Calculation of Valence Subband Structures for Strained Quantum-Wells by Plane Wave Expansion Method Within 6×6 Luttinger-Kohn Model

The valence subband energies and wave functions of a tensile strained quantum well are calculated by the plane wave expansion method within the 6×6 Luttinger Kohn model.The effect of the number and period of plane waves used for expansion on the stability of energy eigenvalues is examined.For practical calculation,it should choose the period large sufficiently to ensure the envelope functions vanish at the boundary and the number of plane waves large enough to ensure the energy eigenvalues keep unchanged within a prescribed range.

2.5D scattering of incident plane SV waves by a canyon in layered half-space

This paper presents a 2.5D scattering of incident plane SV waves by a canyon in a layered half-space by using the indirect boundary element method （IBEM）. A free field response analysis is performed to provide the displacements and stresses on the boundary of the canyon where fictitious uniform moving loads are applied to calculate the Green＇s fi.mctions for the displacements and stresses. The amplitudes of the loads are determined by the boundary conditions. The free field displacements are added to the fictitious uniform moving loads induced displacements and the total response is obtained. Numerical calculations are performed for a canyon with homogenous and in one layer over bedrock. The effects of the thickness and stiffness of the layer on the amplification are studied and discussed.

Dynamic soil-tunnel interaction in layered half-space for incident plane SH waves

The dynamic soil-tunnel interaction is studied by indirect boundary element method （IBEM）, using the model of a rigid tunnel in layered half-space, which is simplified to a single soil layer on elastic bedrock, subjected to incident plane SH waves. The accuracy of the results is verified through comparison with the analytical solution. It is shown that soil-tunnel interaction in layered half-space is larger than that in homogeneous half-space and this interaction mechanism is essentially different from that of soil-foundation-superstructure interaction.

Diffraction of plane P waves around an alluvial valley in poroelastic half-space

Diffraction of plane P waves around an alluvial valley of arbitrary shape in poroelastic half-space is investigated by using an indirect boundary integral equation method. Based on the Green＇s fimctions of line source in poroelastic half-space, the scattered waves are constructed using the fictitious wave sources close to the interface of the valley and the density of ficti- tious wave sources are determined by boundary conditions. The precision of the method is verified by the satisfaction extent of boundary conditions, and the comparison between the degenerated solutions and available results in single-phase case. Finally, the nature of diffraction of plane P waves around an alluvial valley in poroelastic half-space is investigated in detail through nu- merical examples.

A 1D time-domain method for in-plane wave motions in a layered half-space

A 1D finite element method in time domain is developed in this paper and applied to calculate in-plane wave motions of free field exited by SV or P wave oblique incidence in an elastic layered half-space. First, the layered half-space is discretized on the basis of the propagation characteristic of elastic wave according to the Snell law. Then, the finite element method with lumped mass and the central difference method are incorporated to establish 2D wave motion equations, which can be transformed into 1D equations by discretization principle and explicit finite element method. By solving the 1D equations, the displacements of nodes in any vertical line can be obtained, and the wave motions in layered half-space are finally determined based on the characteristic of traveling wave. Both the theoretical analysis and the numerical results demonstrate that the proposed method has high accuracy and good stability.

The Bianisotropic Formulation of the Plane Wave Method from Faraday’s and Ampere’s Laws

The plane wave numerical technique is recast from Ampere’s and Faraday’s laws for materials that are characterized with a bianisotropic form of the constitutive relations. The populating expressions are provided for the eigenvalue matrix system that can be directly solved for the angular frequencies and field profiles when bianisotropy is included. To demonstrate the computation process and expected state diagrams and field profiles, numerical computation examples are provided for a bianisotropic Bragg Array with central defect. It is shown that the location of the magnetoelectric tensor elements has a significant effect on the eigenstates of an equivalent isotropic (anisotropic) structure. One form of the magnetoelectric tensor (diagonal elements only) leads to the observation of merging states and the formation of exceptional points. The numerical approach presented can be implemented as an add-on to the familiar plane wave numerical technique.

