初应力对压电层状结构声表面波传播性能的影响

研究了压电层状结构中初应力对广义Ｒａｙｌｅｉｇｈ波传播相速度和机电耦合性能的影响,通过求解含初应力的运动微分方程,对自由界面电学开路和短路两种情况得到了相应的相速度方程。给出了具体的数值算例,所得结果对于提高和改善声表面波器件性能有参考意义。     

Mechanics of indentation for piezoelectric thin films on elastic substrate

Frictionless normal indentation problem of rigid flat-ended cylindrical, conical and spherical indenters on piezoelectric film, which is either in frictionless contact with or perfectly bonded to an elastic half-space (substrate), is investigated. Both conducting and insulating indenters are considered. With Hankel transform, the general solutions of the homogeneous governing equations for the piezoelectric layer and the elastic half-space are presented. Using the boundary conditions for a vertical point force or a point electric charge, and the boundary conditions on the film/substrate interface, the Green’s functions can be obtained by solving sets of simultaneous linear algebraic equations. The solution of the indentation problem is obtained by integrating these Green’s functions over the contact area with unknown surface tractions or electric charge distribution, which will be determined from the boundary conditions on the contact surface between the indenter and the film. The solution is expressed in terms of dual integral equations that are converted to a Fredholm integral equation of the second kind and solved numerically. Numerical examples are also presented. The comparison between two film/substrate bonding conditions is made. It shows that the indentation rigidity of the film/substrate system is lower when the film is in frictionless contact with the substrate. The effects of the Young’s modulus and Poisson’s ratio of the elastic substrate, indenter electrical condition and indenter prescribed electric potential on the indentation responses are presented.     

The spreading of nonlinear elastic surface waves

A theory for the lateral spreading of a beam of nonlinear surface acoustic waves across the surface of an arbitrary, homogeneous, elastic half-space is developed. The resulting evolution equation generalizes that obtained for uni-directional waves by replacing an ordinary derivative by a diffusion operator of Schrödinger type. The coefficients arising in the evolution equation are related to partial derivatives of the dispersion relation for linearized surface waves on the half space. Details are given for isotropic materials and for two special cases of beams travelling along axes of high elastic symmetry.     

PMN-PT层/弹性基底结构中声表面波特性分析

研究了PMN-PT 压电层/弹性(金刚石) 基底结构中表面波的传播特性,压电层表面是机械自由的,电学边界条件分为电学开路和电学短路,压电层与基底之间采用理想连接. 得到了满足控制方程和边界条件的电弹场以及弹性波在结构中传播时的频散方程,通过数值算例分析了压电材料PMN-PT 的极化方向对弹性波频散曲线和机电耦合系数的影响,以及不同极化方向时弹性位移和电势随结构深度方向的变化,结果可为PMN-PT 压电材料在高频声表面波器件中的应用提供有价值的理论参考.      

Scattering of antiplane shear waves by a submerged crack

The scattering of time harmonic antiplane shear waves by a crack situated parallel to the surface of a homogenious elastic half-space is considered. The problem is investigated for both clamped and stress-free conditions at the surface of the half-space. Singular integral equations are derived for each case and treated numerically by the Gauss-Chebyshev technique. Harmonic stress intensity factors and crack opening displacements are computed as functions of dimensionless frequency, submerged depth-to-crack width ratio, and angle of incidence. Results are obtained for a moderately wide range of frequencies and are set out in graphical form.     

Green’s-function method for modeling surface acoustic wave dispersion in anisotropic material systems and determination of material parameters

A Green’s-function method for modeling propagation of surface acoustic waves in anisotropic nanolayered materials is reviewed. The mathematical model, developed at NIST, provides a computationally efficient inversion algorithm for determination of the material parameters of the film, such as its elastic constants and density, from observed dispersion of the surface acoustic waves. The application of the method to a 306 nm thick TiN film having transverse isotropy on a single crystal Si substrate is discussed as an example. The errors in the values of the parameters determined by using the inversion algorithm and the question of uniqueness of the values of the parameters are discussed in detail. It is suggested that, at least in the example considered in this paper, the SAW dispersion can be used to determine any two parameters of the film, provided other parameters are known by independent measurements. In particular, the values of c₁₁ and the density of the film, obtained from the measured SAW dispersion, are the most reliable and the value of c₄₄ is the least reliable. The method is extended to account for defective bonding between the film and the interface and the effect of an intermediate layer of silica between the film and the substrate.     

Analysis of comb transducers with sliding teeth

Ultrasonic comb transducer generates surface acoustic waves on an elastic substrate by periodic traction exerted by its vibrating periodic teeth on the substrate surface. In this paper, the comb teeth are actually sliding elastic spacers between an acoustic buffer and the substrate. The incident wave in acoustic buffer scatters on periodic spacers producing interface waves in the system which transform into Rayleigh waves at the transducer edges. The full-wave theory of interface wave generation is presented, concluded by efficiency estimation of transformation of the incident wave into the surface wave in the substrate and of the surface waves back to bulk waves in the acoustic buffer. Numerical examples presented for all aluminum substrate, buffer and teeth show the 11-teeth comb combined efficiency for generation and detection on the level of ?40 dB for optimized teeth height.     

