Propagation of SH waves in an irregular monoclinic crustal layer

The present paper discusses the dispersion equation for SH waves in a monoclinic layer over a semi-infinite elastic medium with an irregularity. In the absence of the irregularity, the dispersion equation reduces to standard dispersion equation for SH waves in a monoclinic layer over an isotropic semi-infinite medium. The dispersion curves for different size of the irregularity are computed and compared for the half-space without any irregularity. It can be seen that the phase velocity is strongly influenced by the wave number and the depth of the irregularity.     

Overall constitutive description of symmetric layered media based on scattering of oblique SH waves

This papers investigates the scattering of oblique shear horizontal (SH) waves off finite periodic media made of elastic and viscoelastic layers. It further considers whether a Willis-type constitutive matrix (in temporal and spatial Fourier domain) may reproduce the scattering matrix (SM) of such a system. In answering this question the procedure to determine the relevant overall constitutive parameters for such a medium is presented. To do this, first the general form of the dispersion relation and impedances for oblique SH propagation in such coupled Willis-type media are developed. The band structure and scattering of layered media are calculated using the transfer matrix (TM) method. The dispersion relation may be derived based on the eigen-solutions of an infinite periodic domain. The wave impedances associated with the exterior surfaces of a finite thickness slab are extracted from the scattering of such a system. Based on reciprocity and available symmetries of the structure and each constituent layer, the general form of the dispersion and impedances may be simplified. The overall quantities may be extracted by equating the scattering data from TM with those expected from a Willis-type medium. It becomes evident that a Willis-type coupled constitutive tensor with components that are assumed independent of wave vector is unable to reproduce all oblique scattering data. Therefore, non-unique wave vector dependent formulations are introduced, whose SM matches that of the layered media exactly. It is further shown that the dependence of the overall constitutive tensors of such systems on the wave vector is not removable even at very small frequencies and incidence angles and that analytical considerations significantly limit the potential forms of the spatially dispersive constitutive tensors.     

Surface electro-elastic shear horizontal waves in a layered structure with a piezoelectric substrate and a hard dielectric layer

The existence and behaviour of surface electro-elastic shear horizontal waves in a layered structure consisting of a piezoelectric substrate of crystal class 6, 4, 6mm, or 4mm mechanically bonded at its upper surface to an elastic dielectric layer and bounded by an adjacent dielectric medium is considered when the shear bulk wave velocity in the elastic layer is greater than or equal to that in the substrate. The dispersion equation for the existence of the surface electro-elastic SH waves with respect to the phase velocity is obtained which includes all the above crystal classes i.e. the surface wave problems related to all these classes are presented in a single mathematical model. The investigation of the solutions of the dispersion equation is carried out and all the possible cases of the behaviour of the surface electro-elastic SH wave depending on the electro-mechanical coefficients of the layered structure are revealed.     

压电空心圆柱中波的传播

应用三维压电弹性体轴对称模型对压电空心圆柱中波的传播进行了研究. 发现在 圆柱中是否具有压电性质会对波的传播带来显著的差异. 当波长趋向于零时，在压电圆柱中 拟P波的波速渐进趋向于横观各向同性弹性体的准P波波速，而非压电圆柱中拟P波的波速 渐进趋向于一维杆模型中的P波波速；在压电圆柱中拟SV波存在驻波现象. 圆柱中的SH波 同电场无关，所以在压电圆柱和非压电圆柱中SH波具有相同的频散曲线. 应用积分变 换方法将圆柱的控制方程同其侧边界条件相结合，得到了一组动力学方程. 针对具体的侧边 界条件，得到相对应的波导条件和频散方程. 在此基础上通过数值计算模拟了圆柱受到端部 应力脉冲激励后的瞬态响应. 同时讨论了空心圆柱的半径比对轴向波传播的影响.     

