Exact and approximate analysis of surface acoustic waves in an infinite elastic plate with a thin metal layer

For an accurate approximation of the effect of a thin layer over a finite substrate, we consider the displacements are continuous across the interface, while the stress components are obtained from derivatives of displacements. As a result, the stress boundary conditions are transformed to a relationship between stresses in the vicinity of the interface of two layers and density of the metal layer. Through this approximation, we eventually have four equations to solve for the surface acoustic wave dispersion relation of the two-layer structure. The approximate and accurate results are compared with good agreement for small thickness of the metal layer. These results are intended for periodic structures with separate solutions for electroded and unelectroded regions, which can be connected by the continuity boundary conditions for the analysis of the complete structure of typical surface acoustic wave resonators.     

声表面波在厚金属栅阵中的耦合模参数

提出了一种研究声表面波在压电晶体厚金属栅阵中传播特性的理论方法。将有限元和声表面波在周期栅阵中的变分原理分析方法相结合,在陈东培和H.A.Haus理论基础上、用有限元分析金属短路栅对声表面波传输特性的影响,将力学负载贡献的耦合模参数用有限元矩阵表示,使其适用于声表面波在厚金属或任意形状栅条中传输情况,给出了具体理论分析方法和相应的理论表达式。最后,具体研究了几种压电晶体上金、铝或银栅阵中声表面波的传输特性,通过数值计算给出了声表面波的耦合模参数。      

Size-dependent dispersion characteristics in piezoelectric nanoplates with surface effects

In this paper, surface effects on the dispersion characteristics of elastic waves propagating in an infinite piezoelectric nanoplate are investigated by using the surface piezoelectricity model. Based on the surface piezoelectric constitutive theory, the presence of surface stresses and surface electric displacements exerting on the boundary conditions of the piezoelectric nanoplate is taken into account in the modified mechanical and electric equilibrium relations. The partial wave technique is employed to obtain the general solutions of governing equations, and the dispersion relations with surface effects are expressed in an explicit closed form. The impacts of surface piezoelectricity, residual surface stress and plate thickness on the propagation properties of elastic waves are analyzed in detail. Numerical results show that the dispersion behaviors in piezoelectric nanoplates are size-dependent, and there exists a critical plate thickness above which the surface effects may vanish.     

Love waves in layered flexoelectric structures

Abstract

In this paper, the flexoelectric effect on Love waves propagating in a structure with a nanoscale piezoelectric guiding layer deposited on an isotropic elastic substrate is analytically investigated. Transcendental complex dispersion equations are obtained and solved numerically which are corresponding to the electrically open and short conditions at the free surface. A detailed discussion about the dispersion relations of the fundamental mode is subsequently presented. The results indicate that flexoelectricity has a substantial effect on Love wave propagation. The presence of flexoelectricity leads to a complex phase velocity with a negative/positive imaginary part, which means Love waves attenuate/grow over time. In addition, the phase velocity dispersion relations depend greatly on the thickness and flexoelectric coefficients of the guiding layer. The current work is the first attempt to explore the flexoelectric effect on the propagation characteristics of surface acoustic waves (SAWs). And the results would be beneficial to achieve a better performance of SAW devices.     

Thermal stabilization of SAW devices by metal films

The characteristics of surface acoustic waves (SAW) propagating in a structure that consists of a metal layer overlying an YX-cut quartz crystal are numerically analyzed for a wide range of operating temperatures. It is shown that the presence of a metal film of a certain thickness on the surface of an YX-cut quartz crystal considerably improves the thermal stability of the characteristics of SAW propagating in such a structure.     

