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.     

Amplification of acoustic waves in piezoelectric semiconductor plates

Two-dimensional equations for coupled extensional, flexural and thickness-shear motions of thin 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 two-dimensional equations are specialized to crystals of 6 mm symmetry and are simplified by thickness-shear approximation. Propagation of thickness-shear waves and their amplification by a dc electric field are analyzed.     

Two-dimensional electroelastic fundamental solutions for general anisotropic piezoelectric media

I.IntroductionDuetotheirintrinsiccouplingeffectbetweenmechanicalandelectricalfields,piezoelectricmaterialshavebeenwidelyusedintechnologyastransducersandsensorsand,morerecently,asactuatorsinsmartstructures.lnordertooptimizetheirmicrostructuresandunderstand…     

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.     

Further studies on edge waves in anisotropic elastic plates

A modified Stroh-type formalism for edge waves in unsymmetrical anisotropic plates is derived. Explicit expressions of the fundamental matrices for the formalism are presented. The existence conditions for one or two subsonic edge waves in the unsymmetrical anisotropic plates are discussed based on the formalism, and a procedure for finding an explicit secular equation for the edge-wave speed is proposed.     

Electro-elastic fundamental solutions of anisotropic piezoelectric materials with an elliptical hole

By using Stroh' complex formalism and Cauchy's integral method, the electro-elastic fundamental solutions of an infinite anisotropic piezoelectric solid containing an elliptic hole or a crack subjected to a line force and a line charge are presented in closed form. Particular attention is paid to analyzing the characteristics of the stress and electric displacement intensity factors. When a line force-charge acts on the crack surface, the real form expression of intensity factors is obtained. It is shown through a special example that the present work is correct. The project supported by the Fund of the State Education Commission of China for Excellent Young Teachers     

General formalism for plane guided waves in transversely inhomogeneous anisotropic plates

The sextic approach to plane waves in infinite (visco)elastic plates of arbitrary anisotropy and transverse inhomogeneity is outlined. A particular thrust is set on continuous inhomogeneity when the propagator is defined by the Peano expansion. Despite underlying explicit intricacy, the basic framework of the pursued formalism is little affected by a through-plate variation of material. To make it evident, the principal algebraic symmetry of the propagator for unattenuated waves and the ensuing arrangement of the impedance as a Hermitian matrix with specific traits are inferred directly from energy considerations. Staying the same as for homogeneous plates, those features yield useful developments in the broader context of inhomogeneity. The formalism may be expressed in either pair picked among velocity, frequency and wavenumber, but different choices of a dispersion variable are shown to entail analytical dissimilarities. In addition, the impact of the profile symmetry and of the horizontal plane of crystallographic symmetry is examined. The surface-impedance method and some other aspects of the numerical treatment are discussed.     

On the backward Lamb waves near thickness resonances in anisotropic plates

A closed-form expression for the leading-order dispersion coefficient, describing the trend of Lamb-wave branches at their onset from thickness resonances, is derived for an arbitrary anisotropic plate. The sign of this coefficient and hence of the in-plane group velocity near cutoffs decides the existence or non-existence of the backward Lamb waves without a necessity to calculate the dispersion branches. A link between the near-cutoff dispersion of Lamb waves and the curvature of bulk-wave slowness curves in a sagittal plane is analyzed. It is established that a locally concave slowness curve of a bulk mode entails the backward Lamb waves at the onset of branches emerging from this bulk mode resonances of high enough order. A simple sufficient condition for no backward Lamb waves near the resonances associated with a convex slowness curve is also noted. Two special cases are discussed: the first involves the coupled resonances of degenerate bulk waves, and the second concerns quasi-degenerate resonances which give rise to pairs of dispersion branches with a quasilinear positive and negative onset. Occasions of the backward Lamb waves in isotropic plate materials are tabulated.     

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.     

Scattering of guided waves by defective adhesive bonds in multilayer anisotropic plates

We introduce an analytic-numerical method to simulate the interaction between ultrasonic guided waves and defective adhesive bonds in multilayer structures. We replace the thin adhesive layer by equivalent continuous distribution of normal and transversal springs and locally reduce the corresponding spring constants to model localized defects. We then formulate the resulting scattering problem as a linear least squares problem and solve it accordingly. The developed formulation is easy to implement and equally well suited to treating anisotropic as well as isotropic constituent layers. We illustrate the application of the proposed method through the simulation of ultrasound inspection of a three-layer isotropic plate and a sixteen-layer anisotropic plate used in the aeronautical industry, indicating in the simulations the guided modes that will most strongly interact with interfacial defects and computing the scattering resulting from the interaction of these modes with localized defects. We believe that the proposed method will serve both to aid in the design of interface inspections and as a basis for solving inverse scattering problems.     

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.     

Subinterface crack in an anisotropic piezoelectric bimaterial

In this paper, the problem of a subinterface crack in an anisotropic piezoelectric bimaterial is analyzed. A system of singular integral equations is formulated for general anisotropic piezoelectric bimaterial with kernel functions expressed in complex form. For commonly used transversely isotropic piezoelectric materials, the kernel functions are given in real forms. By considering special properties of one of the bimaterial, various real kernel functions for half-plane problems with mechanical traction-free or displacement-fixed boundary conditions combined with different electric boundary conditions are obtained. Investigations of half-plane piezoelectric solids show that, particularly for the mechanical traction-free problem, the evaluations of the mechanical stress intensity factors (electric displacement intensity factor) under mechanical loadings (electric displacement loading) for coupled mechanical and electric problems may be evaluated directly by considering the corresponding decoupled elastic (electric) problem irrespective of what electric boundary condition is applied on the boundary. However, for the piezoelectric bimaterial problem, purely elastic bimaterial analysis or purely electric bimaterial analysis is inadequate for the determination of the generalized stress intensity factors. Instead, both elastic and electric properties of the bimaterial’s constants should be simultaneously taken into account for better accuracy of the generalized stress intensity factors.     

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.