初应力下压电半导体板中SH波的传播特性

针对无限大n-型压电半导体板,论文理论研究了其在初应力作用下水平剪切波的传播特性。基于压电半导体三维宏观理论和边界条件得到色散关系,结合数值算例,系统分析了边界条件、初始载流子浓度、板的厚度和初应力大小对SH波传播特性的影响。此外,讨论了初应力下两种不同材料中的SH波传播。研究显示：较小的初应力对相速度影响很小可忽略,当初应力达到一定值时波速急剧下降;类似地,初应力足够大时衰减才会逐渐加强。计算结果对压电半导体器件设计具有一定的理论指导意义。     

Propagation,reflection, and transmission of SH-waves in slightly compressible,finitely deformed elastic media

The propagation, reflection, and transmission of SH waves in slightly compressible, finitely deformed elastic media are considered in this paper. The dispersion relation for SH-wave propagation in slightly compressible, finitely deformed layer overlying a slightly compressible, finitely deformed half-space is derived. The present paper also deals with the reflection and refraction (transmission) phenomena due to the SH wave incident at the plane interface between two distinct slightly compressible, finitely deformed elastic media. The closed form expressions for the amplitude ratios of reflection and refraction coefficients of the reflected and refracted SH waves are obtained from suitable boundary conditions. For the numerical discussions, we consider the Neo-Hookean form of a strain energy function. The phase speed curves, the variations of reflection, and transmission coefficients with the angle of incidence, and the plots of the slowness sections are presented by means of graphs.     

功能梯度压电夹层结构中SH波的传播

研究了功能梯度压电上、下半空间和均匀压电层组成的夹层结构中SH波的传播性能,上、下功能梯度半空间的材料性能沿垂直于界面方向以指数函数形式变化。首先推导了SH传播时电弹场的解析解,然后利用界面条件得到了行列式形式的频散方程。基于推导的频散方程,通过数值算例表明了材料性能梯度变化、压电层厚度和材料组合方式对相速度的影响,结果对功能梯度压电材料在声波器件中的应用有参考价值。     

PROPAGATION BEHAVIORS OF SHEAR HORIZONTAL WAVES IN PIEZOELECTRIC-PIEZOMAGNETIC PERIODICALLY LAYERED STRUCTURES

This paper investigates shear horizontal （SH） waves propagating in a periodically layered structure that consists of piezoelectric （PE） layers perfectly bonded with piezomagnetic （PM） layers alternately. The explicit dispersion relations are derived for the two cases when the propagation directions of SH waves are normal to the interface and parallel to the interface, respectively. The asymptotic expressions for dispersion relations are also given when the wave number is extremely small. Numerical results for stop band effect and phase velocity are presented for a periodic system of alternating BaTiO3 and Terfenol-D layers. The influence of volume fraction on stop band effect and dispersion behaviors is discussed and revealed.     

PMN-PT夹层弹性半空间结构中SH波的传播Propagation of SH waves in sandwich structures consisting of PMN-PT single crystal layer and elastic half-spaces

分析了弹性上下半空间和PMN‐PT单晶层组成的夹层结构中SH波的传播性质,PMN‐PT单晶沿[011]c方向极化,宏观上呈mm2对称,且晶体沿角度θ方向切割。基于正交各向异性压电材料和各向同性弹性材料的基本方程,得到了夹层结构中SH波传播时行列式形式的频散方程。通过对数值算例进行分析可以看出,PMN‐PT单晶的切割角度和弹性材料属性对结构中的相速度有很大影响,因此波的某些传播性能可以通过材料的设计以及晶体切割的方向来实现,这些结论为声表面波器件的开发和应用提供了理论依据。     

Propagation behavior of SH waves in a piezomagnetic substrate with an orthorhombic piezoelectric layer

The dispersion behavior of the shear horizontal (SH) waves in the coupled structure consisting of a piezomagnetic substrate and an orthorhombic piezoelectric layer is investigated with different cut orientations. The surface of the piezoelectric layer is mechanically free, electrically shorted, or open, while the surface of the piezomagnetic substrate is mechanically free, magnetically open, or shorted. The dispersion relations are derived for four electromagnetic boundary conditions. The dispersion characteristics are graphically illustrated for the layered structure with the PMN-PT layer perfectly bonded on the CoFe₂O₄ substrate. The effects of the PMN-PT cut orientations, the electromagnetic boundary conditions, and the thickness ratio of the layer to the substrate on the dispersion behavior are analyzed and discussed in detail. The results show that, (i) the effect of the cut orientation on the dispersion curves is very obvious, (ii) the electrical boundary conditions of the PMN-PT layer dominate the propagation feature of the SH waves, and (iii) the thickness ratio has a significant effect on the phase velocity when the wave number is small. The results of the present paper can provide valuable theoretical references to the applications of piezoelectric/piezomagnectic structure in acoustic wave devices.     