A two-dimensional analysis of surface acoustic waves in finite elastic plates with eigensolutions

It is generally known that surface acoustic waves, or Rayleigh waves, have different mode shapes in infinite plates. To be precise, there are both exponentially decaying and growing components in plates appearing in pairs, representing symmetric and antisymmentric modes in a plate. As the plate thickness increases, the combined modes will approach the Rayleigh mode in a semi-infinite solid, exhibiting surface acoustic wave deformation and velocity. In this study, the two-dimensional theory for surface acoustic waves in finite plates is extended to include the exponentially growing modes in the expansion function. With these extra equations, we study the surface acoustic waves in a plate with different thickness to examine the coupling of the exponentially decaying and growing modes. It is found that for small thickness, the two groups of waves are strongly coupled, showing the significance of including the effect of thickness in analysis. As the thickness increases to certain values, such as more than five wavelengths, the exponentially decaying modes alone will be able to predict vibrations of surface acoustic wave modes accurately, thus simplifying the equations and solutions significantly. Supported by Qianjiang River Fund established by Zhejiang Provincial Government and Ningbo University and administered by Ningbo University and the National Natural Science Foundation of China (Grant No. 10572065)     

Quasi elasto-electromagnetic surface waves on a piezo-plasma-like layer

Considering a piezo-plasma-like layer with finite thickness and hexagonal symmetry whose main symmetry axis is parallel to the z axis and approximating it by an isotropic medium, we study the coupling of the elastic wave with plasma properties of the medium with and without spatial dispersion and collisions. In this case we investigate the coupled surface quasi elasto-electromagnetic wave propagating on the interface of piezoelectric layer with vacuum. Furthermore, the coupling of elasticity and ion-acoustic waves is investigated.     

SH surface acoustic wave propagation in a cylindrically layered piezomagnetic/piezoelectric structure

SH surface acoustic wave (SH-SAW) propagation in a cylindrically layered magneto-electro-elastic structure is investigated analytically, where a piezomagnetic (or piezoelectric) material layer is bonded to a piezoelectric (or piezomagnetic) substrate. By means of transformation, the governing equations of the coupled waves are reduced to Bessel equation and Laplace equation. The boundary conditions imply that the displacements, shear stresses, electric potential, and electric displacements are continuous across the interface between the layer and the substrate together with the traction free at the surface of the layer. The magneto-electrically open and shorted conditions at cylindrical surface are taken to solve the problem. The phase velocity is numerically calculated for different thickness of the layer and wavenumber for piezomagnetic ceramics CoFe₂O₄ and piezoelectric ceramics BaTiO₃. The effects of magnetic permeability on propagation properties of SH-SAW are discussed in detail. The distributions of displacement, magnetic potential and magneto-electromechanical coupling factor are also figured and discussed.     

Reflection of normal acoustic waves in thin plates from a grating with a periodically distributed mechanical load

Reflection of zero-order normal acoustic waves excited in a thin piezoelectric plate from a set of conducting strips of a finite thickness is studied both theoretically and experimentally. The analysis shows that the effects produced by the short-circuiting of the plate surface and by the elastic load on the impedance ratio of adjacent plate segments are in opposition to each other. These effects can be commensurable, and, hence, for each wave type, there is a certain value of the strip thickness at which the reflection coefficient becomes equal to zero. The experimental results obtained for a shear horizontal normal wave (an SH ₀ wave) propagating in a lithium niobate plate are in good agreement with the theory and justify the use of the equivalent-circuit model in analyzing the properties of reflectors of the type under study.     

两侧有固体层负载时板中Lamb波的传播

本文研究了薄板二面有固体导负载时板中Ｌａｍｂ波的传播，从弹性波理论出发并结合应的边界条件，导出板中Ｌａｍｂ波的色散方程，数值计算表示，不管作为自由状态时板中Ｌａｍｂ波相速（板厚取定时）是大于或小于外层固体的声表面波波速，板中对称及反对称模式的Ｌａｍｂ波相速都随着外层固体层厚度增加而变化并且渐近于外层固体的声表面波波速，数值计算又表明，对很薄的板，板中对称及反对称模式的相速均随负载板的厚度呈线性变化     

Influence of adhesive layer properties on laser-generated ultrasonic waves in thin bonded plates

