Decoupling coefficients of dilatational wave for Biot's dynamic equation and its Green's functions in frequency domain

Green＇s functions for Blot＇s dynamic equation in the frequency domain can be a highly useful tool for the investigation of dynamic responses of a saturated porous medium. Its applications are found in soil dynamics, seismology, earthquake engineering, rock mechanics, geophysics, and acoustics. However, the mathematical work for deriving it can be daunting. Green＇s functions have been presented utilizing an analogy between the dynamic thermoelasticity and the dynamic poroelasticity in the frequency domain using the u-p formulation. In this work, a special term ＂decoupling coefficient＂ for the decomposition of the fast and slow dilatational waves is proposed and expressed to present a new methodology for deriving the poroelastodynamic Green＇s functions. The correct- ness of the solution is demonstrated by numerically comparing the current solution with Cheng＇s previous solution. The separation of the two waves in the present methodology allows the more accurate evaluation of Green＇s functions, particularly the solution of the slow dilatational wave. This can be advantageous for the numerical implementation of the boundary element method （BEM） and other applications.

Lamb waves topological imaging combining with Green’s function retrieval theory to detect near filed defects in isotropic plates

A method of combining Green’s function retrieval theory and ultrasonic array imaging using Lamb waves is presented to solve near filed defects in thin aluminum plates.The defects are close to the ultrasonic phased array and satisfy the near field calculation formula.Near field acoustic information of defects is obscured by the nonlinear effects of initial wave signal in a directly acquired response using the full matrix capture mode.A reconstructed full matrix of inter-element responses is produced from cross-correlation of directly received ultrasonic signals between sensor pairs.This new matrix eliminates the nonlinear interference and restores the near-field defect information.The topological imaging method that was developed in recent ultrasonic inspection is used for displaying the scatterers.The experiments are conducted on both thin aluminum plates containing two and four defects, respectively.The results show that these defects are clearly identified when using a reconstructed full matrix.The spatial resolution is equal to about one wavelength of the selectively excited mode and the identifiable defect is about one fifth of the wavelength.However, in a conventional directly captured image,the images of defects overlap together and cannot be distinguished.The proposed method reduces the background noise and allows for effective topological imaging of near field defects.

A new approach of solving Green's function for wave propagation in an inhomogeneous absorbing medium

A new approach is developed to solve the Green＇s function that satisfies the Hehmholtz equation with complex refractive index. Especially, the Green＇s function for the Helmholtz equation can be expressed in terms of a onedimensional integral, which can convert a Helmholtz equation into a Schrodinger equation with complex potential. And the Schrodinger equation can be solved by Feynman path integral. The result is in excellent agreement with the previous work.

The Interaction of Oblique Flexural Gravity Waves With a Small Bottom Deformation on a Porous Ocean-Bed： Green＇s Function Approach

The interaction of oblique incident water waves with a small bottom deformation on a porous ocean-bed is examined analytically here within the framework of linear water wave theory. The upper surface of the ocean is assumed to be covered by an infinitely extended thin uniform elastic plate, while the lower surface is bounded by a porous bottom surface having a small deformation. By employing a simplified perturbation analysis, involving a small parameter c^（〈〈l ）, which measures the smallness of the deformation, the governing Boundary Value Problem （BVP） is reduced to a simpler BVP for the first-order correction of the potential function. This BVP is solved using a method based on Green＇s integral theorem with the introduction of suitable Green＇s function to obtain the first-order potential, and this potential function is then utilized to calculate the first-order reflection and transmission coefficients in terms of integrals involving the shape function c（x） representing the bottom deformation. Consideration of a patch of sinusoidal ripples shows that when the quotient of twice the component of the incident field wave number propagating just below the elastic plate and the ripple wave number approaches one, the theory predicts a resonant interaction between the bed and the surface below the elastic plate. Again, for small angles of incidence, the reflected wave energy is more as compared to the other angles of incidence. It is also observed that the reflected wave energy is somewhat sensitive to the changes in the flexural rigidity of the elastic plate, the porosity of the bed and the ripple wave numbers. The main advantage of the present study is that the results for the values of reflection and transmission coefficients obtained are found to satisfy the energy-balance relation almost accurately.

