The effect of the boundary conditions on in-plane and out-of-plane stress field in three dimensional plates weakened by free-clamped V-notches

Dealing with the material microstructure an analytical multiscale model has recently been developed by Sih. Physically, the different orders of the stress singularities are related to the different constraints associated with the defect thought as a microscopic V-notch at the tip of the main crack. Irregularities of the material microstructure tend to curl the crack tip being the clamped-free boundary conditions the more realistic and general representation of what occurs on the microscopic V-notch. As a result, mixed mode conditions are always present along the V-notch bisector line.It is known for a long time that at the antisymmetric (mode II) stress distribution ahead of the crack tip generates a coupled out-of-plane singular mode. Recent theoretical and numerical analyses have demonstrated that this out-of-plane mode due to three-dimensional effects occurs also in the case of large V-notches where the mode II stress field is no longer singular. In addition, when the notch opening angle is non-zero, the three-dimensional singular stress state is strongly influenced by the plate thickness.The aim of this paper is to investigate the effect of free-fixed boundary conditions along the notch edges in three dimensional plates weakened by pointed V-notches and quantify the intensity of the out-of-plane singularity occurring under this constraint configuration. For the sake of simplicity a macronotch is considered rather than a micronotch. A synthesis of the magnitude of the stress state through the plate thickness is carried out by using the mean value of the strain energy density over a given control volume embracing the notch tip. The capability of the strain energy density to capture all the combined effects due to the out-of-plane mode make it a powerful parameter at every scale levels.     

Brittle Fracture of Rounded V-Notches in Isostatic Graphite under Static Multiaxial Loading

While a large bulk of experimental results from cracked specimens of polycrystalline graphite under pure modes of loading, in particular under mode I loading, can be found in the literature, only a very limited number of tests have been carried out on notches. At the best of the author knowledge dealing with the specific case of V-notches under mixed mode loading (tension + torsion) no results can be found in the literature. With the aim to fill this lack, the problem of mixed mode (I + III) brittle fracture of polycrystalline graphite is investigated systematically here for the first time. The present study considers cylindrical specimens weakened by circumferential notches characterized by different acuities. A new complete set of experimental data is provided considering different geometrical configurations by varying the notch opening angle and the notch tip radius. The multiaxial static tests have been performed considering different values of the mode mixity ratio (i.e. the ratio between the nominal stress due to tension and that due to torsion loading). A criterion based on the local strain energy density previously applied by the same authors only to pure modes of loading is extended here to the case of tension and torsion loadings applied in combination. The proposed criterion allows a sound assessment of the fracture loads.     

Finite element modeling of the interaction of laser-generated ultrasound with a surface-breaking notch in an elastic plate

The interaction of surface acoustic waves generated by laser line source in the thermoelastic regime with surface notches are investigated. The finite element method is used to establish the model of the transient displacement field for surface notches with various depths and orientation. The magnitude of the signal enhancement in the near field and the mechanism by which this occurs are explained. The positions of notches were evaluated by the reflected Rayleigh wave. The depths and orientations of the notches were also determined using a shear wave that was generated through mode conversion of a surface acoustic wave at the notch tip. The results agree with previously published experimental measurements.     

On three-dimensional stress analysis of periodic notched plates under tension

By using the finite element method, three-dimensional models of a number of periodic blunt and sharp notches subjected to tension loading are investigated. The aim of this research is to investigate the thickness effect on the location of maximum stress and notch stress intensity factor (NSIF) of corresponding blunt and sharp periodic notches respectively. With this aim, different number of periodic notches as well as different notch opening angles are examined. While for two-dimensional plates weakened by periodic notches some results are available in the literature, this paper first faces the problem of three-dimensional cases. A total of about 100 geometrical configurations are investigated. It is found that, the effect of plate thickness of periodic notched components can be characterized by the relative value with respect to the depth of the notch (H/t). For the blunt periodic notches with relatively higher values of H/t ratio, the value of the maximum tensile stress is located near the free surface. On the contrary for lower values of H/t, it is placed at the middle plane. The same behaviour is observed for sharp periodic notches in terms of notch stress intensity factors.     

