A new type of acoustic modes of vibration of thin piezoelectric plates: Quasi-longitudinal normal modes

Using ST-cut quartz crystal plates as an example, a new type of normal modes of acoustic vibrations is described. The modes propagate along the x axis with a velocity close or equal to that of longitudinal bulk waves propagating in the same direction and have a longitudinal component of elastic displacement no less than two orders of magnitude greater than the two other components (the shear-horizontal and shear-vertical ones) throughout the whole plate thickness. The domain of existence of the quasi-longitudinal modes consists of a set of limited zones that contain the “allowed” values of the plate thickness H/λ (H is the plate thickness and λ is the wavelength) and are separated by “forbidden” zones corresponding to common Lamb modes. The closeness (or coincidence) of the velocities of a quasi-longitudinal mode in the plate and a longitudinal bulk wave in an unbounded crystal is a necessary but not sufficient condition for the existence of the aforementioned type of modes in ST,x quartz.     

Shear-horizontal acoustic wave propagation in piezoelectric bounded plates with metal gratings

In this paper, shear-horizontal (SH) acoustic wave propagation in metal gratings deposited on piezoelectric bounded plates is investigated. The spectral characteristics of the electromechanical coupling coefficient are studied first, which are very important for acoustic wave device designs. And, an effective mathematic method based on even- and odd base functions is also presented for overcoming the large frequency thickness product problem. Then, the characteristics of the grating modes are studied, and the nature and characteristics of the stop bands are investigated fully. The results show that the width and attenuation of the stop bands are dominated by the electromechanical coupling coefficient at the frequency centers of the stop bands.     

Hybridization of acoustic waves in piezoelectric plates

The interaction (hybridization) of different types of acoustic waves of zero and higher orders propagating in lithium niobate piezoelectric plates is theoretically investigated. Different crystallographic orientations of the plates and different directions of wave propagation in them are considered. It is shown that, for an electrically free plate with the propagation direction along any of the crystallographic axes, the dispersion curves have intersection points and hybridization is absent. However, when the propagation direction slightly changes or when one of the plate surfaces is short-circuited, the dispersion curves separate and the waves become coupled. A quantitative coefficient characterizing the degree of wave hybridization with allowance for both mechanical and electric coupling is introduced. It is shown that the dependence of this coefficient on the product of the plate thickness by the wave frequency determines the extent of separation of the dispersion curves of interacting waves. The phenomenon under study is of both fundamental and practical interest, for example, in connection with the problem of an efficient excitation of nonpiezoactive acoustic waves in piezoelectric plates.     

Developable modes in vibrated thin plates

We investigate the normal modes of a developable cone singularity as observed in a circular sheet supported by a rigid circular frame and pushed at its center. When the center of the sheet is in addition submitted to a sinusoidal forcing, two types of bending modes, named here rolling and tilt modes, are parametrically excited. The rolling mode is an angular oscillation of the concave sector of the developable cone structure. If the amplitude of vibration is high enough, the rolling mode amplitude increases dramatically giving rise to both a continuous rotation of the concave sector and a material angular displacement of the sheet, similar to that produced by a moving wrinkle in a carpet.     

Ultimately thin metasurface wave plates

Optical properties of a metasurface which can be considered a monolayer of uniaxial metamaterials ‐ parallel‐plate and nanorod arrays – are investigated. It is shown that such metasurface acts as an ultimately thin sub‐100 nm wave plate. This is achieved via an interplay of epsilon‐near‐zero and epsilon‐near‐pole behavior along different axes in the plane of the metasurface allowing for extremely rapid phase difference accumulation in very thin metasurface layers. These effects are shown to not be disrupted by non‐locality and can be applied to the design of ultrathin wave plates, Pancharatnam‐Berry phase optical elements and plasmon‐carrying optical torque wrench devices.

