二维周期性复合介质中弹性波的能带结构

用平面波展开方法,研究弹性波在二维周期性复合介质中的传播问题.由 Pb柱体嵌入 epoxy基体组成的复合介质,其弹性波带结构中,存在很大的完全带隙。研究了柱体的横截面形状、组元的体积占有率及复合介质的材料组成等因素对带结构的影响.在C柱体和epoxy基体组成的复合介质中,也观察到完全禁带的出现。但是,相反情况,由epoxy柱体和Pb或C基体组成的材料中,均无完全禁带出现。     

Propagation of surface acoustic waves in a piezoelectric medium with a periodic groove structure

A system of equations is formulated to describe the propagation of surface acoustic waves in a piezoelectric substrate whose surface has a periodic structure formed by transverse grooves. Dependences of the reflection coefficient and the wave velocity on the geometry of the periodic structure (the width and the depth of the grooves) are obtained in a wide range of variation of these parameters for five different orientations in various piezoelectric crystals (quartz, lithium niobate, lithium tantalate, and langasite).     

Dispersion relation of piezoelectric periodic structure

The coupled dispersion relation resulting from the interaction of acoustic waves with an infinity long conducting grating deposited along the pure mode axis of a piezoelectric crystal of trigonal class is specified and its implications on different kinds of mode coupling are discussed.     

Coupled charge density waves in nearly one dimensional systems

A mean field theory of coupling between charge density waves CDW in linear chain systems is described. It is shown that interchain coupling can stabilize CDW's and lead to a semiconducting behavior. The model is applied to semiconducting TCNQ salts.     

Electromechanical tailoring of structure with periodic piezoelectric circuitry

In this paper, we study the integration of piezoelectric transducers and electrical circuitry onto a mechanical host structure to form an electromechanical periodic system. This scheme enables us to take advantage of the unique wave propagation characteristics of spatially periodic systems and thus manipulate the energy flow/distribution in the host mechanical structure. Different from most previous investigations where spatial periodicity is typically due to the periodic discontinuities in the mechanical structure, in the proposed scheme the mechanical structure can remain to be continuous without being altered. Instead, the electrical circuitry consists of periodic branches which, when coupled to the mechanical structure through the piezoelectric transducers, yields repetitive subsystems in the electromechanical integrated system. The circuitry elements can be online tunable, effectively making the energy manipulation adaptive to excitation variations. A transfer matrix-based approach is adopted in the dynamic analysis of the integrated system, where each subsystem is represented by two state vectors with a transfer matrix relating them. Given the repetitive nature of the subsystems due to periodicity, analysis on the entire system is conducted by focusing on one single subsystem. Systematic analysis is carried out to demonstrate the characteristics of wave propagation and attenuation in terms of propagation constants as well as the mechanical and electrical responses. Effects of circuitry tuning are also discussed through detailed parametric studies. Implications and potential applications of the proposed scheme are illustrated.     

Excitation of shear waves due to the interband absorption of laser radiation in a piezoelectric semiconductor-dielectric layered structure

Optical piezoelectric generation of shear bulk acoustic waves by volume-distributed electric fields in the vicinity of a hard planar interface between a piezoelectric semiconductor and a dielectric is described theoretically. Nonstationary and nonuniform electric fields are formed as a result of the spatial separation of electrons and holes photoexcited in the piezoelectric semiconductor due to the interband absorption of laser radiation. Frequency regions where the efficiency of the optical piezoelectric excitation of shear waves increases when the surface of the piezoelectric semiconductor is loaded by another piezoelectric with a high acoustic impedance are found. Numerical estimates of the applicability of the immobile hole model are presented.     

C*-Algebras associated with one dimensional almost periodic tilings

For each irrational number, 0<α<1, we consider the space of one dimensional almost periodic tilings obtained by the projection method using a line of slope α. On this space we put the relation generated by translation and the identification of the “singular pairs”. We represent this as a topological spaceX _α with an equivalence relationR _α. OnR _α there is a natural locally Hausdorff topology from which we obtain a topological groupoid with a Haar system. We then construct the C^*-algebra of this groupoid and show that it is the irrational rotation C^*-algebra,A _α. Research supported by the Natural Sciences and Engineering Research Council of Canada and the Fields Institute for Research in Mathematical Sciences.     

