正交各向异性弹性层/压磁半空间结构中Love波的传播

分析了正交各向异性弹性层/压磁半空间结构中Love波的传播特性,得到了Love波传播时的解析解,基于推导的频散方程,数值分析了正交各向异性层的切割角度对Love波频散关系的影响,结果显示相速度对切割角度有很大的依赖性。     

Love wave propagation in layered magneto-electro-elastic structures with initial stress

Summary An analytical approach is taken to investigate Love wave propagation in layered magneto-electro-elastic structures with initial stress, where a piezomagnetic (piezoelectric) material thin layer is bonded to a semi-infinite piezoelectric (piezomagnetic) substrate. The magneto-electrically open and short conditions are applied to solve the problem. The phase velocity of the Love wave is numerically calculated for the magneto-electrically open and short cases, respectively. The effect of the initial stress on the phase velocity and the magneto-electromechanical coupling factor are studied in detail for piezomagnetic ceramics CoFe₂O₄ and piezoelectric ceramics BaTiO₃. We find that the initial stress has an important effect on the Love wave propagation in layered piezomagnetic/piezoelectric structures.     

非饱和地基中Love波的传播特性

基于非饱和多孔介质的波动方程,考虑了土中水,气体与土骨架之间的粘性耦合作用,建立了弹性半空间上非饱和土层中Love波的弥散方程。首先分析了饱和度与频率对非饱和孔隙介质中剪切波速的影响。然后运用数值方法得到了不同饱和度下土层中多种Love模态波的弥散特性和位移分布情况,并用图表的形式给出。数值计算结果表明,上覆非饱和土层中Love波的传播速度和衰减系数不仅具有频散性,而且与土层的饱和度有关。在不同饱和度时的高模态(n≥2)的Love波的截止频率值不同。此外,讨论了饱和度对Love波水平位移幅值的影响。     

Shear waves in magneto-elastic transversely isotropic (MTI) layer bonded between two heterogeneous elastic media

This paper studies shear wave propagation in magneto-elastic transversely isotropic material, sandwiched between a layer and a half-space of heterogeneous elastic materials. Elastic constants of the layer and half-space are assumed to vary in a parabolic form with depth. Whittaker’s functions and variable separable techniques have been employed to calculate the interior deformations; consequently, we obtain a general dispersion relation for shear wave. Effects of various affecting parameters on phase velocity of shear wave are considered through some numerical examples. In addition, a comparative study has been carried out for three examples of sandwiched layer, namely Beryl, Magnesium and isotropic.     

The propagation of Love waves in a fluid-saturated porous anisotropic layer

Summary The paper concerns the propagation of Love waves in a transverse-isotropic fluid-saturated porous layer overlaying an elastic nonhomogeneous half-space. Using the Biot's theory for the porous layer and the theory of elasticity for the lower medium, the dispersion equation has been derived. This complex transcendental equation that relates frequency, phase velocity, anisotropy factor of the layer and the inhomogeneity character of the half-space has been solved with the aid of successive approximation method. The effect of anisotropy and heterogeneity has been shown graphically.With 2 Figures     

非理想界面功能梯度压电/压磁层状半空间结构中的SH波

研究非理想界面下功能梯度压电/压磁层状半空间结构中SH波的传播特性。界面性能由“弹簧”模型表征, 假设功能梯度压电层材料性能沿层厚度方向指数变化, 其表面为电学开路。推导了频散方程, 并结合数值算例分析了界面性能、功能梯度压电层的梯度变化和厚度对相速度的影响。研究结果对功能梯度压电/压磁复合材料在声波器件中的应用提供了理论依据。     

The effect of inhomogeneity and anisotropy on Stoneley waves

Summary In this paper we study the dispersion equation of Stoneley waves that are travelling in an inhomogeneous elastic half-space over an anisotropic homogeneous elastic half-space.The phase velocity is calculated as a function of the wave number. The results indicate that the effect of anisotropy on such waves is small and can be neglected, while the effect of inhomogeneity is very pronounced. The results show that Stoneley waves do not exist after some cut-off value of the wave number.     

Effect of magnetic field and initial stress on the propagation of interface waves in transversely isotropic perfectly conducting media

Elasto-dynamical equations for transversely isotropic solids have been employed to investigate the general theory of transversely isotropic magneto-elastic interface waves in conducting media under initial hydrostatic tension or compression. Particular cases of interface waves such as Rayleigh, Love and Stoneley waves have been investigated in details. In all cases, the wave velocity equations have been deduced which are in complete agreement with the corresponding results of classical surface waves of the same types where magnetic fields and initial stresses are absent. Results obtained in this paper may be considered as more general and important in the sense that the corresponding results of classical surface waves due to Rayleigh, Love and Stoneley can readily be deduced from our results as special cases. Numerical calculations and graphs have been presented in the case of Love waves and conclusions are drawn.     