Some Universal Properties of the Green’s Functions Associated with the Wave Equation in Bounded Partially-Homogeneous Domains and Their Use in Acoustic Tomography

Direct and inverse scattering problems connected with the wave equation in non-homogeneous bounded domains constitute challenging actual subjects for both mathematicians and engineers. Among them one can mention, for example, inverse source problems in seismology, nondestructive archeological probing, mine prospecting, inverse initial-value problems in acoustic tomography, etc. In spite of its crucial importance, almost all of the available rigorous investigations concern the case of unbounded simple domains such as layered planar or cylindrical or spherical structures. The main reason for the lack of the works related to non-homogeneous bounded structures is the extreme complexity of the explicit expressions of the Green’s functions. The aim of the present work consists in discovering some universal properties of the Green’s functions in question, which reduce enormously the difficulties arising in various applications. The universality mentioned here means that the properties are not depend on the geometrical and physical properties of the configuration. To this end one considers first the case when the domain is partially-homogeneous. Then the results are generalized to the most general case. To show the importance of the universal properties in question, they are applied to an inverse initial-value problem connected with photo-acoustic tomography.

Comparison of Linear Level I Green-Naghdi Theory with Linear Wave Theory for Prediction of Hydroelastic Responses of VLFS

Very Large Floating Structures (VLFS) have drawn considerable attention recently due to their potential significance in the exploitation of ocean resources and in the utilization of ocean space. Efficient and accurate estimation of their hydroelastic responses to waves is very important for the design. Recently, an efficient numerical algorithm was developed by Ertekin and Kim (1999). However, in their analysis, the linear Level I Green-Naghdi (GN) theory is employed to describe fluid dynamics instead of the conventional linear wave (LW) theory of finite water depth. They claimed that this linear level I GN theory provided better predictions of the hydroelastic responses of VLFS than the linear wave theory. In this paper, a detailed derivation is given in the conventional linear wave theory framework with the same quantity as used in the linear level I GN theory framework. This allows a critical comparison between the linear wave theory and the linear level I GN theory. It is found that the linear level I GN theory can be regarded as an approximation to the linear wave theory of finite water depth. The consequences of the differences between these two theories in the predicted hydroelastic responses are studied quantitatively. And it is found that the linear level I GN theory is not superior to the linear wave theory. Finally, various factors affecting the hydroelastic response of VLFS are studied with the implemented algorithm.

恩智浦携手立达信和GreenWave Reality推出先进的智能家居照明解决方案

恩智浦半导体NXP Semiconductors（NASDAQ：NXPI）携手Green Wave Reality和立达信集团（Leedarson Ljghting）在香港国际灯饰展上推出了智能照明解决方案，并同时展示了多款智能CFL、LED灯泡及灯具。其中，

恩智浦、立达信和Green Wave Reality推出智能家居照明解决方案

2011年10月27日，恩智浦半导体NXP Semiconductors（NASDAQ：NXPI）携手Green Wave Reality和立达信集团（Leedarson Lighting）在香港国际灯饰展上推出了智能照明解决方案，并同时展示了多款智能CFL、LED灯泡及灯具，智能联网灯泡大约有50只。智能家居、智能酒店、智能商店和智能办公室等样板智能照明方案均在展位展出。

A Central Numerical Scheme to 1D Green-Naghdi Wave Equations

A numerical scheme based on hybrid central finite-volume and finite-difference method is presented to model Green-Naghdi water wave equations. The governing equations are reformulated into the conservative form, and the convective flux is estimated using a Godunov-type finite volume method while the remaining terms are discretized using finite difference method. To enhance the robustness of the model, a central-upwind flux evaluation and a well-balanced non- negative water depth construction are incorporated. Numerical tests demonstrate that present model has the advantages of stability preserving and numerical efficiency.

