Amplification of acoustic waves in laminated piezoelectric semiconductor plates

Summary Two-dimensional equations for coupled extensional, flexural and thickness-shear motions of laminated plates of piezoelectric semiconductors are obtained systematically from the three-dimensional equations by retaining lower order terms in power series expansions in the plate thickness coordinate. The equations are used to analyze extensional waves in a composite plate of piezoelectric ceramics and semiconductors. Dispersion and dissipation due to semiconduction as well as wave amplification by a dc electric field are discussed.     

Low-frequency dispersion of fundamental waves in anisotropic piezoelectric plates

Low-frequency onset of the fundamental branches in piezoplates is studied with a view to identify the impact of piezoelectric coupling. General analytical expressions for the zero- and leading-order terms of the velocity versus wavenumber expansion in an anisotropic homogeneous piezoplate are obtained. On this ground, it is shown what types of anisotropy and electric boundary conditions enable the onset parameters of fundamental branches to be piezoactive. Particular attention is given to the linear dispersion at the origin of two upper fundamental branches. This property is entirely caused by the piezoeffect, being ruled out for elastic plates. An invariant hierarchy is established between the zero-order velocities of the fundamental waves under different electric boundary conditions in homogeneous and functionally graded plates. It is shown that some of these velocities in a metallized plate become piezoactive specifically if the piezoplate is functionally graded.     

Generalized Rayleigh surface waves in a piezoelectric semiconductor half space

Meccanica - In this paper, plane strain surface waves, also named generalized Rayleigh surface waves, in a transversely isotropic piezoelectric semiconductor half space are investigated. The...     

Long-wavelength dispersion of acoustic waves in transversely inhomogeneous anisotropic plates

Long-wavelength onset of the fundamental branches is described for a free anisotropic plate with arbitrary through-plate variation of material properties. Main attention is given to the flexural branch. Closed-form expressions for the leading-order dispersion coefficient of the velocity and displacement are derived for a generic case and exemplified for the various types of either continuous, or discrete, or periodic inhomogeneity and for the monoclinic symmetry. The relevance of the static averaging is examined in detail. The bounds for the slope of the flexural velocity branch are established. The upper fundamental branches are considered for the case when these are uncoupled inplane and shear horizontal ones.     

Dispersion of elastic guided waves in piezoelectric infinite plates with inversion layers

In this work, we study the dispersion of elastic waves in piezoelectric infinite plates with ferroelectric inversion layers. The motivation is to analyze the effect of ferroelectric inversion layers on wave dispersion and resonant behavior under impulsive line loads. A semi-analytical finite-element (SAFE) method has been adopted to analyze the problem. Two model problems are considered for analysis. In one, the plate is composed of a layer of 36° rotated y-cut LiNbO₃ with a ferroelectric inversion layer. In the other, material is PZT-4 with a ferroelectric inversion layer. Comparison with experimental results, reported in the literature for isotropic materials, shows a very good agreement with theoretical predictions obtained using SAFE method. Furthermore, comparison of the resonance frequencies of the S₁ modes, calculated using KLM approximation (f₀ = C_d/2h) and SAFE method, are illustrated for each problem. The frequency spectra of the surface displacements show that resonant peaks occur at frequencies where the group velocity vanishes and the phase velocity remains finite, i.e., a minimum in the dispersion curve below the cut-off frequency. The effect of the ratio of the thicknesses of the inversion layer (IL) and the plate on the frequencies and strength of the resonant peaks is examined. It is observed that for PZT-4 with 50% IL to plate thickness ratio the frequency for the second resonant peak is about twice that for the first one. Results are presented showing the dependence of resonant frequencies on the material properties and anisotropy. Materials selection for single-element harmonic ultrasound transducers is a very important factor for optimum design of transducers with multiple thickness-mode resonant frequencies. The theoretical analysis presented in this study should provide a means for optimum ultrasound transducer design for harmonic imaging in medical applications.     

On diffraction of acoustic and electric waves in piezoelectric medium by an absorbent half-plane electrode

Diffraction of incident acoustic and incident electric waves in a transversally isotropic piezoelectric medium at the boundary of a half-plane absorbent electrode is systematically investigated using the quasi-hyperbolic approximation. The electrode is assumed to be very thin so that its thickness and stiffness can be neglected. By exact inversion, the explicit expressions for the scattering waves are obtained. A closed form solution is obtained by applying Laplace transformations and the Wiener–Hopf technique. By means of the Cagniard–de Hoop method a detailed investigation of the structure of the electro-acoustic wave is conducted. The mode conversion between electric and acoustic waves, the effect of electro-acoustic head wave, the Bleustein–Gulyaev surface wave and the structure of the wave in terms of the type of the incident wave (acoustic or electric) and its angle of incidence are analyzed in detail. It is shown that in piezoelectric materials, absorbent electrodes are neither completely opaque nor completely transparent to electric and acoustic waves. The dynamic field intensity factors at the tip of the electrode are functions of the angle of incidence and time; they are derived explicitly and discussed through a detailed numerical analysis.     

