles have assessed the stability limits using performance measures derived for road vehicles. This study proposes an alternative performance measure for assessing roll stability limits of off-road vehicles. The roll dynamics of an off-road mining vehicle operating on random rough terrains are investigated, where the two terrain-track profiles are synthesized considering coherency between them. It is shown that a measure based on steady-turning root-mean-square lateral acceleration corresponding to the sustained period of unity lateral-load-transfer-ratio prior to the absolute-rollover, could serve as a reliable measure of roll stability of the vehicle operating on random rough terrains. The robustness of proposed performance measure is demonstrated considering sprung mass center height variations and different terrain excitations. The simulation results revealed adverse effects of terrain elevation magnitude on the roll stability, while a relatively higher coherency resulted in lower terrain roll-excitation and thereby enhanced vehicle roll stability. Terrains with relatively higher waviness increased the magnitude of lower spatial frequency components, which resulted in reduced roll stability limits.     

The effective elastic moduli of a random packing of spheres

The effective incremental elastic moduli of a random packing of identical elastic spheres are derived. Although the method of derivation is suitable for any initial deformed configuration that induces compressive forces between any spheres in contact, specific results are given only for the cases in which this corresponds to that of a hydrostatic compression or a uniaxial compression. For additional simplicity it is assumed that the spheres are either infinitely rough or perfectly smooth.     

Nonlinear inversion of strong scatterer of elastic wave for two parameters in half-space

The inversion of strong scatterer embedded in the half-space is an important problem in engineering and a very difficult nonlinear problem in mathematics, for which the Born iterative method is of no effect. In this paper the moment method is used in the discretization procedure. A numerical approach is presented by employing the regularization technique and DBI (distorted Born iterative) method. The simulation results show that the approach presented is efficient. Project supported by the Research Fund for the Doctoral Program of Higher Education (RFDP: 98048705).     

Elastodynamic inversion for shape reconstruction and type classification of flaws

Two linearized inverse scattering methods are investigated to reconstruct the shape of flaws in the elastic solid. One is based on the Born approximation and the other is based on the Kirchhoff approximation. The Born inversion is sensitive to the volumetric flaw but not to a crack-like flaw. On the other hand, the Kirchhoff inversion reacts to both boundaries of volumetric and crack-like flaws. The combined use of Born and Kirchhoff inversions leads to the classification method of flaw type. The performance of the proposed classification procedure is demonstrated by the numerical simulations and then by the experimental measurements for the two-dimensional models of flaws. An example for the three-dimensional shape reconstruction is also shown by using the numerically calculated backscattering amplitudes.     

半空间SH波方程非线性井间双参数反演

以半空间的ＳＨ波方程出发,采用Ｂｏｒｎ迭代法求解半空间弹性介质中密度和剪切模量分布的非线性反演问题。首先,采用矩量法和正则化方法,给出井间反演积分方程的离散形式,然后应用Ｂｒｏｎ迭代法求解非线性反演问题。     

On higher gradients in continuum-atomistic modelling

Continuum-atomistic modelling denotes a mixed approach combining the usual framework of continuum mechanics with atomistic features like e.g. interaction or rather pair potentials. Thereby, the kinematics are typically characterized by the so-called Cauchy–Born rule representing atomic distance vectors in the spatial configuration as an affine mapping of the atomic distance vectors in the material configuration in terms of the local deformation gradient. The application of the Cauchy–Born rule requires sufficiently homogeneous deformations of the underlying crystal. The model is no more valid if the deformation becomes inhomogeneous. Nevertheless the development of microstructures with inhomogeneous deformation is inevitable. In the present work, the Cauchy–Born rule is thus extended to capture inhomogeneous deformations by the incorporation of the second-order deformation gradient. The higher-order equilibrium equation as well as the appropriate boundary conditions are presented for the case of finite deformations. The constitutive law for the Piola–Kirchhoff stress and the additional higher-order stress are represented for the simplified case of pair potential-based energy density functions. Finally, a deformation inhomogeneity measure is introduced and studied for a particular non-homogeneous simple-shear like deformation.     

Correction of the near threshold behavior of electron collisional excitation cross-sections in the plane-wave Born approximation

The modeling of NLTE plasmas requires the solution of population rate equations to determine the populations of the various atomic levels relevant to a particular problem. The equations require many cross sections for excitation, de-excitation, ionization and recombination. A simple and computational fast way to calculate electron collisional excitation cross-sections for ions is by using the plane-wave Born approximation. This is essentially a high-energy approximation and the cross section suffers from the unphysical problem of going to zero near threshold. Various remedies for this problem have been employed with varying degrees of success. We present a correction procedure for the Born cross-sections that employs the Elwert–Sommerfeld factor to correct for the use of plane waves instead of Coulomb waves in an attempt to produce a cross-section similar to that from using the more time consuming Coulomb Born approximation. We compare this new approximation with other, often employed correction procedures. We also look at some further modifications to our Born Elwert procedure and its combination with Y.K. Kim's correction of the Coulomb Born approximation for singly charged ions that more accurately approximate convergent close coupling calculations.     

INTERVAL ANALYSIS OF FUZZY-RANDOM HEAT CONDUCTION IN COMPOSITE TUBES

IntroductionThere are a lot of uncertainties such as fuzziness and random in the design andmanufacture in engineering.In generally speaking,methods to deal with the fuzzy-randomproblems are first to transfer the fuzzy set to real number set,and then the p…     

Effective wave propagation along a rough thin-elastic beam

Two methods for computing the complex-valued effective wavenumber of a rough beam in the context of linear time-harmonic theory are presented. The roughness of the beam is modelled as a continuous random process of known characteristic length and root-mean-square amplitude for either the beam mass or the beam rigidity. The first method is based on a random sampling method, with the effective wave field calculated as the mean of a large ensemble of wave fields for individual realisations of the roughness. The individual wave fields are calculated using a step approximation, which is validated for a deterministic problem via comparison to results produced by an integral equation approach. The second method assumes a splitting of the length scale of the fluctuations and an observation scale, employing a multiple-scale approximation to derive analytical expressions for the effective attenuation rate and phase change. Numerical comparisons show agreement of the results of the random sampling method and the multiple-scale approximation for a wide range of parameters. It is shown that the effective wavenumbers only differ by a real constant between the cases of varying beam mass and rigidity.