GREEN FUNCTION在齿轮箱故障诊断中的运用

为了找出齿轮箱故障的定量规律，通过对齿轮箱的振动信号的测试及分析，发现ＧＲＥＥＮＦＵＮＣＴＩＯＮ对齿轮箱故障的诊断行之有效，并且成功地找出了Ｇ１０、Ｇ１０′等齿轮箱故障的定量诊断参数．

A non-perturbation approach in temperature Green function theory

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Implementation of the Integrated Green’s Function Method for 3D Poisson’s Equation in a Large Aspect Ratio Computational Domain

The solution of Poisson’s Equation plays an important role in many areas, including modeling high-intensity and high-brightness beams in particle accelerators. For the computational domain with a large aspect ratio, the integrated Green’s function method has been adopted to solve the 3D Poisson equation subject to open boundary conditions. In this paper, we report on the efficient implementation of this method, which can save more than a factor of 50 computing time compared with the direct brute force implementation and its improvement under certain extreme conditions.

A hybrid method integrating Green's function Monte Carlo and projected entangled pair states

This paper introduces a hybrid approach combining Green’s function Monte Carlo(GFMC)method with projected entangled pair state(PEPS)ansatz.This hybrid method regards PEPS as a trial state and a guiding wave function in GFMC.By leveraging PEPS’s proficiency in capturing quantum state entanglement and GFMC’s efficient parallel architecture,the hybrid method is well-suited for the accurate and efficient treatment of frustrated quantum spin systems.As a benchmark,we applied this approach to study the frustrated J_(1)–J_(2) Heisenberg model on a square lattice with periodic boundary conditions(PBCs).Compared with other numerical methods,our approach integrating PEPS and GFMC shows competitive accuracy in the performance of ground-state energy.This paper provides systematic and comprehensive discussion of the approach of our previous work[Phys.Rev.B 109235133(2024)].

Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function

This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.

Singularity-free Green's function for EM sources embedded in a stratified medium

We present a method to unify the calculation of Green＇s functions for an electromagnetic（EM） transmitting source embedded in a homogeneous stratified medium.A virtual interface parallel to layer interfaces is introduced through the source location.The potentials for Green＇s function are derived by decomposing the partial wave solutions to Helmholtz＇s equations into upward and downward within boundaries.The amplitudes of the potentials in each stratum are obtained recursively from the initial amplitudes at the source level.The initial amplitudes are derived by coupling with the transmitting sources and following the discontinuity of the tangential electric and magnetic fields at the source interface.Only the initial terms are related to the transmitting sources and thus need to be modified for different transmitters,whereas the kernel connected with the stratified media stays unchanged.Hence,the present method can be easily applied to EM transmitting sources with little modification.The application of the proposed method to the marine controlled-source electromagnetic method（MCSEM） demonstrates its simplicity and flexibility.

The Green's function of the harmonic horizontal force applied at the interior of the saturated half-space soil

By using integral transform methods, the Green(s functions of horizontal harmonic force applied at the interior of the saturated half-space soil are obtained in the paper. The general solutions of the Biot dynamic equations in frequency domain are established through the use of Hankel integral transforms technique. Utilizing the above- mentioned general solutions, and the boundary conditions of the surface of the half-space and the continuous conditions at the plane of the horizontal force, the solutions of the boundary value problem can be determined. By the numerical inverse Hankel transforms method, the Green(s functions of the harmonic horizontal force are obtainable. The degenerate case of the results deduced from this paper agrees well with the known results. Two numerical examples are given in the paper.

The research on the highly efficient calculation method of 3-D frequency-domain Green function

The traditional calculation method of frequency-domain Green function mainly utilizes series or asymptotic expansion to carry out numerical approximation, however, this method requires very careful zoning, thus the computing process is complex with many cycles, which has greatly affected the computing efficiency. To improve the computing efficiency, this paper introduces Gaussian integral to the numerical calculation of the frequency-domain Green function and its partial derivatives. It then compares the calculation result with that in existing references. The comparison results demonstrate that, on the basis of its sufficient accuracy, the method has greatly simplified the computing process, reduced the zoning and improved the computing efficiency.