Quasi-Dynamic Green’s Functions for Efficient Full-Wave Integral Formulations for Microstrip Interconnects

Integral formulations are widely used for full-wave analysis of microstrip interconnects. A weak point of these formulations is the inclusion of the proper planar-layered Green’s Functions (GFs), because of their computational cost. To overcome this problem, usually the GFs are decomposed into a quasi-dynamic term and a dynamic one. Under suitable approximations, the ?rst may be given in closed form, whereas the second is approximated. Starting from a general criterion for this decomposition, in this paper we derive some simple criteria for using the closed-form quasi-dynamic GFs instead of the complete GFs, with reference to the problem of evaluating the full-wave current distribution along microstrips. These criteria are based on simple relations between frequency, line length, dielectric thickness and permittivity. The layered GFs have been embedded into a full-wave transmission line model and the results are ?rst benchmarked with respect to a full-wave numerical 3D tool, then used to assess the proposed criteria.

恩智浦携手立达信和Green Wave Reality推出先进的智能家居照明解决方案

恩智浦半导体NXP携手Green Wave Reality和立达信集团（Leedarson Lighting）在香港国际灯饰展上推出了智能照明解决方案，并同时展示了多款智能CFL、LED灯泡及灯具。其中，采用基于IP的JenNet-IP（基于6LowPAN）网络软件的恩智浦GreenChip智能照明核心技术。可将灯泡转换成智能型可控设备，使其成为全球物联网的一部分。恩智浦以广泛的合作伙伴生态系统为依托，提供可扩展、安全的行业标准解决方案。现已发展成为行业领先的智能照明技术供应商。

Green-Wave Traffic Theory Optimization and Analysis

This paper analyzed the applicable conditions of the Green-Wave traffic theory, used two-phase signal control concept to optimize the Green-Wave traffic theory, put forward specific program for cross intersections and T-intersections. The analysis concluded that the optimized Green-Wave traffic theory is favorable to improve road safety and reduce vehicle fuel consumption and reduce vehicle emissions and other aspects.

用并矢Green函数的矢量本征函数展开式评价偏心对随钻电磁波电阻率测井响应的影响

采用圆柱坐标系下径向成层介质中磁流源并矢Green函数的矢量本征函数展开式计算电磁波电阻率的测井响应,考察井眼内仪器偏心对测井响应的影响。计算时采用径向成层圆柱形地层模型并假设在每一圆柱层内地层是均匀各向同性的,这样每层介质内的电磁波是对称的柱面波和各阶非对称波的叠加。计算结果表明:仪器偏心的影响随频率的升高而增加;对于电阻性(电导性)钻井液,地层电阻率越低(越高)越需要对仪器偏心的影响进行校正。

径向成层介质的Green函数及其在随钻电磁波电阻率测量中的应用

采用递推矩阵方法计算径向成层介质的Green函数,根据圆柱形层界面处电场和磁场的连续性条件得到确定待定系数的矩阵方程组,并通过递推方法快速求解。采用将变型Bessel函数的指数项单独列出的方式有效地解决了Green函数计算中的上溢问题。用得到的Green函数对随钻电磁波电阻率测量仪器进行数值模拟,分析钻铤的影响规律、井眼校正方法和仪器的径向探测深度。结果表明,只须改变方程组中源项元素的位置,可以方便地得到源点和场点在任意层时的Green函数,形式简洁,易于编程。在仪器测量范围内金属钻铤对随钻电磁波电阻率测量仪器的影响可近似视为恒定,在井眼直径较小且钻井液电导率较低的情况下无须对随钻电磁波电阻率测量仪器进行井眼校正,仪器的径向探测深度并非只取决于仪器参数,也与侵入带电导率、地层电导率以及井眼因素有关。所得到的结论可为随钻电磁波电阻率测量仪器的研制和使用提供理论指导。

