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Thickness-twist waves in piezoelectric plates are widely used as the operating modes for acoustic wave resonators, filters, sensors, and other devices (Mindlin, 1965; Mindlin, 1967; Pearman, 1968; Bleustein, 1966; Bleustein, 1969; Yang et al., 2008a; Yang & Guo, 2006). Acoustic waves in these devices are driven by an alternating voltage applied to the electrodes deposited on the plates. Therefore there has been continuing research effort on the effect of electrodes (Ballato & Lukaszek, 1974; Kosinski, 2003; Wang & Shen, 2005; Yang et al., 2005). Recently, due to the need of device miniaturization, there has been growing research interest on electrode configurations. Electrodes of varying thickness have been used to adjust the vibration distribution in plates (Pao et al., 2007; Yang et al., 2007a; Wang et al., 2008). Electrode shape has also been analyzed for design optimization. In Yang et al. (2007b) it was shown that electrodes with corners cause field concentration and should be avoided in general. Optimal electrode size and shape were determined in Mindlin (1968) and Yang et al. (2008b). On the other hand, a vibrating elastic (or piezoelectric) body when put in contact with a viscous fluid changes its resonant frequencies due to the inertia and viscosity of the fluid. Equivalently, the speed of a propagating wave in a body in contact with a fluid is also affected by the fluid. This effect has been used to make various fluid sensors for measuring fluid viscosity or density (Kanazawa & Gordon, 1985; Josse et al., 1990; Reed et al., 2001; Kim et al., 1991; Vogt et al., 2004; Guo & Sun, 2008; Peng et al., 2006). More references can be found in a review article (Benes et al., 1995). For fluid sensor applications, vibration modes of a body without a normal displacement at its surface are of general interest. Thickness-shear and thickness-twist modes in a plate (Kanazawa & Gordon, 1985; Josse et al., 1990; Reed et al., 2001), torsional modes of a circular shaft (Kim et al., 1991; Vogt et al., 2004), and anti-plane surface waves (Guo & Sun, 2008; Peng et al., 2006) are modes with tangential surface displacements only and have been used for fluid sensor applications. To establish the relation between wave frequency and fluid density or viscosity, a coupled problem of fluid-structure interaction needs to be solved. This usually

This paper presents a stress function based iterative approach for predicting the free edge stresses in piezoelectric laminates upon polynomial assumption. The polynomial stress function based iterative approach is quite different from the traditional plate and shell theories, where the polynomial stress fields are adopted instead of displacement field functions. The stress boundary conditions are prescribed at the surfaces and applied at the free edges so that the stress components satisfy the boundary conditions automatically. The complementary virtual work is adopted to derive the governing equations resulting in a set of fourth order coupled differential equations. Some results are given to study the efficiency and accuracy of the proposed methodology. The proposed approach can be used as an efficient tool for analysis of free edge stresses in piezoelectric composite structures.

Purpose This paper aims to propose a simple but robust three-node triangular membrane element with rational drilling DOFs for efficiently analyzing plane problems. Design/methodology/approach This new element is developed within the general framework of unsymmetric FEM. The element test functions are determined by using a conforming displacement field which is slightly different with the classical Allman’s interpolations, while a self-equilibrated stress field formulated based on the analytical airy stress solutions is adopted as the trial functions. To ensure the correctness between the drilling DOFs and the true rotations in elasticity, reasonable constraints are introduced through the penalty function method. Moreover, the special quadrature strategy is used for operating related integrations for future enrichment of element behavior. Findings Numerical benchmark tests reveal that this new triangular membrane element has exceptional prediction capabilities. In particular, this element can correctly reproduce a rigid body rotation motion and correctly undertake the external in-plane twisting moments; thus, it is a reasonable choice for being used to formulate flat shell elements or to be connected with other kind of elements with physical rotational DOFs. Originality/value This work provides a new approach for developing high-performance lower-order elements with simple formulations and good numerical accuracies.

Vibration frequencies and trapped modes for thickness-shear vibrations of infinite and finite partially electroded circular AT-cut quartz plates are obtained by solving the two-dimensional scalar differential equations derived by Tiersten and Smythe. The Mathieu and modified Mathieu equations are derived from the governing equation using coordinate transform and collocation method is used to deal with the boundary conditions. The current study provides a theoretical way for conducting the vibration analysis of circular quartz resonators.