Love waves on a half-space with a gradient piezoelectric layer by the geometric integration method

The propagation of Love waves on an elastic homogeneous half-space with a piezoelectric gradient covering layer is studied by the geometric integration method in this article. First, the state transfer equation of a Love wave is derived from the governing equations and constitutive relations. Then, the transfer matrix of the state vector is obtained by solving the state transfer equation of a Love wave and then the stiffness matrix is obtained. By combining transfer matrices and the stiffness matrices of the gradient covering layer and the homogeneous half-space, the total surface stiffness matrix of a Love wave is obtained. Lastly, the application of the electrically open circuit and short circuit conditions and mechanically traction-free conditions gives the frequency dispersive relation of a Love wave. For the gradient covering layer, the material constants at the bottom of the covering layer may be greater or smaller than that at the top of the covering layer. The two situations and three kinds of gradient profiles for each of these two situations are investigated. The numerical results show that the Love wave speed is sensitive to not only the material constants at the bottom and the top of the covering layer, but also the gradient profiles of the covering layer.     

Surface waves in fibre-reinforced anisotropic elastic media

The aim of this paper is to investigate surface waves in anisotropic fibre-reinforced solid elastic media. First, the theory of general surface waves has been derived and applied to study the particular cases of surface waves — Rayleigh, Love and Stoneley types. The wave velocity equations are found to be in agreement with the corresponding classical result when the anisotropic elastic parameters tends to zero. It is important to note that the Rayleigh type of wave velocity in the fibre-reinforced elastic medium increases to a considerable amount in comparison with the Rayleigh wave velocity in isotropic materials.     

Influence of yielding base and rigid base on propagation of Rayleigh-type wave in a viscoelastic layer of Voigt type

The present study aims to study the propagation of Rayleigh-type wave in a layer, composed of isotropic viscoelastic material of Voigt type, with the effect of yielding base and rigid base in two distinct cases. With the aid of an analytical treatment, closed-form expressions of phase velocity and damped velocity for both the cases are deduced. As a special case of the problem it is found that obtained results are in good agreement with the established standard results existing in the literature. It is established through the study that volume-viscoelastic and shear-viscoelastic material parameter and yielding parameter have significant effect on phase and damped velocities of Rayleigh-type wave in both the cases. Numerical calculations and graphical illustration have been carried out for both the considered cases in the presence and the absence of viscoelasticity. A comparative study has been performed to analyse the effect of layer with yielding base, traction-free base and rigid base on the phase and damped velocities of Rayleigh-type wave.     

Propagation of Love waves in an elastic layer with void pores

The paper presents a study of propagation of Love waves in a poroelastic layer resting over a poro-elastic half-space. Pores contain nothing of mechanical or energetic significance. The study reveals that such a medium transmits two types of love waves. The first front depends upon the modulus of rigidity of the elastic matrix of the medium and is the same as the love wave in an elastic layer over an elastic half-space. The second front depends upon the change in volume fraction of the pores. As the first front is well-known, the second front has been investigated numerically for different values of void parameters. It is observed that the second front is many times faster than the shear wave in the void medium due to change in volume fraction of the pores and is significant     

Analysis of wave motion at the boundary surface of orthotropic thermoelastic material with voids and isotropic elastic half-space

The purpose of this research is to study the effect of voids on the surface wave propagation in a layer of orthotropic thermoelastic material with voids lying over an isotropic elastic half-space. The frequency equation is derived on the basis of the developed mathematical model under the boundary conditions for welded and smooth contacts. The dispersion curves giving the phase velocity and attenuation coefficient versus the wave number enable one to reveal the effects of voids and anisotropy for welded contact boundary conditions. The specific loss and amplitudes of the volume fraction, normal stress, and temperature change for welded contact are obtained and presented graphically for a particular model showing the voids and anisotropy effects. Some special cases are also deduced.     

Wave propagation at the imperfect boundary between transversely isotropic thermodiffusive elastic layer and half-space

The aim of the present investigation is to study surface wave propagation at the imperfect boundary between two transversely isotropic thermodiffusive elastic objects: a layer of finite thickness and a half-space, in the context of the Green–Lindsay theory. The secular equation for surface waves in a compact form is derived after the mathematical model has been developed. The phase velocity and attenuation coefficient are obtained for stiffness (normal and tangential), thermal conductance, and for the case of a welded contact. The dispersion curves for these quantities are presented to depict the effect of stiffness and thermal relaxation times. The amplitudes of displacements, temperature, and concentration at the free plane boundary, as well as the specific loss of energy, are obtained and presented graphically. The special cases are considered and the results are compared with the known ones.     