Surface wave transference in a piezoelectric cylinder coated with reinforced material

The present study deals with the propagation of a polarized shear horizontal(SH)wave in a pre-stressed piezoelectric cylinder circumscribed by a self-reinforced cylinder.The interface of the two media is assumed mechanically imperfect.For obtaining the dispersion relation,the mathematical formulation has been developed and solved by an analytical treatment.The effects of various parameters,i.e.,the thickness ratio,the imperfect interface,the initial stress,the reinforcement,and the piezoelectric and dielectric constants,on the dispersion curve are observed prominently.The dispersion curves for different modes have been also plotted.The consequences of the study may be used for achieving optimum efficiency of acoustic wave devices.     

Influences of the wall thickness on the granular dispersion in a dense gas–solid coaxial jet

The granular dispersion for different wall thicknesses of the inner channel in a dense gas–solid coaxial jet is investigated by morphology. In the wave dispersion, the Kelvin–Helmholtz instability has a strong influence on the granular stream. However, increasing the wall thickness damps the K–H instability, namely weakens the wave dispersion. Consequently, the non-dimensional wavelength increases and the non-dimensional amplitude decreases as the wall thickness increases for the same annular gas velocity. The instability analysis combining with the modification of the vorticity thickness of the annular gas stream indicates that the non-dimensional wavelength increases linearly with the non-dimensional modified vorticity thickness. The relation between the amplitude of the granular dispersion and the non-dimensional modified vorticity thickness is reliable for the wave dispersion as well. In addition, the granular dispersion angle is proportional to the annular gas velocity, which slightly depends on the wall thickness.     

SHEAR-HORIZONTAL WAVES IN A ROTATED Y-CUT QUARTZ PLATE WITH AN ISOTROPIC ELASTIC LAYER OF FINITE THICKNESS

We study shear-horizontal (SH) waves in a rotated Y-cut quartz plate carrying an isotropic elastic layer of finite thickness.The three-dimensional theories of anisotropic elasticity and isotropic elast...     

透射边界高频失稳机理及其消除方法——SH波动

用有限元法求解近场波动问题,须选取人工边界条件以实现对无限域稳定、高效的数值模拟. 该文探讨了SH波导 有限元数值模拟中透射边界引发的高频失稳问题. 从离散模型出发,分析了内节点与人工边界节点运动方程频散曲线之间的匹配关系,揭示了高频失稳的一种机理,即二者相互耦合所 得计算方案支持自发从人工边界向计算区域内行进的高频波动. 提出通过调整内节点运动方程以改变这一匹配关系,从而消除失稳的措施. 理论分析与数值结果表明该措施能有效地消除高频振荡失稳.     

Characteristics of shear horizontal waves in magnetically affected ultra-thin films accounting for surface effect

Consider a nano-scaled film which is made from highly conductive materials and is subjected to a uniform and constant magnetic field at the vicinity of its surfaces. The characteristics of the propagated shear horizontal (SH) waves within such a nanostructure are of particular interest. By decomposing the magnetically affected nanofilm into the surface layers and the bulk, surface elasticity is adopted and their equations of motion for the SH waves are constructed. The demonstrated dispersion curves reveal that the SH waves can propagate or be damped within the nanofilm in two manners: symmetric and asymmetric. Thereafter, the roles of the magnetic field strength and the thickness on the dispersion curves and phase velocities of both symmetric and asymmetric SH waves are addressed. Additionally, the limitations of the classical continuum theory in predicting the characteristics of SH waves are displayed and discussed.     

ELASTIC SH WAVE PROPAGATION IN PERIODIC LAYERED COMPOSITES WITH A PERIODIC ARRAY OF INTERFACE CRACKS

The interaction of anti-plane elastic SH waves with a periodic array of interface cracks in a multi-layered periodic medium is analyzed in this paper. A perfect periodic structure without interface cracks is first studied and the transmission displacement coefficient is obtained based on the transfer matrix method in conjunction with the Bloch-Floquet theorem. This is then generalized to a single and periodic distribution of cracks at the center interface and the result is compared with that of perfect periodic cases without interface cracks. The dependence of the transmission displacement coefficient on the frequency of the incident wave, the influences of material combination, crack configuration and incident angle are discussed in detail. Compared with the corresponding perfect periodic structure without interface cracks, a new phenomenon is found in the periodic layered system with a single and periodic array of interface cracks.     