Transmission analysis of ultrasonic Lamb mode conversion in a plate with partial-thickness notch

Mode conversions of Lamb waves can occur upon encountering damage or defect such as a notch, leading to newly-converted modes apart from wave reflection and transmission. In this paper, the transmission of the fundamental Lamb modes symmetrical S0 and anti-symmetrical A0 with anti-symmetrical notches were investigated in steel plates within the relatively short propagation distance. The group velocity and modal energy of the converted modes were analyzed using simulations and experiments. Two-dimensional finite difference time domain (2D-FDTD) method was employed to calculate the scattering field and extract numerical trends for simulation study and experimental confirmation. Both simulations and experiments revealed that the apparent group velocities of the converted modes in the transmitted signals subject to the notch positions. To describe the mode conversion degree and evaluate the notch severity, wave packets of the originally-transmitted modes and newly-converted modes were separated and corresponding mode energy percentages were analyzed at different notch severities. Frequency-sweeping measurements illustrated that the modal energy percentages varied monotonically over the notch-depth increase with a statistically consistency (R = 1.00, P < 0.0004).     

孤子内波导致海洋环境噪声垂直指向性异常分析

依据近场波数积分、远场耦合简正波相结合的二维噪声场模型,侧重理论研究孤子内波所在扇区,环境噪声垂直阵响应的变化,分析了某些孤子内波情形下垂直阵环境噪声水平凹槽变深这一异常现象的原因:孤子内波离垂直阵较近时,远离内波的海面噪声源多,其激发的简正波能量由低号耦合到高号,在垂直阵处高号简正波能量对环境噪声场贡献增大,导致环境噪声水平凹槽加深;对于大尺度、多波包孤子内波,其范围相对较大,内波所在区的局部简正波本征值和本征函数产生的变化影响显著,使低号简正波衰减变快,而高号衰减慢,导致接收阵处高号简正波能量增加,低号简正波变弱,这样,无论孤子内波群靠近或离接收阵远,都将使垂直阵环境噪声水平凹槽加深。      

声场中空化气泡的耦合振动及形状不稳定性的研究

计算了两个具有非球形扰动的气泡所组成系统的能量,并基于Lagrange方程得到了有声相互作用的非球形气泡的动力学方程和形状稳定性方程,研究了声场中非球形气泡间相互作用力对非球形气泡的形状不稳定性和气泡形状模态振幅的影响.研究结果表明声场中具有非球形扰动的气泡之间的耦合方式有两种:形状耦合模式和径向耦合模式,气泡之间的耦合方式取决于气泡形状扰动模态.由形状耦合及径向耦合产生的气泡之间的相互作用力能够改变单个气泡的形状不稳定及形状模态振幅,具体影响因素取决于声场驱动条件、气泡形状模态、相邻气泡的初始半径.     

Ultrasonic guided wave parameters for detection of axial cracks in feeder pipes of PHWR nuclear power plants

The dispersion curves for the feeder pipes in PHWR nuclear power plants were determined. The wave modes used for the detection of notches in the feeder pipe were confirmed as F(m,2) and/or L(0,1) by an analysis of short time Fourier transformation (STFT). The axial notches in the straight pipe were not detectable, but an axial notch in a bent pipe was detected with the mode at the frequency of 500 kHz. Initial F(m,2) and/or L(0,1) modes contains a circumferential displacement and might be converted to certain complicated modes in the bent region, which is sensitive to the axial notch. The circumferential guided wave technique was also applied for quantitative evaluation of the axial notches. The waves generated by a rocking motion of the transducer along the circumferential direction were estimated as the circumferential guided waves after a review of the acquired data and the dispersion curves.     

Experimental study of the A0 and S0 Lamb waves interaction with symmetrical notches

The aim of this work is to study the fundamental Lamb modes interaction with defects in isotropic plates. For these experimental investigations, symmetrical notches with various depths milled in aluminum plates are considered. Moreover, the incident Lamb wave of a specific mode is generated by means of two identical thin piezoceramic transducers placed at the opposite sides of the plate. The waves scattered by the notch are recorded with conventional transducers located on the plate surface in front and behind the defect. The selection of the A₀ or the S₀ modes is obtained by exciting the transducers with anti-phased or in-phased signals, respectively. Furthermore, a calibration process is investigated to correct errors caused by the presence of the receiver between the emitters and the defects. The power reflection and transmission coefficients are then obtained and the power balance is verified. Finally, these measurements are compared successfully with those obtained by a numerical method using the finite-element modeling described in a previous work.     

