Propagation of Magnetoelastic Shear Waves Through a Regularly Laminated Medium with Metallized Interfaces

An exact solution is found for magnetoelastic shear waves in an infinite structure consisting of three metallized layers. The core layer is ferrite and the face layers are nonmagnetic dielectrics. The wave process in the layers is described by a linearized system of magnetoelastic equations. The problem posed is reduced to a system of linear algebraic equations. The existence conditions for an undamped solution to this system yield the existence conditions for magnetoelastic bulk waves. The dispersion relations derived are analyzed in detail     

Localization of wave motions in a fluid-filled cylinder

The properties of harmonic surface waves in a fluid-filled cylinder made of a compliant material are studied. The wave motions are described by a complete system of dynamic equations of elasticity and the equation of motion of a perfect compressible fluid. An asymptotic analysis of the dispersion equation for large wave numbers and a qualitative analysis of the dispersion spectrum show that there are two surface waves in this waveguide system. The first normal wave forms a Stoneley wave on the inside surface with increase in the wave number. The second normal wave forms a Rayleigh wave on the outside surface. The phase velocities of all the other waves tend to the velocity of the shear wave in the cylinder material. The dispersion, kinematic, and energy characteristics of surface waves are analyzed. It is established how the wave localization processes differ in hard and compliant materials of the cylinder __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 4, pp. 72–86, April 2008.     

Dispersion Spectrum of an Anisotropic Waveguide with Sector-Shaped Cross Section and Fixed Boundary

The dispersion equations are derived analytically for normal elastic waves in a longitudinally anisotropic cylindrical waveguide with circular cross-section and a sector-shaped channel of arbitrary angular measure. The boundary surfaces of the channel are covered with flexible, inextensible membranes. The cylindrical portion of the lateral surface is rigidly fixed. A numerical analysis of the dispersion equations reveals spectral branches of traveling normal waves with different types of symmetry of cross-sectional displacements and different circumferential wave numbers. Some features of the spectrum due to variation in the angular measure are established __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 9, pp. 46–51, September 2005.     

Surface waves at the interface between an inviscid fluid and a dipolar gradient solid

This paper is about the dispersion analysis of surface waves propagating at the interface between an inviscid fluid and a higher gradient homogeneous elastic solid modelled as a dipolar gradient continuum. In order to compare the results, a second gradient model is also evaluated. The analysis is carried out by finding the roots of the secular equation, and by carefully studying their physical meaning. As it is well known, higher gradient continua are dispersive, i.e. phase and group velocities are frequency dependent. As a consequence, the existence of surface waves will indeed depend on frequency. In order to investigate the behaviour of surface waves in this specific fluid–solid configuration, a complete dispersion analysis is performed, with a particular focus on the frequency range in which the phase velocity of shear waves is lower than the speed of waves of the fluid. Surface waves of the type Leaky Rayleigh and Scholte–Stoneley are observed in this frequency range. This work extends the knowledge on surface waves in the case of higher gradient solids and applications of these results can be found in the field of non-destructive damage evaluation in micro structured materials, composites, metamaterials and biological tissues.     

Theory of steady waves in horizontal flow with a linear velocity profile

The structure and characteristics of nonlinear steady waves on the surface of horizontal shear flow of an ideal homogeneous incompressible fluid of finite depth with a linear velocity profile are studied using two-dimensional theory and the Euler approach. The wave motion is considered irrotational. A modification of the first Stokes method is proposed that allows algebraic calculations of terms of perturbation series. Nonlinear dispersion relations are obtained and analyzed for both upstream and downstream traveling waves. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 43–48, May–June, 2006.     

在均匀剪切流动中的Stokes波

本文从Euler方程出发讨论在均匀剪切流动中的Stokes波·把未知函数和波速展开成渐近级数,利用Fredholm择一定理来确定待定常数。得到了在均匀剪切流中二阶波形并研究了均匀剪切流对增水的影响。当流速为零时,本文的结果就退化为已有的在静水中的stokes波。     

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.     