Bleustein–Gulyaev (B–G) waves in a functionally graded transversely isotropic electro-magneto-elastic half-space, in which all parameters exponentially change along the depth direction, are investigated, and the dispersion equations with respect to the phase velocity for electromagnetically open and shorted conditions are obtained. The B–G waves are dispersive because of the inhomogeneity of the material, which is different from a pure substrate. The graded coefficient exhibits different effects on the B–G waves at different electromagnetic circumstances. With the intervention of the functionally graded material, the electro-magneto-mechanical coupling factor can be improved and the penetration depth of the B–G waves can be decreased. The results can be used in the design of high-performance surface acoustic wave devices.

SUMMARY The seismoacoustic scattering due to an irregular fluid–solid interface must be considered when we model the seismic wave propagation in oceanic regions or gulf areas. In this paper, an efficient approach will be presented to treat this kind of problem. The approach can be viewed as an extension of the method originally developed for seismogram synthesis in multilayered solid media with irregular interfaces. In this method, we use the traditional boundary element method to discretize the boundary integral equation in each layer; then define the global matrix propagators by the boundary and continuity conditions in such way that they propagate the information of the element displacements and tractions ‘downwards’ for layers above the source while ‘upwards’ for layers below the source, finally solve the problem in the source layer. The main idea of the method is to use the global matrix propagators to suppress the tremendous increase in the memory requirement appearing in the traditional boundary element method when modelling wave propagation in multilayered media. As for the fluid–solid interface, the direct application of the above method is difficult since the global matrix propagators in fluid layers are much different from those defined in solid layers. By using the pressure as the variable inside the fluid layer, we can treat the acoustic wave propagation as a Helmoltz problem. The global matrix propagators can then be extended into the same size as those defined for solid layers by using the standard boundary conditions at the fluid–solid interface (i.e. normal traction continuity, zero tangential traction and normal displacement continuity). By the extended global matrix propagators we can thus propagate the information of the acoustic wave into the elastic wavefield and further obtain the results of the elastic wave propagation in arbitrary solid layers. To demonstrate the validity and feasibility of our method, we should compare our numerical results with the existing solutions. For problems of irregularly layered structures, however, we do not have exact (analytic) solutions. Therefore, it is important to compare the results calculated by completely different numerical methods to ensure validity. For such purpose, we calculate the cases of a plane P wave vertically incident onto two basin-like fluid–solid structures and an SV wave source located below a basin-like fluid–solid interface, of which the synthetic seismograms are accessible from the existing publications. Our results show almost complete agreement with those calculated by the reflection/transmission matrix method and those calculated by the discrete wavenumber method. Second, we calculate the synthetic time domain waveforms for a model with and without a basin-like fluid layer. Comparison observation clearly shows the effects of the fluid layer on the seismic ground motion at land in which seismologists or geophysicists may be of great and practical interests. Furthermore, we take into account the case when an explosive source is located in a fluid layer and illustrate that the method can simulate the water reverberation in the sea. That makes significant sense to deep ocean acoustic experiments.

The propagation of thickness-twist waves in an inhomogeneous piezoelectric plate with an imperfectly bonded interface is investigated. Based on the spring-type relation, the imperfectly bonded interface is dealt with, and the exact solution is obtained from the equations of the linear theory of piezoelectricity. The amplitude ratio between the incident wave and the reflected wave, the displacement component and the stress component are all obtained and plotted. Both theoretical analysis and numerical examples show that the effect of the mechanical imperfection on the wave propagation is more evident than that of the electrical imperfection. When the incident wave frequency and the mechanical imperfect parameter meet some particular relation, no reflected waves can appear in the piezoelectric plate. The results are of fundamental importance to the design of resonators and other devices when imperfect joints are considered.