On propagation of anti-plane shear waves in piezoelectric plates with surface effect

Based on the surface piezoelectricity model, the anti-plane or horizontally polarized shear (SH) waves propagating in an infinite piezoelectric plate of nano-thickness are investigated to show the surface effect on wave characteristics. The influence on the overall properties of piezoelectric structures resulting from the surface effect is treated as a spring force exerting on the boundary of the bulk. The frequency equations of anti-symmetric and symmetric waves are presented analytically for the electrically short-circuited case. Numerical results show that the wave properties are size-dependent, and the surface effect becomes very pronounced at a high frequency.     

Dynamic interaction of anti-plane shear waves with arc-shaped interfacial crack in piezoelectric media

The dynamic interaction between anti-plane shear waves with arc-shaped interfacial crack of piezoelectric media is considered here. The region of the debonding is modeled as an arc-shaped interfacial crack with non-contacting faces. The electric permeable and impermeable boundary conditions are adopted to get the disturbed solution, respectively. The crack opening displacement and the electric potential are represented by Chebyshev polynomials and a system of equations is derived. The calculation results show that the piezoelectric coefficient has remarkable effect on the crack opening displacement.     

Bleustein-Gulyaev waves in a functionally graded piezoelectric material layered structure

This work presents a theoretical study of the propagation behavior of Bleustein-Gulyaev waves in a layered structure consisting of a functionally graded piezoelectric material (FGPM) layer and a transversely isotropic piezoelectric substrate. The influence of the graded variation of FGPM coefficients on the dispersion relations of Bleustein-Gulyaev waves in the layered structure is investigated. It is demonstrated that, for a certain frequency range of Bleustein-Gulyaev waves, the mechanical perturbations of the particles are restricted in the FPGM layer and the phase velocity is independent of the electrical boundary conditions at the free surface. Results presented in this study can not only provide further insight on the electromechanical coupling behavior of surface waves in FGPM layered structures, but also lend a theoretical basis for the design of high-performance surface acoustic wave (SAW) devices. Supported by the National Natural Science Foundation of China (Grant No. 10632060), the National Basic Research Program of China (Grant No. 2006CB601202), the National 111 Project of China (Grant No. B06024), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20070698064)     

弱界面压电覆层复合结构中的声导波

建立压电覆层复合结构中声导波传播模型,结合弱界面“弹簧”模型,推导了压电覆层复合结构存在刚性、滑移联接界面等几种不同界面条件下声导波的广义频散方程,数值计算钛锆酸铅基压电陶瓷覆层复合结构在不同界面条件下声导波的频散曲线,分析了界面特性对导波传播相速度的影响。数值计算和分析表明为了能够有效地评价界面的特性,选择合适的声波模式和声波频率是非常重要的。实验结果验证了界面假设的有效性,为进一步深入研究以多模式声导波参量为基础的压电覆层复合结构界面特性参数反演方法提供了理论基础。     

Propagation of Bleustein-Gulyaev waves in a prestressed layered piezoelectric structure

Based on the theories of nonlinear continuum mechanics, piezoelectricity and elastic waves in solids, theoretical analysis of Bleustein-Gulyaev surface acoustic wave propagation in a prestressed layered piezoelectric structure are described. Numerical calculations are performed for the case that the layer and the substrate are identical LiNbO(3) except that they are polarized in opposite directions. It is found that an almost linear behavior of the relative change in phase velocity versus the initial stress is obtained for both surface electrically free and shorted cases. Potential applications in the design of acoustic wave devices are suggested.     

Acoustic waves in structure "piezoelectric plate-polymeric nanocomposite film"

Paper is devoted to the investigation of SH(0) acoustic waves propagating in structure "piezoelectric plate-polymeric nanocomposite film". The analysis was carried out by the example of the polymeric nanocomposite film based on high-pressure polyethylene with various contents of CdS nanoparticles and lithium tantalate and lithium niobate plate. The resonant attenuation of investigated waves for the certain ratios of plate and film thicknesses was found. The obtained results open the prospects of the development of structures for SH(0) waves consisting of nanocomposite polymeric substrates and thin piezoelectric plates. Such structures may be useful for development of various thermostable chemical and biological sensors and signal processing devices.     