Mode III Notch Fracture Toughness Assessment for Various Notch Features

In the present paper, two stress-based failure criteria are proposed to predict the notch fracture toughness for three different notch features under pure mode III loading. These criteria are developed based on the two well-known failure concepts of the point-stress and the mean-stress previously used for predicting brittle fracture in notched members under various loading conditions. The validity of the criteria is verified through the comparison of their theoretical predictions with a bulk of test data reported in the open literature on mode III fracture of graphite notched round bars. Very good agreement is shown to exist between the experimental and theoretical results. Moreover, the comparison revealed that the mean-stress criterion is more accurate than the point-stress criterion in predicting mode III brittle fracture of V-notches and semicircular notches.     

一种水平变化波导中声传播问题的耦合模态法

针对介质参数及海底边界水平变化波导中的声传播问题,本文基于多模态导纳法提出一种能量守恒且便于数值稳定求解的耦合模态方法.将声压表示为一组正交完备的本地本征函数之和,对声压满足的Helmholtz方程在本地本征函数上作投影,推导出关于声压模态系数的二阶耦合模态方程组.耦合矩阵直观描述水平变化因素对模态耦合的贡献.为避免直接求解二阶耦合模态方程组可能遇到的数值发散问题,将其重构为两个耦合的一阶演化方程组,引入导纳矩阵并使用Magnus数值积分方法获得稳定的声场解.利用该耦合模态方法数值计算水平变化波导中的声场,并与COMSOL参考解比较,结果表明该耦合模态理论能够精确求解水平变化波导中的点源及分布源传播问题.     

Circumferential and longitudinal defect detection using T(0,1) mode excited by thickness shear mode piezoelectric elements

Different kinds of defects, such as corrosions, notches and cracks etc, exist in pipes. Mode choice is important since unfortunately not all ultrasonic guided wave modes are suitable for these kinds of defect detection. T(0,1) mode which is non-dispersive is the lowest and fastest torsional mode and most suitable for defect detection in pipes. Two completely different artificial defects including longitudinal and circumferential defects are processed successively in a 4-m-long, 60-mm-OD, 3.5-mm-wall steel pipe. T(0,1) mode at 45 kHz is excited to detect these defects using thickness shear mode piezoelectric elements. Experimental results show that two kinds of defects are detectable using T(0,1) mode. Comparing with longitudinal modes, torsional modes are dominant in pipe inspection for their sensitivities to different kinds of defects.     

A rigorous study of the rf fields in complex cavities with gradual transitions

Based on mode coupling theory, the general form of coupled second order differential equations for the longitudinal rf standing-wave amplitudes in a complex cavity with gradual transition is developed. The TM type non-principal modes generated due to mode conversion are systematically taken into account. Comparisions of numerical results including or excluding TM modes are made for several examples and some interesting results are obtained.     

Application of generalized complex modes to the calculation of the forced response of three-dimensional poroelastic materials

Finite element models based on Biot's {u,P} formulation for poroelastic materials are widely used to predict the behaviour of structures involving porous media. The numerical solution of such problems requires however important computational resources and the solution algorithms are not optimized. To improve the solution process, a modal approach based on an extension of the complex modes technique has been proposed recently and applied successfully to a simplified mono-dimensional problem. In this paper, this technique is investigated in the case of three-dimensional poroelastic problems. The technique is first recalled, then analytical proof of the stability of the model are given followed by considerations of numerical improvements of the method. An energetic interpretation of the generalized complex modes is then given and some numerical results are presented to illustrate the performance of the approach.     