圆形区域多圆孔对SH波散射Green函数解

利用多极坐标变换、Graf加法公式及波函数展开法研究圆形区域内多圆孔缺陷存在时对圆形域边界作用反平面稳态脉冲SH波散射Green函数解。给出各圆孔对SH波散射产生含未知系数的散射波函数,用叠加原理写出圆形域介质内总波场,据边界条件、Graf加法公式及Fourier积分变换获得确定未知系数的无穷线代数方程组;由计算精度进行有限项截断求解,确定问题的Green函数解。用算例结果验证该方法的可行性。

三维裂隙介质中弹性波Green函数的Weyl积分解研究

给出了三维裂隙介质中弹性波Ｇｒｅｅｎ函数的Ｗｅｙｌ积分解表达式，由于该积分解建立在平面波基础上，因而在与三维裂隙介质等价的各向异性介质中Ｇｒｅｅｎ函数的解形式变得非常简洁明了．通过在不含裂隙、含饱和水裂隙和干裂隙情况下对Ｗｅｙｌ积分解的计算，表明了公式的正确性，而且也说明了利用该公式可节省机时和工作量．

全非线性深水波的Green-Naghdi理论研究

全非线性深水波的数值模拟对于深海工程有着重要意义.应用二维深水G-N理论的控制方程,得到深水LevelⅢG-N理论和LevelⅣG-N理论的线性解析解.采用深水LevelⅢ和LevelⅣG-N理论对单色波进行数值模拟.提出适用于G-N理论的非线性造波边界条件,使用线性造波边界条件的结果与使用非线性边界条件的结果基本一致,因此可以使用线性造波边界叠加的方法来模拟不规则波.采用深水LevelⅢG-N理论模拟全非线性双色波和不规则波,并与线性解析解进行比较,结果表明使用深水LevelⅢG-N理论并配合线性造波边界条件来模拟全非线性深水不规则波是可行的.

采用Green-Naghdi方程和有限元法计算浅水船波

采用波动方程 /有限元法求解 Green-Naghdi ( G-N)方程计算船舶在有限水深区域的兴波和波浪阻力。把行驶船舶对水面的扰动作为移动压力直接加在 Green-Naghdi方程里 ,以描述运动船体和水面的相互作用 ,并以此来计算水面波动、船底水动压力和波浪阻力。G-N方程比浅水方程增加一个非线性的频散项 ,以补充有限水深对浅水船波的影响。采用随船运动网格的有限元法 ,以 Series 60 CB=0 .6船作为算例给出浅水船波的计算结果 ,并与浅水方程的结果进行了比较。计算结果表明 ,当船速小于临界速度时 ,由于频散的影响 ,G-N方程给出的船后尾波波高比浅水方程的结果大 ,同时波浪阻力也比浅水方程的结果有所提高。当船速大于临界速度时 ,G-N方程的计算结果与浅水方程基本相同 。

横观各向同性饱和土中柱面载荷的动力Green函数

基于饱和介质的三维波动理论的Biot模型,利用Fourier展开和Hankel变换,并借助算子理论,给出了圆柱坐标系下横观各向同性饱和土波动方程的非轴对称通解;利用通解,建立了饱和土层及饱和半空间的精确动力刚度矩阵;借助刚度矩阵,给出层状横观各向同性饱和地基中,作用沿土层深度方向分布的竖向和水平柱面载荷时的动力Green函数,进而解决了利用间接边界元法分析桩-饱和土动力相互作用的关键问题.

矩形波导的时空域并矢Green函数

本文应用Laplace变换法求出了矩形波导的时空域并矢Green函数。这一方法亦可以用来求解如圆波导、同轴线等柱形波导的时空域并矢Green函数。讨论了矩形波导TE_(10)模细线激励的退化情形,得出与现有结果一致的时空域标量Green函数。