Anomalous dispersion of SH acoustic waves in a piezoelectric sandwich structure

A transformation of the dispersion spectrum of shear horizontal (SH) acoustic eigenwaves in a sandwich structure due to a piezoelectric effect is described. The structure consists of two plates separated by a gap whose thickness is considerably less than the wavelength. Under these conditions, acoustic fields induced in the plates interact through the piezoelectric effect. The piezoelectric effect brings about a distortion and divergence of the initially (in the zeroth approximation) independent dispersion curves; i.e., all points of intersection of the dispersion curves disappear. Each of the new dispersion branches is formed by a set of adjacent portions of initial branches. A change in the wave number (or in the frequency) results in a periodic gradual displacement of the localization zone of the acoustic field from one plate to the other.     

Shear horizontal surface waves on piezoelectric ceramic with layered structure

This paper presents theoretical and experimental results describing the propagation of SH (shear, horizontal) surface waves on a piezoelectric ceramic with a surface layer of different polarization than that in the substrate. An analytical formula for the group velocity of the SH surface waves is developed. The velocity of impulses of the SH surface waves is determined experimentally. Further, the theoretical results are compared to the experimental values.     

Love waves in a layered functionally graded piezoelectric structure under initial stress

Abstract

To study the effect of initial stress on the propagation behavior of Love waves in a layered functionally graded piezoelectric structure, a mathematical model is established. The piezoelectric layer is taken as exponentially graded material where as half-space is taken as simply elastic substratum. The coupled electromechanical field equations are solved analytically to obtain the mechanical displacements and electrical potential functions for the piezoelectric layer and elastic substrate. The dispersion relations are obtained for electrically open and short cases. The higher mode Love wave propagation has been considered. For numerical interpretation of the results, four sets of piezoelectric layer and elastic substrate have been taken into consideration. Graphical representation reveals about the effect of initial stress and the effect of inhomogeneity parameter on the phase velocity against wave number for electrically open and electrically short cases, respectively.     

Study on localization of plane elastic waves in disordered periodic 2-2 piezoelectric composite structures

Considering the effect of mechanic-electric coupling, the propagation and localization of plane elastic waves in disordered periodic layered piezoelectric composite structures are studied. The transfer matrix between two consecutive unit cells is obtained by means of the continuity conditions and the expression of the localization factors in disordered periodic structures is presented by regarding the variables of mechanical and electrical fields as the elements of state vectors. As examples, numerical results of localization factors are presented and discussed. It can be seen from the results that ordered periodic structures possess the properties of frequency passbands and stopbands and the phenomenon of wave localization in disordered periodic structures is observed, and the larger the coefficient of variation is, the larger the localization factor or the stronger the degree of wave localization is. The characters of wave propagation and localization are very different for different sorts of piezocomposites or different structural sizes, and even for same sorts of piezocomposites and same structural sizes the characters of wave propagation and localization are also very different for different non-dimensional wavenumbers. We may design different piezocomposites or adjust the structural sizes to control the characters of wave propagation and localization.     

Shear surface acoustic waves in the stratified structure piezoelectric—High-temperature granular superconductor

The interaction of a Gulyaev-Bluestain surface wave with a granular high-temperature superconducting (HTSC) medium has been investigated. For piezoelectrics of symmetry 4mm and 6mm, dispersion equations have been derived that describe the characteristics of surface acoustic waves (SAWs). The temperature dependences of the SAW attenuation and phase have been calculated forZnO andBa ₂Si₂TiO₃ crystals. It is shown that at temperatures higher than the critical temperature an attenuation jump and a phase shift are observed. The effect intensifies with increase in the electromechanical coupling coefficient and with decrease in the thickness of the HTSC film. For theBa ₂Si₂TiO₃ crystal the attenuation jump and phase shift are11 dB/cm and38 deg/cm, respectively, at a frequency of820 MHz. The results obtained can also be generalized for periodic HTSC structures and can be used to design frequency-selective devices and fast-response bolometric photodetectors. Tomsk State University of Control Systems and Radioelectronics. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 49–52, April, 1999.