This paper studies quantitatively the generation of Lamb waves in thin bonded plates subjected to laser illumination, after considering the viscoelasticity of the adhesive layer. The displacements of such plates have been calculated in the frequency domain by using the finite element method, and the time domain response has been reconstructed by applying an inverse fast Fourier transform. Numerical results are presented showing the normal surface displacement for several configurations: a single aluminum plate, a three-layer bonded plate, and a two-layer plate. The characteristics of the laser-generated Lamb waves for each particular case have been investigated. In addition, the sensitivity of the transient responses to variations of material properties (elastic modulus, viscoelastic modulus, and thickness) of the adhesive layer has been studied in detail.     

研究激光激发的声表面波与材料近表面缺陷的振荡效应

根据激光激发声表面波的热弹运动方程及热传导方程, 采取有限元技术对方程进行求解, 得到声表面波传播波形图. 当声表面波经过近表面缺陷时, 声表面波与近表面缺陷之间产生一种振荡效应, 通过近表面缺陷的振荡波形幅值存在一个逐渐增加后又逐渐减小的过程. 当声表面波经过不同深度的近表面缺陷时, 振荡信号中心频率存在一定的变化规律. 数值仿真结果表明: 当近表面缺陷深度从0.1 mm到0.5 mm变化时, 振荡效应产生的振荡信号中心频率从0.4 MHz到0.76 MHz变化, 振荡信号中心频率与近表面缺陷深度呈近似线性关系, 这为近表面缺陷的定量检测提供了一种理论基础.     

The propagation of Lamb waves in a plate bordered with layers of a liquid.

The influence of liquid layers on the propagation of Lamb waves in a plate of finite thickness is studied theoretically. The dispersion equations of Lamb waves in a plate bordered with layers of liquids are derived. Numerical solutions of the equations show that the phase velocity of Lamb waves changes with the thickness of the liquid layers. For the lowest antisymmetrical mode of very thin plates, the numerical results calculated from the dispersion equations are compared with those derived from the bending wave acoustic impedance approach. The limitation of the latter is discussed. Applications of Lamb waves pertinent to biosensing are also presented.     

Application of a laser/EMAT system for using shear and LS mode converted waves

Quantitative time-of-flight analysis of laser-generated shear waves and longitudinal-shear mode-converted waves has demonstrated an effective method for non-contact monitoring of the thickness of metal plates. Q-switched Nd:YAG laser pulses with energies of approximately 18 mJ, delivered to the material surface via an optical fibre and focused to a line source by a cylindrical lens, excited surface waves, longitudinal and shear waves. Bulk waves propagated through the plate to be reflected from the far surface. Returning waves were detected using an electro-magnetic acoustic transducer (EMAT) sensitive to in-plane motion. The compilation of B-scans generated as the sensor head was moved along the material's surface to produce a 2-D intensity profile made any changes in the plate thickness easy to visualise. The longitudinal-shear (L-S) and shear-longitudinal (S-L) mode-converted waves provided a method of simultaneously monitoring two different points on the far surface enabling any changes in the material thickness to be clearly identified. This method was used to determine the thickness of aluminium samples ranging in from 5 to 70 mm.     

Integral array of acoustic sensors for micro-liter liquid discrimination

It is shown experimentally that the sensing properties of normal acoustic waves propagating in a piezoelectric plate are sensitive to the mass load and the viscosity and electric conductivity of a liquid deposited on the plate. The sensing properties depend on (a) the direction of propagation, (b) the mode number for each direction, and (c) the plate thickness normalized to the acoustic wavelength for each mode and each direction. Based on these properties, a prototype of an acoustic liquid sensor array with different patterns of selectivity is developed and tested. The sensors are located on a single plane of a piezoelectric plate and do not use any sorbent film for sensing. The array is capable of identifying types and sorts of liquids according to their physical effects on the absorption of normal waves with different numbers. The total number of acoustic responses is presented in the form of histograms that are acoustic images of the analyzed substances’ flavors. Having no sorbent film improves the reliability and long-term consistency of sensing.     