前缘弯掠风扇叶尖涡的数值分析与PIV实验

本文采用三维Navier-stokes方程、κ-ε两方程湍流模型和SIMPLE算法,对空调用前缘弯掠开式斜流风扇转子叶尖涡的三维流动特性进行了数值分析与PIV实验测量。结果表明:沿子午面流动的主气流与从叶顶外侧吸入的气流之间的卷吸作用导致在吸力面叶顶区域产生了叶尖涡。叶尖涡从25％叶顶弦长位置到50％弦长位置不断发展,同时沿吸力面向下游移动;叶尖涡随后逐渐向压力面移动;叶尖涡从75％叶顶弦长位置至转子下游逐渐耗散,沿着一条与叶轮旋向相反的斜线向转子下游发展,大致持续到转子下游65％叶顶弦长位置。计算结果和PIV的实测结果吻合,表明用 CFD工具可以预测流场,同时为前缘弯掠开式斜流转子在大型中央空调室外机上的应用和风机系统的优化设计及其降噪提供了重要的内流数据。     

Superfocussing in a metal-coated tetrahedral tip by dimensional reduction of surface-to edge-plasmon modes

Metal-coated dielectric tetrahedral tips (T-tip) have long been considered to be interesting structures for the confinement of light to nanoscopic dimensions, and in particular as probes for scanning near-field optical microscopy. Numerical investigations using the Finite-Difference Time-Domain (FDTD) method are used to explore the operation of a T-tip in extraction mode. A dipole source in close proximity to the apex excites the tip, revealing the field evolution in the tip, the resulting edge and face modes on the metal-coated surfaces, and the coupling from these modes into highly directional radiation into the dielectric interior of the tip. These results are the starting point for illumination-mode numerical investigations by a Volume Integral equation method, which compute the field distribution that develops in a T-tip when a Gaussian beam is incident into the tip, and which show that a highly confined electric field is produced at the apex of the tip. The process of light confinement can be considered as a superfocussing effect, because the intensity of the tightly confined light spot is significantly higher than that of the focussed yet much wider incident beam. The mechanism of superfocussing can be considered as a dimensional reduction of surface plasmon modes, where an edge plasmon is the most important link between the waveguide-modes inside the tip and the confined near field at the apex.     

Mode coupling between first- and second-order whispering-gallery modes in coupled microdisks

The mode characteristics for two coupled microdisks are investigated by the finite-difference time-domain technique. In the two coupled micodisks, mode coupling between the same order whispering-gallery modes (WGMs) results in coupled WGMs with split mode wavelengths. The numerical results show that the split mode wavelengths of the coupled first- and second-order WGMs can have a crossing point in some cases, which can induce anticrossing mode coupling between them and greatly reduce the mode Q factor of the coupled first-order WGMs. The time variation of mode field pattern shows the transformation between the coupled first- and second-order WGMs.     

On the study of the vibrational energy levels of Arsine molecule

We compare two formalisms applied to the vibrational modes of the molecule of AsH₃ of C_3v molecular symmetry group. Indeed, the close stretching modes of this molecule may be considered as those of a three-dimensional oscillator whereas the bending modes may be considered either as a one-dimensional oscillator of symmetry A₁ and a two-dimensional oscillator of symmetry E or as an approximate three-dimensional oscillator. So, we have applied the U(p + 1) formalism to the both stretching and bending modes and introduced coupling terms acting on an appropriate coupled vibrational basis through a local mode formalism. We have then compared the result of our fitting with those obtained with the coupling of a local mode formalism adapted to the stretching vibrations with a normal mode formalism for the bending ones. Finally we compare our results with other methods recently proposed in the literature.     

A coaxial HOM coupler for a superconducting RF cavity and its low-power measurement results

A resonant buildup of beam-induced fields in a superconducting radio frequency (RF) cavity may make a beam unstable or a superconducting RF cavity quench. Higher-order mode (HOM) couplers are used for damping higher-order modes to avoid such a resonant buildup. A coaxial HOM coupler based on the TTF (TESLA Test Facility) HOM coupler has been designed for the superconducting RF cavities at the Proton Engineering Frontier Project (PEFP) in order to overcome notch frequency shift and feed-through tip melting issues. In order to confirm the HOM coupler design and finalize its structural dimensions, two prototype HOM couplers have been fabricated and tested. Low-power testing and measurement of the HOM couplers has shown that the HOM coupler has good filter properties and can fully meet the damping requirements of the PEFP low-beta superconducting RF linac.