     

Optimum acoustic wave second-harmonic generation in piezoelectric semiconductors

The phenomenological approach has been used to study analytically the acoustic wave second harmonic generation in piezoelectric semiconductors in the presence of the d.c. electric and an oscillating electromagnetic field (OEF). It has been suggested that the second harmonic acoustic flux (SHAF) can be enhanced considerably by the application of an OEF polarized in the direction of the propagating acoustic wave. The SHAF exhibits a maximum at Ω = ω, where Ω is the frequency of the OEF and ω is the frequency of the acoustic wave. The SHAF also shows a maximum at d.c. electric fields for which the average drift velocity of the carriers is equal to the velocity of sound. It is found that for a typical case of n-type nondegenerate InSb (77°K, n = 2·5 × 10¹⁴ cm^?3) that the SHAF is enhanced by a factor of 10³ over its value in the absence of OEF. The present analysis is valid in the low frequency region only (i.e. ql ? 1).     

声表面波在压电晶体表面上的聚焦特性

研究了压电晶体表面上圆弧形叉指换能器产生的声表面波的聚焦现象。用作者提出的压电晶体表面激发的严格矢量场理论来计算会聚的表面波声场,取代了比较流行的源于光学的标量角谱理论。理论分析表明介质的各向异性对声束的会聚特性有很大的影响,如焦长和焦点附近声场的对称性。在实验中可以用光学暗场法来观察声表面波场的会聚。尽管各向异性介质或各向异性压电晶体上表面波声场的会聚都非常复杂,实验的结果和理论分析比较一致。     

Dispersion of waves and characteristic wave surfaces in functionally graded piezoelectric plates

An inhomogeneous layer element method is presented to analyze the dispersion of waves and characteristic wave surfaces in plates of functionally graded piezoelectric material (FGPM). In this method, the FGPM plate is divided into a number of layered elements. The elemental elastic and electric properties are assumed as linear functions of the thickness to adopt the variety of the material property of FGPM. The Hamilton principle is applied to determine the governing equations. The phase velocity surface, phase slowness surface, phase wave surface, group velocity surface, group slowness surface, and group wave surface for FGPM plate are formulated using Rayleigh quotient and the orthogonality condition of the eigenvectors. These six surfaces are then used to illustrate the characteristics of waves in FGPM plates. Numerical examples are presented using the present formulations to analyze dispersions and characteristics of waves in FGPM plates.     

Surface acoustic wave propagation and acoustoelectric interaction in multilayered piezoelectric semiconductors

In the past years, the acoustoelectric interaction has been used in a number of different devices such as acoustic amplifiers, acoustoelectric convolvers and acoustic coupled transport devices. Recent developments in synthesized semiconductor superlattices with high quality heterostructures have been found to be useful in a new generation of high performance devices such as the High Electron Mobility Transistor. The objective of this paper is to extend the use of these superlattices to acoustoelectric devices. A complete theory of acoustoelectric interaction in layered piezoelectric semiconductor has been developed. The acoustic propagation equations have been solved together with the continuity, transport and Poisson equations. The free carrier transport properties are accounted for using a mobility tensor to describe the two-dimensional behavior. The acoustical and electrical boundary conditions have been used to obtain mechanical displacement and electric field expressed in terms of Bloch functions. The effect of longitudinal D.C. applied field on SAW attenuation or amplification is also considered.     

Convective amplification of parametrically generated acoustic wave in a piezoelectric semiconductor plasma

Using hydrodynamic model of semiconductor plasmas and coupled-mode theory of interacting waves, we have analytically investigated parametric interaction in a magnetised piezoelectric semiconductor plasma in non-relativistic domain. The temperature dependence of momentum transfer collision frequency of electrons due to their heating by the pump is assumed to induce nonlinearity in the medium. We have derived a dispersion relation which finally gives four unstable acoustic modes; two forward amplifying modes and two backscattered attenuating modes. We have also obtained an expression for the critical pump amplitude ( ) at and around which gains and phase velocities of amplifying acoustic modes become least dependent on the pump amplitude and static magnetic field . The required can be readily obtained from a pulsed 10.6 μm CO₂ laser. The magnetic field is found to shift the critical point towards lower pump amplitudes. Received 5 September 2000 and Received in final form 5 March 2001     

Controlling flexural waves in thin plates by using transformation acoustic metamaterials

In this study, we design periodic grille structures on a single homogenous thin plate to achieve anisotropic acoustic metamaterials that can control flexural waves. The metamaterials can achieve the bending control of flexural waves in a thin plate at will by designing only one dimension in the thickness direction, which makes it easier to use this metamaterial to design transformation acoustic devices. The numerical simulation results show that the metamaterials can accurately control the bending waves over a wide frequency range. The experimental results verify the validity of the theoretical analysis. This research provides a more practical theoretical method of controlling flexural waves in thin-plate structures.     

