Estimation of ultrasonic guided wave mode conversion in a plate with thickness variation

The hybrid boundary element method aimed at analyzing Lamb wave scattering from defects can provide us with an excellent numerical tool for tackling complicated mode conversion phenomena under waveguide thickness variation. In this paper, utilization of hybrid boundary element modeling for specific Lamb wave mode incidence situations with special energy distributions along the structural cross section is proposed for estimating reflection and transmission from various scatterers, such as a step discontinuity and tapered parts of a waveguide, etc. Interaction of individual Lamb wave modes with scatterers that represent arbitrary thickness variation along the direction of guided wave propagation is investigated by calculating the scattered fields for varying incident modes, frequency, and scatterer shape. The mode conversion phenomena through step discontinuity in a plate are also experimentally explored. The theoretical predictions of reflection and transmission by boundary element methods and the utility of dispersion curves are compared with experiments for specific modes. Results in this paper can be used to improve inspection sensitivity and penetration power for a variety of practical NDE applications, notably those in which thickness variation is found. In addition, the feasibility of inspecting sections located behind a waveguide thickness variation region and subsequent mode control will also be discussed.     

Estimating terminal velocity of rough cracks in the framework of discrete fractal fracture mechanics

In this paper we first obtain the order of stress singularity for a dynamically propagating self-affine fractal crack. We then show that there is always an upper bound to roughness, i.e. a propagating fractal crack reaches a terminal roughness. We then study the phenomenon of reaching a terminal velocity. Assuming that propagation of a fractal crack is discrete, we predict its terminal velocity using an asymptotic energy balance argument. In particular, we show that the limiting crack speed is a material-dependent fraction of the corresponding Rayleigh wave speed.     

The effects of element shape on the critical time step in explicit time integrators for elasto‐dynamics

In this paper, the effects of element shape on the critical time step are investigated. The common rule‐of‐thumb, used in practice, is that the critical time step is set by the shortest distance within an element divided by the dilatational (compressive) wave speed, with a modest safety factor. For regularly shaped elements, many analytical solutions for the critical time step are available, but this paper focusses on distorted element shapes. The main purpose is to verify whether element distortion adversely affects the critical time step or not. Two types of element distortion will be considered, namely aspect ratio distortion and angular distortion, and two particular elements will be studied: four‐noded bilinear quadrilaterals and three‐noded linear triangles. The maximum eigenfrequencies of the distorted elements are determined and compared to those of the corresponding undistorted elements. The critical time steps obtained from single element calculations are also compared to those from calculations based on finite element patches with multiple elements. Copyright © 2014 John Wiley & Sons, Ltd.     

可调谐手征超表面电磁特性研究进展

手征超表面是由具有特定电磁响应的平面手征单元结构构成的超薄超材料,由于其具有自由控制电磁波的奇异能力而引起了极大的关注.通过在超表面设计中加入可调谐材料,可以实现其功能受外部激发控制的可调谐或可重构的超器件,为动态调谐电磁波开辟了新的道路.本文介绍了可调/可重构手征超表面电磁特性的一些理论基础,当线偏振光进入可调谐手征...     

A finite element model for shape memory behavior

This paper deals with a finite element implementation concerning the shape memory behavior. Shape memory behavior is usually driven by temperature changes. This model allows the simulation of problems integrating complex mechanical loading effects under random temperature variations. According to the relationship between stress and strain, the shape fixation during cooling phases and the memory effect during heating phase are modelised through a hereditary behavior needing incremental formulation developments. The step by step process introduces an additional fixed stress. Simulations request, for complex geometries including boundary conditions, a finite element approach. Thermodynamic developments are presented in order to define energetic balance and dissipations. In this paper, we propose to generalize this dependence of elastic modulus variations. A formulation for random mechanical loading and temperature variations is proposed. An experimental validation is proposed about shape memory alloy polymer DP5.     

Comparison of implicit and explicit hybridizable discontinuous Galerkin methods for the acoustic wave equation

We describe implicit and explicit formulations of the hybridizable discontinuous Galerkin method for the acoustic wave equation based on state‐of‐the‐art numerical software and quantify their efficiency for realistic application settings. In the explicit scheme, the trace of the acoustic pressure is computed from the solution on the two elements adjacent to the face at the old time step. Tensor product shape functions for quadrilaterals and hexahedra evaluated with sum factorization are used to ensure low operation counts. For applying the inverse mass matrix of Lagrangian shape functions with full Gaussian quadrature, a new tensorial technique is proposed. As time propagators, diagonally implicit and explicit Runge–Kutta methods are used, respectively. We find that the computing time per time step is 25 to 200 times lower for the explicit scheme, with an increasing gap in three spatial dimensions and for higher element degrees. Our experiments on realistic 3D wave propagation with variable material parameters in a photoacoustic imaging setting show an improvement of two orders of magnitude in terms of time to solution, despite stability restrictions on the time step of the explicit scheme. Operation counts and a performance model to predict performance on other computer systems accompany our results. Copyright © 2015 John Wiley & Sons, Ltd.     