Symmetries and exact solutions of the shallow water equations for a two-dimensional shear flow

This paper considers nonlinear equations describing the propagation of long waves in two-dimensional shear flow of a heavy ideal incompressible fluid with a free boundary. A nine-dimensional group of transformations admitted by the equations of motion is found by symmetry methods. Two-dimensional subgroups are used to find simpler integrodifferential submodels which define classes of exact solutions, some of which are integrated. New steady-state and unsteady rotationally symmetric solutions with a nontrivial velocity distribution along the depth are obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 41–54, September–October, 2008.     

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.     

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.     

具有表面效应的压电半空间中的表面波

纳米科技的快速发展使压电纳米结构在纳米机电系统中得到广泛应用,形成了诸如纳米压电电子学等新的研究方向.与传统的宏观压电材料相比,在纳米尺度下压电材料往往呈现出不同的力学特性,而造成这种差异的原因之一便是表面效应.本文基于Stroh公式、Barnett-Lothe积分矩阵及表面阻抗矩阵,研究计入表面效应的任意各向异性压电半空间中的表面波传播问题,导出了频散方程.针对横观各向同性压电材料,假设矢状平面平行于材料各向同性面,发现Rayleigh表面波和B-G波解耦,并得到各自的显式频散方程.结果表明,Rayleigh表面波的波速小于偏振方向垂直于表面的体波,而B-G波的波速小于偏振方向垂直于矢状平面的体波.以PZT-5H材料为例,用数值方法考察表面残余应力和电学边界条件对表面波频散特性的影响发现:表面残余应力只对第一阶Rayleigh波有明显的影响;电学开路情形的B-G波比电学闭路情形的B-G波传播快.本文工作可为纳米表面声波器件的设计或压电纳米结构的无损检测提供理论依据.     

Features of how surface waves form in a cylinder made of a hard material and filled with a fluid

The properties of harmonic surface waves in an elastic cylinder made of a rigid material and filled with a fluid are studied. The problem is solved using the dynamic equations of elasticity and the equations of motion of a perfect compressible fluid. It is shown that two surface (Stoneley and Rayleigh) waves exist in this waveguide system. The first normal wave generates a Stoneley wave on the inner surface of the cylinder. If the material is rigid, no normal wave exists to transform into a Rayleigh wave. The Rayleigh wave on the outer surface forms on certain sections of different dispersion curves. The kinematic and energy characteristics of surface waves are analyzed. As the wave number increases, the phase velocities of all normal waves, except the first one, tend to the sonic velocity in the fluid from above __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 9, pp. 48–62, September 2007.     

Monochromatic surface waves on impermeable boundaries in two-component poroelastic media

The dispersion relation for surface waves on an impermeable boundary of a fully saturated poroelastic medium is investigated numerically over the whole range of applicable frequencies. To this aim a linear simplified model of a two-component poroelastic medium is used. Similarly to the classical Biot’s model, it is a continuum mechanical model but it is much simpler due to the lack of coupling of stresses. However, results for bulk waves following for these two models agree very well indeed which motivates the application of the simplified model in the analysis of surface waves. In the whole range of frequencies there exist two modes of surface waves corresponding to the classical Rayleigh and Stoneley waves. The numerical results for velocities and attenuations of these waves are shown for different values of the bulk permeability coefficient in different ranges of frequencies. In particular, we expose the low and high frequency limits, and demonstrate the existence of the Stoneley wave in the whole range of frequencies as well as the leaky character of the Rayleigh wave.     

Primary instabilities of liquid film flow sheared by turbulent gas stream

Evolution of excited waves on a viscous liquid film has been investigated experimentally for the annular gas–liquid flow in a vertical tube. For the first time the dispersion relations are obtained experimentally for linear waves on liquid film surface in the presence of turbulent gas flow. Both cocurrent and countercurrent flow regimes are investigated. As an example of comparison with theory, the experimental data are compared to the results of calculations based on the Benjamin quasi-laminar model for turbulent gas flow. The calculation results are found to be in good agreement with experiments for moderate values of film Reynolds number.     