Acoustical wave propagator for time-domain flexural waves in thin plates

In this paper, an explicit acoustical wave propagator technique is introduced to describe the time-domain evolution of acoustical waves in two-dimensional plates. A combined scheme with Chebyshev polynomial expansion and fast Fourier transformation is used to implement the operation of the acoustical wave propagator. Through this operation, the initial wave packet at t = 0 is mapped into the wave packet at any instant t > 0. By comparison of the results of the exact analytical solution and the Euler numerical method, we find that this new Chebyshev-Fourier scheme is highly accurate and computationally effective in predicting the acoustical wave propagation in thin plates. This method offers an opportunity for future study of dynamic stress concentration and time-domain energy flow in coupled structures.     

Large Lamb wave band gap in phononic crystals thin plates

We suggest that Lamb wave band gaps in one-dimensional phononic crystals can be substantially enlarged by using multiple heterostructures which consist of several pieces of phononic crystal with different ratios of the thickness to the lattice period. This is possible because each substructure shows a different band gap and the band structure of a Lamb wave is strongly affected by the ratio of the plate thickness to the lattice period. This effect has been demonstrated by using finite element simulations on two different one-dimensional systems. PACS 63.20.-e; 62.65.+k; 41.20.Jb; 43.20.+g     

New automatic localization technique of acoustic emission signals in thin metal plates

In acoustic emission (AE) measurement, the information of the arrival time is very important for event location, event identification and source mechanism analysis. Manual picks are time-consuming and sometimes subjective, especially in the case of large volumes of digital data. Various techniques have been presented in the literature and are routinely used in practice such as amplitude threshold, analysis of the long-term average/short-term average (LTA/STA), high-order statistics or artificial neural networks.A new automatic determination technique of the first arrival times of AE signals is presented for thin metal plates. Based on Akaike’s information criterion, proposed algorithm of the first arrival detection uses a specific characteristic function, which is sensitive to change of frequency in contrast to others such as envelope of the signal. The approach is applied to data sets of three different tests. Reliable results show the potential of our approach.     

Structural, electrical and piezoelectric properties of LiNbO3 thin films for surface acoustic wave resonators applications

In this work, 0.30 μm thick LiNbO₃ layers have been deposited by sputtering on nanocrystalline diamond/Si and platinised Si substrates. The films were then analyzed in terms of their structural and optical properties. Crystalline orientations along the (0 1 2), (1 0 4) and (1 1 0) axes have been detected after thermal treatment at 500 °C in air. The films were near-stoichiometric and did not reveal strong losses or diffusion in lithium during deposition or after thermal annealing. Pronounced decrease of the roughness on top of the LiNbO₃ layer and at the interface between LiNbO₃ and diamond was also observed after annealing, compared to the bare nanocrystalline diamond on Si substrate. Furthermore, ellipsometry analysis showed a better density and a reduced thickness of the surface layer after post-deposition annealing. The dielectric constant and losses have been measured to 50 and less than 3.5%, respectively, for metal/insulator/metal structures with 0.30 μm thick LiNbO₃ layer. The piezoelectric coefficient d₃₃ was found to be 7.1 pm/V. Finally, we succeeded in switching local domain under various positive and negative voltages.     

Conventional electromagnetic acoustic transducer development for optimum Lamb wave modes

Lamb waves are normally utilized for inspecting thin metal sheets. Wheel type probes using piezoelectric oscillators have generally been used as the sensors for Lamb waves. Recently, the electromagnetic acoustic transducer (EMAT) has been developed and is beginning to be used as a Lamb wave detector. We have developed a useful type of transducer for Lamb waves. The new EMAT consists of a meander coil with a narrow distance of 2.5 mm and has a symmetrical structure in the vertical direction for both surface sides. The new EMAT can generate Lamb waves with variable wavelengths corresponding to the frequency range from approximately 300 kHz to 2.5 MHz and multiple modes, and can also generate selected symmetrical and anti-symmetrical mode Lamb waves. It is demonstrated that the optimum Lamb wave mode could be produced by the appropriate positioning of the EMATs and controlling the phase (same or inversed) of the electrical signal driving the device. The described EMAT can be used to examine steel (or other material) sheets of different thickness. It is also shown that the S0 (0.3 MHz) mode Lamb wave is the most effective for the deepest (up to 6 mm) penetration.     