纳米分子器件量子传导中的Green's Function模型

将纳米分子器件的电极和分子本体作为一个系统,考虑到入射电子在原子电极和分子本体中的传导,在电极与分子之间界面上的透射的量子状态,在满足Fisher-Lee关系式的基础上,一个新型的Green’sFunction被设计出来。这一理论模型把三个区域上的不同量子状态完整地表达在一个方程式里,符合物理学基本原理,可以系统地用来研究纳米分子器件的量子传导特性。

New Derivation of Ordinary Differential Equations for Transient Free-Surface Green Functions

Based on the Laplace transform, a direct derivation of the ordinary differential equations for the three-dimensional transient free-surface Green function in marine hydrodynamics is presented. The results for the 3D Green function and all its spatial derivatives are a set of fourth-order ordinary differential equations, which are identical with that of Clement (1998). All of these results may be used to accelerate numerical computation for the time-domain boundary element method in marine hydrodynamics.

Study on Characteristics of 3-D Translating-Pulsating Source Green Function of Deep-Water Havelock Form and Its Fast Integration Method

The singularities, oscillatory performances and the contributing factors to the 3-＇D translating-pulsating source Green function of deep-water Havelock form which consists of a local disturbance part and a far-field wave-like part, are analyzed systematically. Relative numerical integral methods about the two parts are presented in this paper. An improved method based on LOBATTO rule is used to eliminate singularities caused respectively by infinite discontinuity and jump discontinuous node from the local disturbance part function, which makes the improvement of calculation efficiency and accuracy possible. And variable substitution is applied to remove the singularity existing at the end of the integral interval of the far-field wave-like part function. Two auxiliary techniques such as valid interval calculation and local refinement of integral steps technique in narrow zones near false singularities are applied so as to avoid unnecessary integration of invalid interval and improve integral accordance. Numerical test results have proved the efficiency and accuracy in these integral methods that thus can be applied to calculate hydrodynamic performance of floating structures moving in waves.

Numerical Treatments and Applications of the 3D Transient Green Function

How to evaluate time-domain Green function and its gradients efficiently is the key problem to analyze ship hydrodynamics in time domain. Based on the Bessel function, an Ordinary Differential Equation （ODE） was derived for time-domain Green function and its gradients in this paper. A new efficient calculation method based on solving ODE is proposed. It has been demonstrated by the numerical calculation that this method can improve the precision of the time-domain Green function. Numeiical research indicates that it is efficient to solve the hydrodynamic problems.

Green's functions for uniformly distributed loads acting on an inclined line in a poroelastic layered site

Based on one type of practical Biot＇s equation and the dynamic-stiffness matrices ofa poroelastic soil layer and half-space, Green＇s functions were derived for unitformly distributed loads acting on an inclined line in a poroelastie layered site. This analysis overcomes significant problems in wave scattering due to local soil conditions and dynamic soil-structure interaction. The Green＇s functions can be reduced to the case of an elastic layered site developed by Wolf in 1985. Parametric studies are then carried out through two example problems.

Hydroelastic Analysis of Very Large Floating Structures Using Plate Green Functions

Great attention has been paid to the development of very large floating structures. Owing to their extreme large size and great flexibility, the coupling between the structural deformation and fluid motion is significant. This is a typical problem of hydroelasticity. Efficient and accurate estimation of the hydroelastic response of very large floating structures in waves is very important for design. In this paper, the plate Green function and fluid Green function are combined to analyze the hydroelastic response of very large floating structures. The plate Green function here is a new one proposed by the authors and it satisfies all boundary conditions for free-free rectangular plates on elastic foundations. The results are compared with some experimental data. It is shown that the method proposed in this paper is efficient and accurate. Finally, various factors affecting the hydroelastic response of very large floating structures are also studied.

Green's function of multi-layered poroelastic half-space for models of ground vibration due to railway traffic

This study proposes a Green＇s function, an essential representation of water-saturated ground under moving excitation, to simulate ground borne vibration from trains. First, general solutions to the governing equations of poroelastic medium are derived by means of integral transform. Secondly, the transmission and reflection matrix approach is used to formulate the relationship between displacement and stress of the stratified ground, which results in the matrix of the Green＇s function. Then the Green＇s function is combined into a train-track-ground model, and is verified by typical examples and a field test. Additional simulations show that the computed ground vibration attenuates faster in the immediate vicinity of the track than in the surrounding area. The wavelength of wheel-rail unevenness has a notable effect on computed displacement and pore pressure. The variation of vibration intensity with the depth of ground is significantly influenced by the layering of the strata soil. When the train speed is equal to the velocity of the Rayleigh wave, the Mach cone appears in the simulated wave field. The proposed Green＇s function is an appropriate representation for a layered ground with shallow ground water table, and will be helpful to understand the dynamic responses of the ground to complicated moving excitation.