Impedance Analytical Method of Wave Run-up and Reflection from A Slotted-Wall Caisson Breakwater

An impedance analytical method （IAM） is developed to study the interaction of plane water wave with a slotted-wall caisson breakwater. The non-linear boundary condition at the slotted-wall is expressed in terms of flow resistance. A set of algebraic expressions are obtained for free surface elevation inside and outside chamber, and reflection coefficient. The prediction of the reflection coefficients shows that the relative widths of the chamber inducing the minimum reflection coefficient for a slotted-wall caisson breakwater are in a range of 0.10～0.20, which are smaller than that （0.15～0.25） for a perforated-wall caisson breakwater. The reflection coefficients and free surface elevation obtained by the present model are compared with that of laboratory experiments carried out by previous researchers.

3D elastic waveform modeling with an optimized equivalent staggered-grid finite-difference method

Equivalent staggered-grid(ESG) as a new family of schemes has been utilized in seismic modeling,imaging,and inversion.Traditionally,the Taylor series expansion is often applied to calculate finite-difference(FD) coefficients on spatial derivatives,but the simulation results suffer serious numerical dispersion on a large frequency zone.We develop an optimized equivalent staggered-grid(OESG) FD method that can simultaneously suppress temporal and spatial dispersion for solving the second-order system of the 3 D elastic wave equation.On the one hand,we consider the coupling relations between wave speeds and spatial derivatives in the elastic wave equation and give three sets of FD coefficients with respect to the P-wave,S-wave,and converted-wave(C-wave) terms.On the other hand,a novel plane wave solution for the 3 D elastic wave equation is derived from the matrix decomposition method to construct the time-space dispersion relations.FD coefficients of the OESG method can be acquired by solving the new dispersion equations based on the Newton iteration method.Finally,we construct a new objective function to analyze P-wave,S-wave,and C-wave dispersion concerning frequencies.The dispersion analyses show that the presented method produces less modeling errors than the traditional ESG method.The synthetic examples demonstrate the effectiveness and superiority of the presented method.

3D Diffraction of obliquely incident SH waves by twin infinitely long cylindrical cavities in layered poroelastic half-space

Abstract This paper studies three-dimensional diffraction of obliquely incident plane SH waves by twin infinitely long cylindrical cavities in layered poroelastic half-space using indirect boundary element method. The approach is validated by comparison with the literature, and the effects of cavity interval, incident frequency, and boundary drainage condition on the diffraction are studied through numerical examples. It is shown that, the interaction between two cavities is significant and surface displacement peaks become large when two cavities are close, and the surface displacement may be significantly amplified by twin cavities, and the influence range with large amplification can be as wide as 40 times of the cavity radius. Surface displacements in dry poroelastic case and saturated poroelastic cases with drained and undrained boundaries are evidently different under certain circumstances, and the differences may be much larger than those in the free-field response.

Effects of orientation and shape of holes on the band gaps in water waves over periodically drilled bottoms

The complete band gaps （CBGs） of shallow water waves propagating over bottoms with periodically drilled holes are investigated numerically by the plane wave expansion method. Four different patterns are considered, containing triangular, square, hexagonal and circular cross-sectioned holes arranged into triangular lattices. Results show that the width of CBGs can be changed by adjusting the orientation of noncircular holes and the effect of hole shape on the width of the maximal CBGs is discussed.

反平面线源荷载作用下浅埋圆形非完全粘结隧道动力响应研究

为加深理解波源距离和非完全粘结对地震波散射的影响规律,结合位移不连续模型、波函数展开法、Graf公式和镜像方法推导了反平面线源荷载下浅埋圆形非完全粘结隧道动力响应的级数解,并通过衬砌内外边界条件残余量与级数解截断项数的关系校验了该解的精度。通过对该级数解进行参数分析,系统地探讨了衬砌与围岩的接触刚度、衬砌模量、衬砌厚度、隧道埋深和波源距离等因素对衬砌内表面位移和周向剪应力的影响。结果表明:衬砌与围岩的接触刚度对隧道的动力响应具有显著的影响,尤其在某些较小接触刚度情况下隧道动力响应幅值可能非常大;增大衬砌模量会减小位移,但同时会导致周向剪应力增加;增大衬砌厚度能同时减小位移和周向剪应力;增大隧道埋深会使最大位移和周向剪应力向隧道拱顶附近移动;增大线源与隧道的水平距离会使隧道背波侧相对幅值增大。