大宽厚比冷轧带材三维应力分布的样条有限条分析

本文在轧件宽厚比为６２５的条件下，用三次样条函数有限条法研究了冷轧带材三维应力的分布问题。获得了轧后边浪和中浪两种不同板形条件下的应力分布规律。对板形理论和板形控制技术的发展有指导意义。     

Numerical study of the three-dimensional wave equation using the mesh-free kp-Ritz method

This paper deals with numerical modeling of three-dimensional linear wave propagation based on the mesh-free kp-Ritz method. The mesh-free kernel particle estimate is employed to approximate the 3D displacement field. A system of discrete equations is obtained through application of the Ritz minimization procedure to the energy expressions. Convergence analysis and error estimates of the kp-Ritz method for three-dimensional wave equation are also presented in the paper. From the error analysis, we found that the error bound between the numerical and the exact solution is directly related to the radii of weight functions and the time step length. Effectiveness of the kp-Ritz method for three-dimensional wave equation is investigated by three numerical examples.     

识别薄板中兰姆波和体波的阶梯板方法

斜探头在某些频率下激励出的兰姆波,其群速度与体波的传播速度相近,所以通过判断传播速度不易区分出兰姆波和体波。通过数值模拟和实验,分别研究了激励频率为2 MHz的纵波和S0模态兰姆波在阶梯板上的反射特性,发现:在阶梯板上入射S0模态兰姆波时,有反射回波;而入射纵波时,无反射回波。基于这种反射特性的差别,提出了一种利用阶梯板区别薄板中兰姆波和体波的方法,该方法可用于确认探头的激励特性。     

NiTi合金形状记忆效应的微观机制研究进展

NiTi合金具有优异的形状记忆功能和良好的生物体兼容性,近年来对它的应用研究受到工程界和医学界的重视,同时对NiTi合金形状记忆效应的微观机制的研究也在逐步深入.介绍了NiTi合金的主要特性及影响其形状记忆功能的主要因素,总结了NiTi合金的形状记忆效应和超弹性的微观机制研究现状,并指出了需对该合金进一步研究的一些问题.     

Hybrid Ultrasonic TOFD Imaging of Weld Flaws Using Wavelet Transforms and Image Registration

Ultrasonic time of flight diffraction (TOFD) is an effective weld crack inspection technique. Due to the intensity of diffraction wave is rather weak compared with the lateral wave and the bottom echo wave, thus the signal-to-ratio (SNR) of TOFD image is low. A new dichotomous method is comprised of two steps that contains wavelet shrinkage and image registration is proposed in this paper to reduce the noise and improve the resolution of TOFD images as well. In order to evaluate the reliability of our proposed method in this paper, we have established the experiment system, and sampled a number of TOFD data with random distribution of noise characteristics. We adopted one-dimension wavelet transform and two-dimension wavelet transform in the very beginning of the first step of the proposed algorithm respectively. The SNR of the result obtained in this step is improved significantly compared with the classic algorithms. Next, the image registration is applied. After the registered images have been added to form a new one, then it comes to the final result that shows not only the SNR but also the definition of the image is enhanced effectively.     

补偿模糊神经网络的改进及其在通风空调故障诊断中的应用

对传统补偿模糊神经网络(CFNN)的算法进行了改进,提出了动态调整学习步长的方法,避免了较大震荡,同时加快了迭代速度,与定学习步长的方法相比,学习速度和误差精度都有大大提高,最后通过仿真实验证明该方法在地下通风空调系统故障诊断中,具有收敛速度快,诊断精度高,并且适应性强等优点.     

Shape optimization of a breakwater

In this paper, we optimize the shape of a breakwater which protects a harbour basin from incoming waves. More specifically, our objective is reducing the harbour resonance due to long-range ocean waves. We consider the complex-valued Helmholtz equation as our model state equation and minimize the average wave height in the harbour basin with the shape of the breakwater as optimization variable. The geometry is described by the level set method, i.e. the domain is given as the subzero level set of a function. In contrast to many publications we use the volume expression of the shape derivative, which lends itself naturally to a level set update via a transport equation. The model problem features intrinsic geometric constraints which we treat in the form of forbidden regions. We guarantee feasibility of the iterates by projecting the gradient onto a suitable admissible set.     

Symmetrical frictionless indentation over a uniformly expanding contact region—I. Basic analysis

The study of two-dimensional wave propagation in a half-space due to indentation by a rigid smooth indentor of a general shape at a non-uniform velocity is approached by assuming that the indentor shape and displacement history can be represented by polynomial curves in, respectively, a spatial variable and the time. As a first step symmetric indentation over a contact region expanding at a constant sub-Rayleigh wave speed is considered. Since superposition will yield more general forms attention is confined to polynomials homogeneous of degree $\text{n ? 1}$ with n + 1 terms and arbitrary coefficients. By homogeneous function techniques all the field variables in the half-space for any $\text{n}$ are obtained as single integrals. Conditions for the existence of singularities in the stresses and particle velocities are examined and some general results with bearing on the indentation problem are discussed.     