Effect of a biasing electric field on the propagation of antisymmetric Lamb waves in piezoelectric plates

Based on the theories of anisotropic elasticity, piezoelectricity and elastic waves in solids, the propagation of antisymmetric Lamb waves in a biasing electric field is investigated in this paper. By solving the coupled differential equations of motion under a biasing electric field, the phase velocity equations of antisymmetric Lamb wave modes for electrically open and shorted cases are obtained, respectively. The beating effect arising from the difference between the phase velocity of the zero-order symmetric mode and antisymmetric mode exists in the plate when the plate has a thickness comparable to or slightly larger than the wavelength. The influence of the biasing electric field on the phase velocity, beat wavelength, mechanical displacement and stress fields for the lowest two antisymmetric modes of Lamb waves are discussed in detail. From the calculated results, it is seen that the phase velocity of the fundamental antisymmetric mode is especially sensitive to the applied biasing electric field.     

Effect of a biasing electric field on the propagation of symmetric Lamb waves in piezoelectric plates

This paper is concerned with the effect of a biasing electric field on the propagation of Lamb waves in a piezoelectric plate. On the basis of three dimensional linear elastic equations and piezoelectric constitutive relations, the differential equations of motion under a biasing electric field are obtained and solved. Due to the symmetry of the plate, there are symmetric and antisymmetric modes with respect to the median plane of the piezoelectric plate. According to the characteristics of symmetric modes (odd potential state) and antisymmetric modes (even potential state), the phase velocity equations of symmetric and antisymmetric modes of Lamb wave propagation are obtained for both electrically open and shorted cases. The effect of a biasing electric field on the phase velocity, electromechanical coupling coefficient, stress field and mechanical displacement of symmetric and antisymmetric Lamb wave modes are discussed in this paper and an accompanying paper respectively. It is shown that the biasing electric field has significant effect on the phase velocity and electromechanical coupling coefficient, the time delay owning to the velocity change is useful for high voltage measurement and temperature compensation, the increase in the electromechanical coupling coefficient can be used to improve the efficiency of transduction.     

Coupled piezoelectric vibrations of quartz plates

The contributions of coupling with the electric field and mass of electrode coatings are taken into account in solutions of equations governing coupled thickness-shear, flexure and face-shear vibrational modes in rotated-Y-cut quartz plates.     

Hot-wire anemometry in acoustic waves

 Experimental techniques developed for the measurement of the acoustic velocity oscillation without a superimposed steady flow in gases using a hot-wire anemometer are reported. The techniques developed include amplitude and phase calibrations in standing waves.     

Nonsteady-state problem of the emission of acoustic waves by a cylindrical piezoelectric transducer near a planar boundary

We study processes developing when a cylindrical piezoceramic shell with split electrodes located near a planar boundary is excited by nonsteady-state electrical signals. We solve the problem using the Laplace integral transform with respect to time. The boundary conditions are satisfied in the space of the originals. Under these conditions, the unknowns are found from a system of Volterra integral equations. We present the calculation results and their analysis. Translated from Prikladnaya Mekhanika, Vol. 33. No. 12, pp. 60–67, December, 1997.     

Modelling of thin piezoelectric layers on plates

The derivation of plate equations for a plate consisting of two layers, one anisotropic elastic and one piezoelectric, is considered. Power series expansions in the thickness coordinate for the displacement components and the electric potential lead to recursion relations among the expansion functions. Using these in the boundary and interface conditions, a set of equations are obtained for some of the lowest-order expansion functions. This set is reduced to six equations corresponding to the symmetric (in-plane) and antisymmetric (bending) motions of the elastic layer. These equations are given to linear (for the symmetric equations) or quadratic (for the antisymmetric equations) order in the thickness. It is noted that it is, in principle, possible to go to any order, and that it is believed that the corresponding equations are asymptotically correct. A few numerical results for guided waves along the plate and a 1D actuator case illustrate the accuracy.     

Bending of functionally graded piezoelectric rectangular plates

By introducing two displacement functions as well as two stress functions, two independent state equations with variable coefficients are derived from the three-dimensional theory equations of piezoelasticity for transverse isotropy. A laminated approximation is used to transform the state equations to those with constant coefficients in each sub-layer. The bending problem of a functionally graded rectangular plate is then analyzed based on the state equations. Numerical results are presented and the effect of material gradient index is discussed. Supported by the National Natural Sciences Foundation of China (No. 10002016).     

Harmonic waves in elastic sandwich plates

Motions of a sandwich plate with symmetric facings are studied in the framework of the three-dimensional equations of elasticity. Both the core and facings are assumed to be isotropic and linearly elastic.Harmonic wave solutions, which satisfy traction-free face conditions and continuity conditions of tractions and displacements at the interfaces, are obtained for four cases: symmetric plane strain solutions for extensional motion, antisymmetric plane strain solutions for flexural motion, and solutions for the symmetric and antisymmetric SH-waves. The dispersion relation for each of these cases is obtained and computed. In order to exhibit the effect of the ratios of facing to core thicknesses, elastic stiffnesses and densities, on the dynamic behavior of sandwich plates, dispersion curves are computed and compared for plates with thick, light, and soft facings as well as for plates with thin, heavy, and stiff facings. Asymptotic expressions of dispersion relations for extensional, flexural, and symmetric SH-waves are obtained in explicit form, as the frequencies and wave numbers approach zero.The thickness vibrations in sandwich plates are studied in detail. The resonance frequencies and modal functions of the thickness-shear and thickness-stretch motions are obtained. Simple algebraic formulas for predicting the lowest thickness-shear and the lowest thickness-stretch frequencies are deduced. The orthogonality of the thickness modal functions is established.