A universal solution to one-dimensional oscillatory integrals

How to calculate the highly oscillatory integrals is the bottleneck that restraints the research of light wave and electromagnetic wave＇s propagation and scattering. Levin method is a classical quadrature method for this type of integrals. Unfortunately it is susceptible to the system of linear equations＇ ill-conditioned behavior. We bring forward a universal quadrature method in this paper, which adopts Chebyshev differential matrix to solve the ordinary differential equation （ODE）. This method can not only obtain the indefinite integral＇ function values directly, but also make the system of linear equations well-conditioned for general oscillatory integrals. Furthermore, even if the system of linear equations in our method is ill-conditioned, TSVD method can be adopted to solve them properly and eventually obtain accurate integral results, thus making a breakthrough in Levin method＇s susceptivity to the system of linear equations＇ ill-conditioned behavior.     

Stochastic wave finite element for random periodic media through first-order perturbation

Wave propagation features in random guided elastic media are considered in this paper. A formulation named stochastic wave finite element (SWFE) is offered. This formulation allows wave characteristics definition by means of a stochastic finite element model. The case of spatially homogeneous random properties is dealt with, through a parametric probabilistic technique. Numerical experiments show the effectiveness of the proposed approach to predict the statistics of guided wave propagation characteristics (means and standard deviations) when compared to Monte Carlo calculations.     

Numerical approximation of electromagnetic signals arising in the evaluation of geological formations

The integration of complicated oscillatory functions arises in computational electromagnetics when evaluating signals produced by the propagation of electromagnetic radiation through the anisotropic layers of a geological formation. The computation of exact integrals involves the evaluation of Sommerfeld integrals. The matrix-pencil method is used for the numerical approximation of such signals. Numerical results show accuracy and robustness of the method for the approximation of these signals, and efficiency in their numerical integration. Sampling frequency is discussed and numerical efficiency is improved by down-sampling.     

A partition of unity enriched dual boundary element method for accurate computations in fracture mechanics

We introduce a novel enriched Boundary Element Method (BEM) and Dual Boundary Element Method (DBEM) approach for accurate evaluation of Stress Intensity Factors (SIFs) in crack problems. The formulation makes use of the Partition of Unity Method (PUM) such that functions obtained from a priori knowledge of the solution space can be incorporated in the element formulation. An enrichment strategy is described, in which boundary integral equations formed at additional collocation points are used to provide auxiliary equations in order to accommodate the extra introduced unknowns. In addition, an efficient numerical quadrature method is outlined for the evaluation of strongly singular and hypersingular enriched boundary integrals. Finally, results are shown for mixed mode crack problems; these illustrate that the introduction of PUM enrichment provides for an improvement in accuracy of approximately one order of magnitude in comparison to the conventional unenriched DBEM.     

Dynamic properties of the Fisher–Kolmogorov–Petrovskii–Piscounov equation with the deviation of the spatial variable

We consider the problem of the density wave propagation of a logistic equation with the deviation of the spatial variable and diffusion (the Fisher–Kolmogorov equation with the deviation of the spatial variable). The Ginzburg–Landau equation was constructed in order to study the qualitative behavior of the solution near the equilibrium state. We analyzed the profile of the wave equation and found conditions for the appearance of oscillatory regimes. The numerical analysis of the wave propagation shows that, for a fairly small spatial deviation, this equation has a solution similar to that the classical Fisher–Kolmogorov equation. An increase in this spatial deviation leads to the existence of the oscillatory component in the spatial distribution of solutions. A further increase in the spatial deviation leads to the destruction of the traveling wave. This is expressed in the fact that undamped spatiotemporal fluctuations exist in a neighborhood of the initial perturbation. These fluctuations are close to the solution of the corresponding boundary value problem with periodic boundary conditions. Finally, when the spatial deviation is large enough we observe intensive spatiotemporal fluctuations in the whole area of wave propagation.     

融合电磁超声载波的声发射传播特性分析

电磁声发射是通过对缺陷导电结构件施加非接触式电磁载荷,进而激发声发射应力波,并据此效应来进行构件无损检测.本文针对电磁声发射信号不适合较远距离传播问题,融合电磁超声技术,实现对声发射应力波的载波远距离传输.文章首先从自由电子运动理论出发,从微观层面上研究电流对金属位错激活能的影响,推导出定向漂移的自由电子与位错碰撞时所产生的能量交换;其次搭建了融合电磁超声载波的电磁声发射有限元模型,分析了多个特征源激励下的应力波传播位移;最后利用希尔伯特黄变换方法对载波实验信号进行了分析比较.本文通过对传统的电磁声发射激励端研究、改进,提升电磁超声对电磁声发射应力波的传输特性,拓宽了电磁声发射检测的应用范围.     