Reflection error analysis for wave propagation problems solved by a heterogeneous asynchronous time integrator

Within the framework of dynamic calculations, the hybrid multi–time‐step method proposed by Gravouil and Combescure (GC method) has proven to be an efficient algorithm that enables the use of arbitrary time steps and Newmark time schemes in each subdomain. Nonetheless, when dealing with wave propagation problems, the amount of reflections at the interfaces between subdomains strongly depends on the choice of the time integrators and the time steps used for the simulation study. In this paper, we deal with both one‐ and two‐dimensional wave propagation problems (only the anti‐plane shear wave problem is considered for the two‐dimensional case) with the aim of deriving an analytical estimation of the numerical reflection coefficient at the interface between two linear elastic subdomains having their own time integrators and time scales. The model is approximated using the lowest‐order finite elements, whereas the propagation process is described using harmonic waves. The study is carried out on the explicit/implicit and explicit/explicit integrations using arbitrary time‐step ratios. The numerical reflection coefficient is then analyzed with emphasis on the effect of the time‐step ratio and the direction of incidence.     

A fast 3D shape measurement method based on sinusoidal and triangular fringe projection

Existing methods to measure 3D shape of complex object involve processing more than six captured images to obtain the absolute phase, which limit the measurement speed. This paper presents two sinusoidal fringes and two triangular wave fringes which is used to measure 3D shape of complex object. The two-step phase-shifting sinusoidal fringes and two-step phase-shifting triangular wave fringes are calculated to obtain the wrapped phase, and then the two-step phase-shifting triangular wave fringes are used to determine the fringe order. Due to decrease the number of projection fringes, the speed of measurement increases. The triangular wave fringe carries more information of the object than linear increasing/decreasing ramp fringe in the actual measurement, more noise in the base phase to be overcome, thus improving the measurement accuracy. The benefits can be widely applied in high-speed, real-time 3D measurement of complex shape. Experimental results have demonstrated that the proposed method is simple, but effective.     

Using photon funnels based on metamaterial cloaks to compress electromagnetic wave beams

Based on the metamaterial cloaking technique, we propose the use of a new photon funnel to compress a plane electromagnetic (EM) wave. The theoretical analysis and numerical simulations indicate that the compression ratio can be designed optionally and the compressed wave beam remains the original wave shape without any distortions. Here we apply the method to EM waves but it can be applied to acoustic waves and other fields as well.     

Numerical modelling of elastic wave scattering in frequency domain by the partition of unity finite element method

In this paper, we investigate a numerical approach based on the partition of unity finite element method, for the time‐harmonic elastic wave equations. The aim of the proposed work is to accurately model two‐dimensional elastic wave problems with fewer elements, capable of containing many wavelengths per nodal spacing, and without refining the mesh at each frequency. The approximation of the displacement field is performed via the standard finite element shape functions, enriched by superimposing pressure and shear plane wave basis, which incorporate knowledge of the wave propagation. A variational framework able to handle mixed boundary conditions is described. Numerical examples dealing with the radiation and the scattering of elastic waves by a circular body are presented. The results show the performance of the proposed method in both accuracy and efficiency. Copyright © 2008 John Wiley & Sons, Ltd.     

Iterative zonal wave-front estimation algorithm for optical testing with general-shaped pupils

An iterative zonal wave-front estimation algorithm for slope or gradient-type data in optical testing acquired with regular or irregular pupil shapes is presented. In the mathematical model proposed, the optical surface, or wave-front shape estimation, which may have any pupil shape or size, shares a predefined wave-front estimation matrix that we establish. Owing to the finite pupil of the instrument, the challenge of wave front shape estimation in optical testing lies in large part in how to properly handle boundary conditions. The solution we propose is an efficient iterative process based on Gerchberg-type iterations. The proposed method is validated with data collected from a 15 x 15-grid Shack-Hartmann sensor built at the Nanjing Astronomical Instruments Research Center in China. Results show that the rms deviation error of the estimated wave front from the original wave front is less than lambda/130-lambda/150 after approximately 12 iterations and less than lambda/100 (both for lambda = 632.8 nm) after as few as four iterations. Also, a theoretical analysis of algorithm complexity and error propagation is presented.     

半埋目标低频声波散射反演的一种新算法

半埋目标低频声波散射在数学上归纳为求解带有混合边界的不可穿透的散射体外声场问题,是一个公认的理论难题。本文首次将区域导数法引入边界条件为混合边界不可穿透的散射体的外声场问题中,数值结果证明算法是可行的、正确的,为解决半埋目标低频声波散射物形状识别提供了一种新方法,这在工程实际及军事上均有重要的应用价值。