The determination of elastic parameters of a half-space using a monochromatic vibration field at the surface

The paper presents a method to determine Lamé parameters λ, μ and density ϱ in a layered half-space, using monochromatic vibrations of its surface, excited by a harmonic source which is assumed to be known. The equations governing the vibrations are reduced to the Sturm-Liouville problem in scalar form for Love-type displacements, and in matrix form for the Rayleigh type. The scalar and matrix potentials of the Sturm-Liouville equations can be recovered from the corresponding impedance. Explicit formulas are given to construct the potentials by amplitudes and wavenumbers of normal (progressive) modes and attenuated standing waves. The potentials then are used to determine the elastic parameters and the density. The method can also be used for the acoustic equation.     

The Effect of Surface Inhomogeneities on the Propagation of Elastic Waves

We investigate the effect of the surface inhomogeneities (defects) on the propagation of the elastic waves in a semi-infinite isotropic solid body (half-space). A perturbation-theoretical scheme is devised for small surface defects (in comparison with the relevant elastic disturbances propagating in the body), and the elastic waves equations are solved in the first-order approximation. It is shown that surface defects generate both scattered waves localized (and propagating only) on the surface (two-dimensional waves) and scattered waves reflected back in the body. Directional effects, wave slowness and attenuation by diffusive scattering, or possible resonance effects are discussed.     

Elastic waves in an electro-microelastic solid

The present study is concerned with the wave propagation in an electro-microelastic solid. The reflection phenomenon of plane elastic waves from a stress free plane boundary of an electro-microelastic solid half-space is studied. The condition and the range of frequency for the existence of elastic waves in an infinite electro-microelastic body are investigated. The constitutive relations and the field equations for an electro-microelastic solid are stemmed from the Eringen’s theory of microstretch elasticity with electromagnetic interactions. Amplitude ratios and energy ratios of various reflected waves are presented when an elastic wave is made incident obliquely at the stress free plane boundary of an electro-microelastic solid half-space. It has been verified that there is no dissipation of energy at the boundary surface during reflection. Numerical computations are performed for a specific model to calculate the phase speeds, amplitude ratios and energy ratios, and the results obtained are depicted graphically. The effect of elastic parameter corresponding to micro-stretch is noticed on reflection coefficients, in particular. Results of Parfitt and Eringen [Parfitt, V.R., Eringen, A.C., 1969. Reflection of plane waves from a flat boundary of a micropolar elastic half-space. J. Acoust. Soc. Am. 45, 1258–1272] have also been reduced as a special case from the present formulation.     

Effect of initial stress on the propagation behavior of Love waves in a layered piezoelectric structure

The propagation behavior of Love waves in a layered piezoelectric structure with an initial stress is investigated in this article. It involves a thin piezoelectric layer bonded perfectly to an elastic substrate. Solutions of the mechanical displacement and electrical potential function are obtained for the piezoelectric layer and elastic substrate by solving the coupled electromechanical field equations. The phase velocity equations of the Love wave propagation and the stress fields in the layered piezoelectric structure are obtained for electrical open and short cases on the free surface, respectively. The effect of the initial stress on the phase velocity, the stress fields and the coupled electromechanical factor are discussed, respectively. Three sets of piezoelectric layer–elastic substrate systems are considered, i.e. BaTiO₃ ceramic layer–borosilicate glass substrate, PZT-5H ceramic layer–borosilicate glass substrate, and PZT-5H ceramic layer–SiO₂ glass substrate. It is seen that the phase velocity of the Love wave propagation decreases with the increase of the magnitude of the initial stress. The coupled electromechanical factor increases remarkably, as the magnitude of the initial the stress is greater than 100 MPa. This is useful for the design of acoustic surface wave devices.     

梯度半空间梯度覆层中的Love波

对功能梯度弹性半空间上覆盖一层功能梯度材料中的Love波的频散问题进行了研究，给出 了Love波频散方程的一般形式. 对功能梯度弹性半空间和功能梯度覆层的反平面剪切波的运 动控制方程进行了求解，给出了半空间和覆盖层的位移、应力解析解，给出了Love波在该解析 解下的频散方程. 以覆盖层的剪切弹性模量和质量密度均呈指数函数变化，半空间的剪切弹 性模量和质量密度均呈抛物线变化为例，利用迭代方法对频散方程进行了求解，给出了频散 曲线. 结果显示：在最低阶振型频散曲线中出现截止频率.     