Flexural gravity wave motion over poroelastic bed

Using Biot’s consolidation theory, effect of poroelastic bed on flexural gravity wave motion is analyzed in both the cases of single-layer and two-layer fluids. The model for the flexural gravity waves is developed using linear water wave theory and small amplitude structural response in finite water depth. The effects of permeability and shear modulus of poroelastic bed and time period on flexural gravity wave motion are studied by analyzing the dispersion relation, phase speed, plate deflection, interface elevation and pressure distribution along water depth. Various results for surface gravity waves are analyzed as special cases. The study reveals that bed permeability retards the hydrodynamic pressure distribution along the water depth significantly compared to shear modulus whilst, floating plate deflection decreases significantly with change in shear modulus compared to permeability of the poroelastic bed. The present study can be generalized to analyze various wave–structure interaction problems over poroelastic bed.     

Dispersion Equation for Water Waves with Vorticity and Stokes Waves on Flows with Counter-Currents

The two-dimensional free-boundary problem of steady periodic waves with vorticity is considered for water of finite depth. We investigate how flows with small-amplitude Stokes waves on the free surface bifurcate from a horizontal parallel shear flow in which counter-currents may be present. Two bifurcation mechanisms are described: one for waves with fixed Bernoulli’s constant, and the other for waves with fixed wavelength. In both cases the corresponding dispersion equations serve for defining wavelengths from which Stokes waves bifurcate. Necessary and sufficient conditions for the existence of roots of these equations are obtained. Two particular vorticity distributions are considered in order to illustrate the general results.     

变深度浅水域中非定常船波

以Green—Naghdi(G—N)方程为基础，采用波动方程／有限元法计算船舶经过变深度浅水域时非定常波浪特性．把运动船舶对水面的扰动作为移动压强直接加在Green-Naghdi方程里，以描述运动船体和水面的相互作用．以Series60 CB＝0．6船为算例，给出自由面坡高，波浪阻力在船舶经过一个水下凸包时变化规律，并与浅水方程的结果进行了比较．计算结果表明，当船舶经过凸包时，波浪阻力先增加，后减少，并逐渐趋于正常．同时发现，当船速小于临界速度时(Fr＝√gh＜1．0)，G—N方程给出的船后尾波比浅水方程的结果明显，波浪阻力也比浅水方程的结果有所提高，频率散射必须考虑．当船速大于临界速度时(Fr＝√gh＞1．0)，G—N方程的计算结果与浅水方程差别不大，频率散射的影响可以忽略．     

Dynamic response of a half-space to radial shear surface loadings

Summary The axisymmetric response of an elastic half-space to the sudden application of radial shear surface loadings is investigated in this paper. Exact expressions for the surface displacement components are developed by means of integral transforms and complex functions. Numerical results are presented in diagrams to show the wave propagation on the surface due to the dynamic loadings, and the wave front singularities in the displacement components are particularly discussed. It is found that, for a given point on the half-space surface, Rayleigh surface waves issued from the nearest and farthest disturbances give rise to a jump or a two-sided logarithmic singularity in the displacement components.     

界面剪切力作用下波状液膜流的水动力稳定性

液膜流的水动力稳定性作为保障其高效传热传质性能的重要因素之一,受多种因素的制约和影响. 当气液界面处存在因气流流动而产生剪切力作用时,剪切力将通过改变界面处的边界条件,从而影响液膜流动的稳定性. 基于边界层理论,采用积分法建立了剪切力作用下降液膜表面波演化方程,分析了界面剪切力对水动力稳定性的影响. 研究表明,正向剪切力为不稳定性因素,反向剪切力在较小雷诺数时为不稳定因素,在大雷诺数时为稳定性因素;正向剪切力使临界波数和临界波速增大,反向剪切力使其减小;剪切力对临界波速的影响在不同雷诺数下也有所不同.      

Nonlinear elastic shear waves

Summary The dynamics of one-dimensional two-component shear motion in elastic-isotropic homogeneous media is studied assuming isentropic finite displacements. Wave breaking of initially continuous waves on the infinite interval is discussed for weakly nonlinear waves.The problem of a resonating finite-thickness shear layer in primary resonance for single-component motion exhibits jump discontinuities of particle velocity, shear strain and stress in a finite frequency band near primary resonance.Under certain conditions two-component motion can be reduced to a quasi-single-component motion.