Wave propagation in mechanical waveguide with curved members using wave finite element solution

In this paper, wave propagation in straight and curved mechanical waveguide is investigated. The main objective of the study is to develop a numerical model that can determine the response of the intact or damaged waveguide structure which is subjected to the incident waves. The wave finite element method, which is based on the simple development of standard finite element procedures, is used for the extraction of eigenmodes and analysis of the wave propagation properties. To make an effective use of those eigenmodes, a criterion that is based on the properties of eigensolutions is proposed to condense the mode bases. By using the reduced eigenmode bases, the high frequency wave motion due to the presence of curved part in the waveguide is examined through the wave propagation approach. Numerical analysis indicates that, in order to choose the appropriate wave modes for inspection, it is necessary to obtain both the eigenmode and wave propagation properties, thus the incident wave could be optimised for better monitoring of the structural features and detection of the local damages.     

Finite element analysis of static and dynamic stresses around suddenly punched holes in plates and shells

The magnitude and distribution of stresses around suddenly punched holes in initially stressed plates and shells is of interest to insure that cracks will not precipitate from stress concentration. This problem is of practical interest to pressure vessel designers to preclude catastrophic failure when holes are punched in vessels to release gas. This paper presents a finite element analysis of several problems investigating static and dynamic stress fields around suddenly punched circular holes.

The first problem deals with the investigation of the radial and tangential stress fields in the vicinity of a suddenly punched hole in a stretched, elastic, isotropic plate subjected to an initial hydrostatic stress field. The wave propagation from a punched hole in the plate under a hydrostatic state of stress was solved analytically, using transform techniques, by Miklowitz; the finite element analysis of this problem presented in this paper confirms the analytical solution. Two grid meshes were investigated and results are presented to show the effect of grid mesh on solution accuracy and the power of finite element techniques for solving stress unloading problems. A formula for determining integration step size is found to be a function of the minimum element length and the wave propagation velocity. A similar investigation into the stress effects around a suddenly punched hole in the plate subjected to an initial uniaxial state of stress was also carried out as a prerequisite for the final problem studied.

The last problem is an anisotropic composite shell of varying thickness under an initial stress field due to internal pressure. The static and dynamic stress fields are computed from an unloading wave that radiates outward from a reinforced circular hole that is cut in the shell in 20 μs. A finite-element model of the shell is developed using quadrilateral and triangular plate elements and both in-plane and bending stiffness is included in the analysis as is nonlinear differential stiffening incorporated into the analysis as a single step approximation. Both bending and in-plane waves radiate outward from the cut hole and the dynamic stresses around the hole edge are computed for both unloading waves. The effects of the unloading waves are temporally spaced due to different wave velocities.

The paper demonstrates that fast response stress problems are readily amenable to finite-element analysis. For holes other than circular, the power of finite-element methods is apparent since these shapes lead to mathematically intractable problems if closed form solutions are attempted.     

基于分层模型的复合材料耦合Lamb波频率—波数域特性研究

针对复合材料层合板中耦合Lamb波的传播问题,基于分层模型提出解析建模与有限元数值模拟相结合的方法对其进行预测和评估。利用Legendre正交多项式展开法推导多层各向异性复合材料层合板中耦合Lamb波的控制方程,并对频率-波数域频散特性曲线实现数值求解。基于平面壳单元构建复合材料层合板的有限元模型,采用波结构加载法生成单一Lamb波基本模态,设计复合材料层合板的不同纤维取向、边界和界面约束条件,并经二维傅里叶变换获得有限元模拟数据的频率-波数域频散特性曲线。通过对比验证,结果表明两种方法均有较好的吻合性。     

电磁超声体波方法对内部孔洞缺陷检测研究

电磁超声是一种新型的超声检测方法,其具有非接触、不受工作环境影响、易于激发多种类型的超声波等优点。本文研究了电磁超声体波对结构件内部孔洞缺陷探测问题,首先利用离散点源实现对电磁超声声场的分析;而后利用有限元方法对电磁－结构多场耦合建模,研究超声体波在体内缺陷处的波型转换以及模式转换后爬波在缺陷表面传播情况;最后利用电磁超声体波对孔洞缺陷的尺寸、位置进行了定量检测。有限元计算结果与简化解析求解得到较好的验证,本文为电磁超声对体内孔洞缺陷的应用评估提供良好基础。     

二维圆环结构中弹性波传播的谱单元分析

为研究弹性波在结构中的波场特征,推导建立一种任意四边形二维谱单元,将其应用于二维圆环结构中的波传播行为模拟.以矩形平板结构中弹性导波传播分析为例,通过与传统有限元分析结果对比,验证所建立谱单元的有效性.有裂纹和无裂纹二维圆环结构谱单元模拟结果表明:弹性波在圆环结构中传播会发生频散;圆环结构表面的裂纹对瑞利波的传播影响最大;根据其反射波包位置可以确定损伤位置.     