Surface waves in a periodic two-layered elastic half-space

Summary The paper deals with surface waves propagating through a periodic two-layered elastic half-space. The analysis is performed on the basis of a homogenized model with microlocal parameters. The velocity of the surface wave is obtained as a function of geometric and dynamic properties of the subsequent layers. The numerical examples illustrating the variations of the surface wave velocity are presented.     

Lamb wave propagation in the functionally graded piezoelectric–piezomagnetic material plate

The propagation behaviour of Lamb waves in the functionally graded piezoelectric–piezomagnetic material plate with material parameters varying continuously along the thickness direction is investigated in this paper. The power series technique is employed to solve these variable coefficient ordinary differential equations. Dispersion equations are given for different boundary conditions. In numerical examples, the influence of the variation of each parameter on dispersion curves and cut-off frequency in electrically and magnetically open cases is discussed in detail. Results show that the elastic parameters and density varying along the thickness direction obviously influence the variation of phase velocity. Some variations in electric and magnetic parameters also affect the phase velocity but the influence is too small, while others almost cannot affect the dispersion curves. Cut-off frequency is closely related to two elastic parameters and to density, whereas other parameters almost cannot influence it. All the results can provide theoretical guidance not only for the analysis and design of a magnetoelectric transducer using functionally graded materials, but also for ultrasonic nondestructive evaluation.     

Subsonic interfacial (Stoneley) waves in anisotropic multiferroic bimaterials with a viscous interface

The problem of subsonic interfacial (Stoneley) wave propagation in anisotropic multiferroic bimaterials with a viscous interface is treated. A concise analytical method is constructed for deduction of possible subsonic interfacial wave with varying viscosity of the interface. A numerical scheme and several calculations are given based on the method, which demonstrate interesting results. For an interface constructed by a piezoelectric half-space and a piezomagnetic half-space, when assumed to be non-viscous, calculation shows that it does not permit any subsonic interfacial wave. Yet when the same interface is assumed to be viscous, at least one possible subsonic interfacial wave speed appears which varies with the viscosity of the interface. By introducing the relation between viscosity of certain adhesives and temperature, the possibility of control of interfacial wave speeds through accommodating the working temperature is put forward.     

Bulk wave propagation in layered piezomagnetic/piezoelectric plates with initial stresses or interface imperfections

Bulk wave propagation in laminated piezomagnetic/piezoelectric plates with initial stresses and imperfect interface is investigated using the state space approach. Either electrically and magnetically open or shorted conditions on the top and bottom surfaces are considered. The phase velocity and frequency spectra of the wave are numerically calculated for various electric and magnetic conditions, and normalized modes are also analyzed. Although numerical results do indicate that the initial compressive stress can reduce the phase velocity of the wave propagating in a layered multiferroic structure, the effect is not as obvious as that reported in literature where the initial stresses were taken far beyond the strength of real materials. While the imperfect interface affect the frequency spectra much greater than initial stresses, because imperfection decreases the structural stiffness.     

Theoretical and Experimental Identification of Love Wave Frequency Peaks in Layered Structure ZnO/Quartz SAW Device

In this paper, the layered structure ZnO/Quartz (90^deg rotated ST-cut) is investigated theoretically and experimentally. Both waves, Rayleigh and Love, are analyzed. Dispersion curves of phase velocities, electromechanical coupling coefficient (K ²) and temperature coefficient of frequency (TCF) were calculated as a function of normalized thickness ZnO film (kh _ZnO = 2pih _ZnO /lambda) and the optimum value of h _ZnO was determined for experimental study. Experimental results combined with simulation lead to clearly identify the generated waves and their higher modes in this structure except the mode 0 that shows comparable velocity for both Rayleigh and Love waves. The identification of the wave type was performed by studying the frequency response of the device with or without a droplet of water in the wave path. We also demonstrate that the highest elastic velocity is obtained for the mode 1 of the Love wave. This Love wave mode exhibits very interesting electrical characteristics, good K ², high-frequency rejection, low TCF, and very low attenuation in liquid making it very attractive for gas and liquid sensor applications.     

On formulas for the Rayleigh wave velocity in pre-strained elastic materials subject to an isotropic internal constraint

In the present paper, formulas for the velocity of Rayleigh waves propagating along principal directions of prestrain of an elastic half-space subject to a pure homogeneous prestrain, and an isotropic internal constraint have been derived using the theory of cubic equation. They have simple algebraic form, and hold for any strain-energy function and any isotropic constraint. In undeformed state, these formulas recover the exact value of the Rayleigh wave speed in incompressible isotropic elastic materials. Some specific cases of strain-energy function and isotropic constraint are considered, and the corresponding formulas become totally explicit in terms of the parameters characterizing the material and the prestrains. The necessary and sufficient conditions for existence of Rayleigh wave are examined in detail. The use of obtained formulas for nondestructive evaluation of prestrains and prestresses is discussed.