Estimation methodology for amplitude of second-order harmonic in nonlinear surface acoustic wave measured by optical diffraction method

An estimation methodology for amplitude from the fundamental to fourth-order harmonic composed of nonlinear surface acoustic waves on a LiNbO₃ substrate with a 128° Y-X propagation axis was demonstrated. First, equations for estimation of amplitudes from diffracted light intensity were shown and then numerical simulations of main factors were carried out. Normalized diffraction light intensities due to components of nonlinear surface acoustic waves were measured and their amplitudes were obtained from measured values. Finally, the amplitude of the second harmonic propagating on a gold thin film of about 50 nm thickness was estimated. It was found that the amplitude of the second harmonic increased continuously from 0.8 to 2.0 Å with propagation distance in the thin film.     

Circumferential waves in a composite circular cylinder

Circumferential waves propagating in a layered, circular cylinder are studied. The cylinder consists of an elastic circular core encased in a hollow, circular cylinder of distinctly different elastic properties. Both smooth and bonded contact are considered. The effect of curvature and layer thickness on the phase velocity of the lowest mode(s) is investigated for both an acoustically softer and an acoustically stiffer layer. When the outer radius of the composite cylinder is unbounded, Stoneley waves are a limiting case as the ratio of the radius of the core to the wavelength increases beyond bounds. When the outer radius is finite, waves in a layer and a half-space result for this limit. Some attention is also directed to the limiting case of small layer thickness to the wavelength ratio. In the limit as this ratio vanishes, the motion of the core reduces to that of Rayleigh waves on the curved surface. For smooth contact, the motion of the core becomes uncoupled from that of the layer for this limiting case, and two distinct modes are seen to exist.     

High frequency shear horizontal plate acoustic wave devices

It has been shown recently that shear horizontal acoustic waves propagating in piezoelectric plates whose thickness h is much less than the acoustic wavelength λ possess a number of attractive properties for use in sensor and signal processing applications. In order to exploit the potential benefits of these waves, however, one needs to fabricate devices on very thin plates. We have developed a suitable fabrication method which can be used to realize devices on such thin plates. In this method, the device is first fabricated on a plate of normal thickness (approximately 500 μm) and the substrate is then lapped from the back side to reduce the thickness. The technique has been utilized to realize devices on plates of thickness less than 70 μm. A shear horizontal plate acoustic wave (SH-PAW) delay line of fundamental resonant frequency greater than 25 MHz and insertion loss less than 7 dB has been realized on a 60 μm thick Y – cut, X – propagation lithium niobate substrate. The device also shows strong response near the third harmonic frequency of 75 MHz.     

Dispersion characteristics of transverse surface waves in piezoelectric coupled solid media with hard metal interlayer

The propagation of transverse surface waves in a piezoelectric layer/metal substrate system with one or multiple hard metal interlayer(s) is investigated analytically. The general dispersion equations for the existence of the waves are obtained in a simple mathematic form for class 6 mm piezoelectric materials. The presence of a hard metal interlayer can not only get rid of the undesired mode appearing in the case without an interlayer but shorten the existence range of the phase velocity within which a nonleaky but dispersive mode exists. The effects of the hard interlayer on the phase velocity can be used to manipulate the behavior of the waves and has implications in acoustic wave devices.     

Magnetoelectric effect in thin-film magnetostriction-piezoelectric structures grown on a substrate

The theory of the magnetoelectric effect in a thin magnetoelectric film-passive substrate structure is presented. Based on the simultaneous solution of the constitutive equations and the equations of motion for the film and substrate, the dispersion law has been derived for elastic waves propagating in the sample plane. It has been shown that the elastic vibrations in the substrate propagate in a near-surface layer if the velocity of propagation of elastic vibrations in the substrate is higher than that in the magnetoelectric film. In this case, the substrate thickness almost does not influence the magnitude of the effect.