Finite element solution for reflection of plane harmonic waves from the free surface of a half-space

Reflection of harmonic elastic waves from the free surface of a half-space is investigated using the finite element technique. The waves are assumed to be planar and the half-space is represented by bilinear finite elements of rectangular shape. Before treating the reflections of plane longitudinal and vertical shear waves, the wave propagation in an infinite medium is given in a way which will be directly applicable to the subsequent reflection problem. Numerical results are reported for various values of the wavelength, the angle of incidence and the grid dimensions of the finite elements. Special attention is paid to the representability of the homogeneous medium by the finite elements in such wave propagation problems and to suitable grid dimensions. Finally attention is drawn to two types of solution which do not appear in the exact solution of the reflection problem.     

A spectrally formulated plate element for wave propagation analysis in anisotropic material

A new spectrally formulated plate element is developed to study wave propagation in composite structures. The element is based on the classical lamination plate theory. Recently developed method based on singular value decomposition (SVD) is used in the element formulation. Along with this, a new strategy based on the method of solving polynomial eigenvalue problem (PEP) is proposed in this paper, which significantly reduces human intervention (and thus human error), in the element formulation. The developed element has an exact dynamic stiffness matrix, as it uses the exact solution of the governing elastodynamic equation of plate in frequency–wavenumber domain as the interpolating functions. Due to this, the mass distribution is modeled exactly, and as a result, a single element captures the exact frequency response of a regular structure, and it suffices to model a plate of any dimension. Thus, the cost of computation is dramatically reduced compared to the cost of conventional finite element analysis. The fast Fourier transform (FFT) and Fourier series are used for inversion to time–space domain. This element is used to model plate with ply drops and to capture the propagation of Lamb waves.     

Wave envelope technique for multimode wave guide problems

In this paper we propose a fast method for solving wave guide problems. In particular, we consider the guide to be inhomogeneous, and allow propagation of waves of higher-order modes. Such techniques have been handled successfully for acoustic wave propagation problems with single mode and finite length. This paper extends this concept to electromagnetic wave guides with several modes and infinite in length. The method is shown and results of computations are presented.Research was supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-18107 while the first author was in residence at the ICASE, NASA Langley Research Center, Hampton, VA 23665-5225, and by NASA Grant No. NAG-1-624.     

A finite-element series-expansion technique for linear surface water waves

A numerical method is presented to deal with the propagation of surface water waves in the framework of the linear theory for an inviscid fluid. For particular geometrical configurations of the region in which wave propagation occurs, refraction, diffraction and reflection phenomena can arise simultaneously, so that the solution of the original Berkhoff equation with appropriate boundary conditions becomes essential to achieve an adequate picture of the resulting field. The method is based on a finite element scheme, in which the element matrices are computed by a series expansion technique. The elements are of arbitrary shape, although of constant depth, and two independent numerical approximations are given for the surface-elevation and velocity fields. An application of the method to the propagation of short water waves in a channel connecting two basins of larger dimensions shows that the method can deal with very large domains, at least when compared to the possibilities of the usual finite element approaches.     

Vibration modelling of complex waveguide structures

In this paper, a general wave propagation approach for the vibration analysis of three-dimensional waveguide structures is presented. The analysis is based on a ray tracing method that considers wave propagation and scattering in the formulation, including the effects of decaying near-field wave components. The waveguide dispersion characteristics of straight and curved beams, which govern the propagation and decay of waves as they travel through the different components, are taken into account for different wave types (flexural, torsional, and axial). Separate elements are coupled using reflection and transmission coefficients, and these are derived for a general connection between several non-planar elements. A matrix formulation is used that offers an automatic and concise method for tackling free and forced vibrations problems of complex ring-beam structural systems. The general methodology is demonstrated on simple applications, and the predictions made using the proposed approach are shown to be in excellent agreement with a conventional finite element analysis, with the advantage of reduced computational costs.     

The B‐spline finite element based parabolic wave propagation inside a parallel plate waveguide

A b‐spline based finite element method parabolic wave propagation model is developed and tested against mode summation inside a parallel plate waveguide. The comprehensive numerical analysis of the solution of parabolic wave equation has been done. The algorithm is compared with mode summation in two dimensions. Excellent agreement is observed among the results. © 2013 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2013.     

Special short wave elements for flow acoustics

A numerical formulation based on the Partition of Unity Method (PUM) is proposed for modelling the propagation of short acoustic waves on irrotational mean flows. The method seeks to reduce the pollution error which exists in conventional FE schemes at high frequencies by using a local basis which is enriched by plane wave solutions of the convected Helmholtz equation. Initially the method is demonstrated with reference to a one dimensional model consisting of a variable area converging–diverging duct with mean flow. Next a simple two-dimensional model of a straight duct with uniform flow, is considered. In both cases the accuracy and the conditioning of the numerical solution is investigated for ranges of frequency and Mach number characteristic of aero-engine bypass ducts.