NONLINEAR EVOLUTION SYSTEMS AND GREEN’S FUNCTION

In this paper, we will introduce how to apply Green＇s function method to get the pointwise estimates for the solutions of Cauchy problem of nonlinear evolution equations with dissipative structure. First of all, we introduce the pointwise estimates of the time-asymptotic shape of the solutions of the isentropic Navier-Stokes equations and show to exhibit the generalized Huygen＇s principle. Then, for other nonlinear dissipative evolution equations, we will only introduce the result and give some brief explanations. Our approach is based on the detailed analysis of the Green＇s function of the linearized system and micro-local analysis, such as frequency decomposition and so on.

GREEN FUNCTIONS FOR A DECAGONAL QUASICRYSTALLINE MATERIAL WITH A PARABOLIC BOUNDARY

This investigation presents the Green functions for a decagonal quasicrystalline ma- terial with a parabolic boundary subject to a line force and a line dislocation by means of the complex variable method. The surface Green functions are treated as a special case, and the explicit expressions of displacements and hoop stress at the parabolic boundary are also given. Finally, the stresses and displacements induced by a phonon line force acting at the origin of the lower half-space are presented.

Side Wall Effects on the Hydrodynamics of a Floating Body by ImageGreen Function Based on TEBEM

A novel numerical model based on the image Green function and first-order Taylor expansion boundary element method(TEBEM), which can improve the accuracy of the hydrodynamic simulation for the non-smooth body, was developed to calculate the side wall effects on first-order motion responses and second-order drift loads upon offshore structures in the wave tank. This model was confirmed by comparing it to the results from experiments on hydrodynamic coefficients, namely the first-order motion response and second-order drift load upon a hemisphere, prolate spheroid, and box-shaped barge in the wave tank. Then,the hydrodynamics of the KVLCC2 model were also calculated in two wave tanks with different widths. It was concluded that this model can predict the hydrodynamics for offshore structures effectively, and the side wall has a significant impact on the firstorder quantities and second-order drift loads, which satisfied the resonant rule.

Dynamic stiffness matrix of a poroelastic multi-layered site and its Green's functions

Few studies of wave propagation in layered saturated soils have been reported in the literature.In this paper,a general solution of the equation of wave motion in saturated soils,based on one kind of practical Blot's equation, was deduced by introducing wave potentials.Then exact dynamic-stiffness matrices for a poroelastic soil layer and half- space were derived,which extended Wolf's theory for an elastic layered site to the case of poroelasticity,thus resolving a fundamental problem in the field of wave propagation and soil-structure interaction in a poroelastic layered soil site.By using the integral transform method,Green's functions of horizontal and vertical uniformly distributed loads in a poroelastic layered soil site were given.Finally,the theory was verified by numerical examples and dynamic responses by comparing three different soil sites.This study has the following advantages:all parameters in the dynamic-stiffness matrices have explicitly physical meanings and the thickness of the sub-layers does not affect the precision of the calculation which is very convenient for engineering applications.The present theory can degenerate into Wolf's theory and yields numerical results approaching those for an ideal elastic layered site when porosity tends to zero.

Magnetic Properties of a Mixed Spin-2 and Spin-5/2 Heisenberg Ferrimagnetic System on a Two-Dimensional Honeycomb Lattice： Green＇s Function Approach

The multisublattice Green＇s function technique is applied to study the magnetic properties of a mixed spin-2 and spin-5/2 Heisenberg ferrimagnetic system on a two-dimensional honeycomb lattice. The role of the different interactions in the Hamiltonian is explored. When only the nearest-neighbor interaction and the single-ion anisotropy are included, our results indicate that there are compensation points at finite temperatures. When the next-nearest-neighbor interaction exceeds a minimum value that depends on the other parameters in the Hamiltonian, the compensation point disappears. The next-nearest-neighbor interaction has the effect of changing the compensation temperature.