近场动力学系统中波传播特性的探究

近场动力学是一类基于非局部思想的新固体力学方法,其采用积分形式的控制方程,自然地适用于极端载荷下材料破碎和裂纹发展的模拟,被广泛用于国防安全等领域的研究.但是,非局部性会引入色散效应,对波的传播产生不利影响,制约其对断裂等固体行为的捕捉能力.为此,采用谱分析方法,对近场动力学系统的色散行为进行了全面的研究.发现相比于低频成分,高频成分的色散关系呈现出振荡趋势和零能模式,色散问题更为严重.高频域的色散行为还随波的传播方向发生改变,呈现出沿45°的对称性.而近场动力学系统本身缺乏数值耗散,无法抑制色散问题带来的不利影响.因此,从引入数值耗散的角度出发,在合理保留传统近场动力学理论框架的基础上,建立了黏性引入的控制方程.并考虑固体中常见的体积变形和对高频成分的选择性抑制,构造了相应的黏性力态.最后,在数值研究中模拟了极端载荷下激波的产生,以探究波的间断性对色散行为的影响.发现间断性强的波表现出更为显著的色散行为,呈现出Gibbs不稳定性.这些均能有效地被黏性力态所抑制,验证了所提方法的正确性.这为在近场动力学系统中实现对波传播过程的正确捕捉,获得正确的固体行为提供了重要参考,从而为国防安全领...     

Wave propagation and dispersion in elasto-plastic microstructured materials

A Mindlin continuum model that incorporates both a dependence upon the microstructure and inelastic (nonlinear) behavior is used to study dispersive effects in elasto-plastic microstructured materials. A one-dimensional equation of motion of such material systems is derived based on a combination of the Mindlin microcontinuum model and a hardening model both at the macroscopic and microscopic level. The dispersion relation of propagating waves is established and compared to the classical linear elastic and gradient-dependent solutions. It is shown that the observed wave dispersion is the result of introducing microstructural effects and material inelasticity. The introduction of an internal characteristic length scale regularizes the ill-posedness of the set of partial differential equations governing the wave propagation. The phase speed does not necessarily become imaginary at the onset of plastic softening, as it is the case in classical continuum models and the dispersive character of such models constrains strain softening regions to localize.     

功能梯度圆柱板中的周向衰逝导波

与传播波模态不同,衰逝波模态波数为纯虚数或复数,它们随传播距离呈指数或阻尼式衰减。复数根描述的衰逝波对结构缺陷形状和尺寸的导波检测具有重要作用,但其求解却是非常困难的,通常要借助于各种迭代技术。本文提出一种计算求解衰逝波问题的改进的Legendre正交多项式方法,该方法可将复杂的变系数微分方程组计算转换为特征值求解问题,无需迭代便能计算得到包含实波数域、虚波数域和复波数域的完整的频散曲线。通过具体算例验证了提出方法的正确性。应用提出方法计算了不同梯度圆柱板中的衰逝导波,绘制了三维频散曲线,研究了不同径厚比和梯度场对衰逝导波频散的影响,分析了衰逝导波的位移和应力分布,讨论了衰逝导波的传播特性。     

Wave propagation along a non-principal direction in a compressible pre-stressed elastic layer

The dispersive behavior of small amplitude waves propagating along a non-principal direction in a pre-stressed, compressible elastic layer is considered. One of the principal axes of stretch is normal to the elastic layer and the direction of propagation makes an angle θ with one of the in-plane principal axes. The dispersion relations which relate wave speed and wavenumber are obtained for both symmetric and anti-symmetric motions by formulating the incremental boundary value problem for a general strain energy function. The behavior of the dispersion curves for symmetric waves is for the most part similar to that of the anti-symmetric waves at the low and high wavenumber limits. At the low wavenumber limit, depending on the pre-stress and propagation angle, it may be possible for both the fundamental mode and the next lowest mode to have finite phase speeds, while other higher modes have an infinite phase speed. At the high wavenumber limit, the phase speeds of the fundamental mode and the higher modes tend to the Rayleigh surface wave speed and the limiting wave speeds of the layer, respectively. Numerical results are presented for a Blatz–Ko material and the effect of the propagation angle is clearly illustrated.