考虑地震波输入差异的二维兰州盆地地震效应研究

利用谱元法和多次透射边界相结合的数值模拟方法,探讨了不同地震波输入时,具有大盆地内嵌小盆地特征的二维兰州盆地构造对地表地震波传播、地表峰值加速度(PGA)及其放大系数,以及频域放大特征等影响,分析了地表地震动的放大特征与盆地横向不均匀构造之间的关系。结果表明:1)当输入波的卓越频率接近小盆地最深处的一阶自振频率时,小盆地发生整体共振现象,进而显著改变地震动或放大系数的分布特征。大盆地边缘形成的次生面波在进入更为松散的小盆地时分化为波速差别显著的两阶面波,且盆地较陡一侧边缘形成的面波强度更大。2)无论何地震波入射,盆地内的最强烈地震动集中于小盆地边缘区域,大盆地较陡一侧边缘上方的区域是次强烈地震动放大区,而盆地基底倾角较缓的一侧边缘区域基本无边缘效应。3)兰州盆地基底形状对地震动的分布特征影响强烈,盆地地表地震动的放大系数受输入波的影响明显。4)水平和垂直分量的地震动及放大系数分布特征差别显著,垂直分量上在大盆地较陡一侧边缘及小盆地内形成两个显著放大区,最强烈放大效应区域靠近小盆地中心,而水平分量上的强烈放大区域主要出现在小盆地内的边缘区域。此外,地表不同位置处的频域放大特征也存在明显差别。

深度学习颅骨重建和平面波经颅超声成像方法

为解决颅骨声阻抗失配导致平面波经颅超声成像质量下降的问题,提出一种基于深度学习的颅骨重建技术,结合快速行进法可实现平面波经颅成像的相位畸变校正。根据人类颅骨CT图像设置颅骨形状进行数值仿真,颅骨重建的时间开销为0.97 s,基于重建结果计算平面波的走时平均相对误差约为0.25%,单点目标散射波走时平均相对误差约为0.76%。经颅仿体实验中,强回声点目标图像经过校正之后,平均位置偏移从1.42 mm减少为0.28 mm,半峰全宽从1.82 mm减少为0.99 mm;圆形目标图像经过校正后对比度噪声比从7.5 dB提升为9.8 dB,偏心率从0.31降低为0.24。以上结果表明,该方法能够准确计算经颅超声的走时并且显著改善成像的质量,可用于经颅脑超声成像的相位畸变校正。

含裂纹声子晶体能带分析的改进局部径向基函数配点法

基于直接法局部径向基函数配点法(local radial basis function collocation method,LRBFCM)提出了含裂纹声子晶体反平面弹性波的能带结构计算方法,分析了其能带结构特性,并通过有限元法计算对比验证该数值结果的准确性和有效性.在边界上采用直接法沿方向取局部节点,解决了边界求解不稳定问题,讨论了数值方法的处理技巧对结果的影响.并通过考虑不同声阻抗比、散射体形状(方形、圆形)和裂纹情况,验证了该方法计算含裂纹声子晶体能带结构的适用性.研究了形状参数、配点数对计算结果的影响.最后深入分析了不同长度和位置的裂纹对声子晶体能带结构的影响特性,并进行了对比分析.文章的创新性在于用直接法局部径向基函数配点法解决了含裂纹声子晶体能带结构计算的问题,极大增加了声子晶体的应用价值.研究结果显示:随着裂纹的扩展,能带结构带隙逐渐变窄;当裂纹扩展到一定程度时,金散射体的声子晶体带隙数量会增加,且新增带隙会随着裂纹扩展而变宽,但铝散射体的声子晶体带隙数量会减少;直接法局部径向基函数配点法可以大大提高含裂纹声子晶体能带结构的计算效率和计算精度.