A Mathematical Model for Short-Time Filtration in Poroelastic Media with Thermal Relaxation and Two Temperatures

In this work, we derive a set of governing equations for a mathematical model of generalized thermoelasticity in poroelastic materials. This model predicts finite speeds of propagation of waves contrary to the model of coupled thermoelasticity where an infinite speed of propagation is inherent. Next, we prove the uniqueness of solution of these equations under suitable conditions. We also obtain a reciprocity theorem for these equations. A thermal shock problem for a half-space composed of a poroelastic material saturated with a liquid is then considered. The surface of the half-space is assumed to be traction free, permeable, and subjected to heating. The Laplace transform technique is used to solve the problem. Numerical results for the temperature in the elastic body and fluid, displacement of the elastic body, velocity of the fluid, and stresses for both components are obtained and represented graphically.     

Wave propagation at the boundary surface of elastic and initially stressed viscothermoelastic diffusion with voids media

The present investigation is concerned with the wave propagation at the boundary surface of elastic half-space and initially stressed viscothermoelastic diffusion with voids half-space. The longitudinal and transverse waves are incident obliquely at the plane interface between uniform elastic half-space and initially stressed viscothermoelastic diffusion with voids half-space. It is found that the amplitude ratios of various reflected and transmitted waves are functions of angle of incidence, frequency of incident wave and are influenced by the initial stress, diffusion, voids, elastic and viscoelastic properties of media. The expressions of amplitude ratios and energy ratios are obtained in closed form and computed numerically for a specific model. The variations of energy ratios with angle of incidence are shown graphically. The conservation of energy at the interface is verified.     

Surface Waves in a Stratified Periodic Medium with a Liquid Upper Layer

An approach is proposed to set up the dispersion equations for surface waves in a periodically stratified half-space contacting with a layer of a perfect compressible liquid. The approach is based on the formalism of periodic Hamiltonian systems. The dispersion equations derived are valid for an arbitrary law of variation in the properties with respect to the coordinate of periodicity. The effects of the liquid layer and the inhomogeneity of the elastic medium on the dispersion spectra of surface waves are studied     

多洞室对矢量波散射引起半空间表面位移的边界元解

采用边界元方法研究了半空间中近表面多洞室对矢量波的散射问题,给出了以全空间格林函数为基本解且半空间表面离散的边界积分方程,在这一边界各分方程中,较好的消除了主值积分,在半空间表面进行离散时,采用无限单元与有限单元相结合的方法,大大减少了计算量,提出了精度。     

Bleustein–Gulyaev waves in 6 mm piezoelectric materials loaded with a viscous liquid layer of finite thickness

In this paper, we analyze the propagation of Bleustein–Gulyaev waves in an unbounded piezoelectric half-space loaded with a viscous liquid layer of finite thickness within the linear elastic theories. Exact solutions of the phase velocity equations are obtained in the cases of both electrically open circuit and short circuit by solving the equilibrium equations of piezoelectric materials and the diffusion equation of viscous liquid. A PZT-5H/Glycerin system is selected to perform the numerical calculation. The results show that the mass density and the viscous coefficient have different effects on the propagation attenuation and phase velocity under different electrical boundary conditions. In particular, the penetration depth of the waves is of the same order as the wavelength in the case of electrically short circuit. These effects can be used to manipulate the behavior of the waves and have implications in the application of acoustic wave devices.     

Numerical analysis of the isolation of the vibration due to Rayleigh waves by using pile rows in the poroelastic medium

The isolation of the vibration due to harmonic Rayleigh waves using pile rows embedded in a saturated poroelastic half-space is investigated in this study. Based on Biot’s theory and the potential function method, the free field solution for Rayleigh waves along the surface of the poroelastic half-space is derived first. The fundamental solution for a harmonic circular patch load applied in the poroelastic half-space are obtained in terms of Biot’s theory and the integral transform method. Using Muki’s method and the fundamental solution for the circular patch load as well as the Rayleigh waves solution for the poroelastic half-space, the second kind of Fredholm integral equations in the frequency domain for pile rows are derived. Numerical solution of the integral equations yields the dynamic response of the pile–soil system to incident Rayleigh waves. Influences of various parameters on the vibration isolation effect of piles rows are investigated numerically. Numerical results suggest that for the same vibration source, the same pile rows will produce a better vibration isolation effect for the poroelastic medium than for a single phase elastic medium. Also, stiffer piles tend to have better vibration isolation effect than flexible piles. Moreover, the pile length and the spacing between neighboring piles in each pile row have significant influence on the vibration isolation effect of pile rows.     

Finite-amplitude Love waves in a pre-stressed compressible elastic half-space with a double surface layer

The dispersive behavior of finite-amplitude time-harmonic Love waves propagating in a pre-stressed compressible elastic half-space overlaid with two compressible elastic surface layers of finite thickness is investigated. The half-space and layers are made of different pre-stressed compressible neo-Hookean materials. The dispersion relation which relates wave speed and wavenumber is obtained in explicit form. Results for the energy density and energy flux of the waves are also presented. The special case where the interfaces between the layers and the half-space are principal planes of the left Cauchy–Green deformation tensor is also investigated. Numerical results are presented showing the variation of the Love wave speed with the pre-stress and the propagation angle.