Material property estimation in thin plates using focused,synthetic-aperture acoustic beams

The method developed here exploits the wide angular range of focused acoustic probes and the large synthetic aperture of scanned transducers to permit a rapid and reliable estimation of material properties in thin plates. It is found in several tests with various materials that estimates of elastic behavior using this method agree with contact measurements to within less than 5%. The method utilizes transmission (or reflection) coefficient reconstruction for an infinite thin plate, across a wide range of frequency and wave number, from which elastic property estimates are made. Data collected over a large synthetic acoustic aperture are processed with temporal and spatial Fourier transforms applied to change the acquired data from the coordinate and time domains to the wave number and frequency domains. Extrinsic real-beam effects on the data are accounted for with a complex transducer point analysis. Transmission measurements yield reconstructed data extending to the mode cutoffs, permitting easy and nearly unambiguous estimation of a subset of the elastic stiffnesses. For anisotropic plates, elastic stiffnesses are estimated with an inversion procedure that uses only limited data carefully selected from different portions of the measured scattering coefficient. Estimates are made by reconstructing in a stepwise fashion, based on sensitivity studies, where only one stiffness is estimated from the data at any one time, restricting the optimization to a robust one-dimensional search.     

Parity-time symmetric acoustic system constructed by piezoelectric composite plates with active external circuits

Researches on parity-time (PT) symmetry in acoustic field can provide an efficient platform for controlling the travelling acoustic waves with balanced loss and gain. Here, we report a feasible design of PT-symmetric system constructed by piezoelectric composite plates with two different active external circuits. By judiciously adjusting the resistances and inductances in the external circuits, we obtain the exceptional point due to the spontaneous breaking of PT symmetry at the desired frequencies and can observe the unidirectional invisibility. Moreover, the system can be at PT exact phase or broken phase at the same frequency in the same structure by merely adjusting the external circuits, which represents the active control that makes the acoustic manipulation more convenient. Our study may provide a feasible way for manipulating acoustic waves and inspire the application of piezoelectric composite materials in acoustic structures.     

Transformation of modes of surface acoustic waves in strong KNbO3 and PKN piezoelectric crystals

We consider the transformation of a generalized surface acoustic wave (GSAW) into a Bleustein-Gulyaev (B-G) or Rayleigh wave in the yx and 90-yx-cuts of rhombic KNbO₃ and orthorhombic PKN crystals in the case of slight deviation of the wave vector from the direction of the pure-mode axis. We have numerically analyzed the characteristics of the GSAW, B-G wave, and Rayleigh wave in the KNbO₃ and PKN crystals with strong piezoelectric coupling. It is shown that the GSAW has a mainly transverse component of the mechanical shift in the region of the yx cut. In this case, the electromechanical coupling coefficient has an unprecedented high value. We have analyzed the dependence of the distribution of mechanical shifts and electric potential of the wave propagating into the crystal on the distance from the substrate surface on the open and metallized surfaces; we also consider the dependence of the GSAW velocity in these crystals with variation in the metal film thickness. N. I. Lobachevsky State University, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 5, pp. 445–451, September, 2000.     

各向同性薄板中横穿孔缺陷的超声兰姆波层析成像

本文将地球物理中的跨孔层析重建技术用于兰姆波的定量无损评价。综合射线追踪与代数重建技术(ART),发展了横穿孔缺陷的超声兰姆波层析成像方法。基于Snell定律和费马原理,采用射线追踪方法寻求发射和接收换能器之间超声兰姆波的实际传播路径并计算走时,然后采用ART算法对走时数据进行速度图像重建。给出了具有人工横穿孔缺陷铝板的数值模拟和实验数据的直射线和弯曲射线重建图像。结果表明,弯曲射线ART方法比直射线ART方法重建的缺陷尺寸更接近于缺陷的真实尺寸,并且当考虑射线弯曲时,重建图像的赝象也有所降低。