基于二维声学黑洞的周期板结构弯曲波操控特性研究

声学黑洞(ABH)结构通过按照一定幂函数剪裁结构厚度,致使结构中弯曲波相速度的减小而实现能量聚集,为航空结构中振动能量操控提供新的思路。ABH阵列可以弥补单个ABH中低频弯曲波操控特性的不足,为了研究基于二维ABH的周期板结构的弯曲波操控特性,利用有限元方法研究无限周期ABH结构的能带结构和包含有限周期ABH的板结构声强矢量场特征,分析了含中心平台ABH与无中心平台ABH构成的周期结构中弯曲波传播特征的区别,结合有限元结果明确了平面波展开方法收敛性和适用条件。数值分析结果显示,含中心平台ABH易在低于全波长特征频率时获得表征局部共振的平直带,从ABH全波长特征频率附近开始,含中心平台ABH周期结构对弯曲波能量的定向操控特征区别于无中心平台ABH周期结构。最后研究ABH截面特征参数对弯曲波能带结构的影响规律,结果表明,内嵌式ABH截面的变化对半波长特征频率附近及低于该频率的弯曲波传播影响比较小,减小中心截断厚度、增大中心平台半径以及幂次大于2有助于形成连续且宽频的方向带隙。

钛焊缝的对置串列PCI与脉冲回波TFM组合检测

随着近年来PCI技术及TFM技术的发展与应用,与FMC及PWI所对应的数据处理方式已日渐丰富,从原先优化定性的辅助工具逐步转变为可用于实际检测的整套先进技术。针对钛焊缝检测中PCI技术与TFM技术的组合使用开展了相关分析,进行了二者与FMC和PWI配合使用的不同结合方式的对比试验。结果表明,采用PWI-TFM与对置串列PWI/FMC-PCI组合检测方式,能够优化钛焊缝检测效率与成像质量。

压电纳米声子晶体梁结构表面效应带隙特性研究

通过纳米尺寸下的纯弹性材料环氧树脂和压电材料PZT-4沿着轴向周期性交替排布,提出了压电纳米声子晶体梁结构的力学模型.将表面压电理论与Euler梁理论相结合,结合平面波展开法,建立了计算该模型能带结构的表面效应平面波展开法.进一步地,外加电压和外加轴力被用来研究机电耦合效应对带隙的影响,残余面应力和材料内禀长度被用来研究表面效应对带隙的影响,以及晶胞内PZT-4对环氧树脂的长度比和高宽比被用来研究几何参数对带隙的影响.研究结果和进一步的分析表明,影响规律对基于压电纳米声子晶体梁的纳米机电系统的设计过程和主动控制将起到积极的推动作用.

Electro-mechanical coupling wave propagating in a locally resonant piezoelectric/elastic phononic crystal nanobeam with surface effects

The model of a "spring-mass" resonator periodically attached to a piezoelectric/elastic phononic crystal(PC) nanobeam with surface effects is proposed, and the corresponding calculation method of the band structures is formulized and displayed by introducing the Euler beam theory and the surface piezoelectricity theory to the plane wave expansion(PWE) method. In order to reveal the unique wave propagation characteristics of such a model, the band structures of locally resonant(LR) elastic PC Euler nanobeams with and without resonators, the band structures of LR piezoelectric PC Euler nanobeams with and without resonators, as well as the band structures of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on PZT-4, with resonators attached on epoxy, and without resonators are compared. The results demonstrate that adding resonators indeed plays an active role in opening and widening band gaps. Moreover, the influence rules of different parameters on the band gaps of LR elastic/piezoelectric PC Euler nanobeams with resonators attached on epoxy are discussed, which will play an active role in the further realization of active control of wave propagations.

PLANE WAVES NUMERICAL STABILITY OF SOME EXPLICIT EXPONENTIAL METHODS FOR CUBIC SCHRODINGER EQUATION

Numerical stability when integrating plane waves of cubic SchrSdinger equation is thor- oughly analysed for some explicit exponential methods. We center on the following second- order methods： Strang splitting and Lawson method based on a one-parameter family of 2-stage 2nd-order explicit Runge-Kutta methods. Regions of stability are plotted and numerical results are shown which corroborate the theoretical results. Besides, a tech- nique is suggested to avoid the possible numerical instabilities which do not correspond to continuous ones.

The Plane WavesMethod for Numerical Boundary Identification

We study the numerical identification of an unknown portion of the boundary on which either the Dirichlet or the Neumann condition is provided from the knowledge of Cauchy data on the remaining,accessible and known part of the boundary of a two-dimensional domain,for problems governed by Helmholtz-type equations.This inverse geometric problem is solved using the plane wavesmethod(PWM)in conjunction with the Tikhonov regularizationmethod.The value for the regularization parameter is chosen according toHansen’s L-curve criterion.The stability,convergence,accuracy and efficiency of the proposedmethod are investigated by considering several examples.