An analytical approach is used to investigate the existence and propagation behavior of surface electro-elastic Love waves in an ideally layered structure consisting of a functionally graded piezoelectric substrate and a dielectric layer. The piezoelectric substrate is polarized in the direction perpendicular to the wave propagation plane and its material parameters change continuously along the thickness direction. The dispersion equations for the existence of surface Love waves with respect to phase velocity are obtained for electrically open and shorted cases, respectively. A detailed investigation of the effects of material gradient on dispersion curve, phase velocity, group velocity, and electromechanical coupling factor is carried out. Numerical results show that material gradient significantly affects the fundamental mode of Love waves but has only negligible effects on the high order modes. Large electromechanical coupling factors could be achieved by an appropriate adjustment of gradient coeffici...

An analytical approach is used to investigate the effects of covering layer thickness on the propagation behavior of Love waves in functionally graded piezoelectric materials (FGPMs) covered with a dielectric layer. The piezoelectric substrate is polarized in the direction perpendicular to the wave propagation plane, and its material parameters change continuously along the thickness direction. The dispersion equations for the existence of Love waves with respect to phase velocity are obtained for electrically open and shorted cases, respectively. A detailed investigation of the effects of the covering dielectric layer thickness on dispersion curve, phase velocity, group velocity, and electromechanical coupling factor is carried out. Numerical results show that for a given FGPM, the covering dielectric layer thickness affects significantly the fundamental mode of Love waves but has only negligible effects on the high-order modes. The changes in phase velocity, group velocity, and electromechanical coupling factor due to the change of gradient coefficient of FGPMs could be approached approximately by changing the thickness of the covering dielectric layer, which imply a potential factor for designing new-type surface wave devices with FGPMs.

In this paper, we study the propagation of electro-elastic Love waves in a piezoelectric layered solid consisting of a transversely isotropic piezoelectric ceramic film deposited on an isotropic metal substrate. Dispersion relations are obtained in a very concise mathematical form for both electrically open and shorted circuits. Numerical example is given for a PZT-4/steel system. An interesting phenomenon on the fundamental mode of the Love waves in the case of electrically shorted circuit is realized and validated through the discussion on the limit values of phase velocity using the obtained dispersion relations. This validation appears new and is significant to understand the Love wave modes themselves and to the design of acoustic wave devices.

The existence and propagation of transverse surface waves in piezoelectric coupled solids is investigated, in which perfect bonding between a metal/dielectric substrate and a piezoelectric layer of finite-thickness is assumed. Dispersion equations relating phase velocity to material constants for the existence of various modes are obtained in a simple mathematical form for a piezoelectric material of class 6 mm. It is discovered and proved by numerical examples in this paper that a novel Bleustein–Gulyaev (B–G) type of transverse surface wave can exist in such piezoelectric coupled solid media when the bulk-shear-wave velocity in the substrate is less than that in the piezoelectric layer but greater than the corresponding B–G wave velocity in the same piezoelectric material with an electroded surface. Such a wave does not exist in such layered structures in the absence of piezoelectricity. The mode shapes for displacement and electric potential in the piezoelectric layer are obtained and discussed theoretically. The study extends the regime of transverse surface waves and may lead to potential applications to surface acoustic wave devices.

We analyze the propagation of antiplane or shear-horizontal waves near the interface between two half-spaces of piezoelectric ceramics. The material properties vary in the direction perpendicular to the interface. Both electroded and unelectroded interfaces are considered. Transcendental equations that determine the dispersion relations of the waves are obtained. They reduce to a few known results in the literature as special cases. Different from similar waves in homogeneous materials, the waves obtained are dispersive. The equations for the dispersion relations are solved numerically. It is found that the wave speeds are sensitive to the variation of material properties. This suggests the possibility of manipulating the wave propagation behavior through proper design of materials.

We study theoretically the propagation of thickness-twist waves in an unbounded piezoelectric ceramic plate with unattached electrodes and viscous fluids between the plate surfaces and the electrodes. Based on the theories of piezoelectricity and viscous fluids, an equation that determines the dispersion relations of the waves is obtained, showing the dependence of the phase velocity on material and geometric parameters. Due to the viscosity of the fluid, the dispersion relations are complex in general, representing damped waves with attenuation. The dispersion relations obtained can reduce to the results of a few special cases with known results. The results of the present paper are useful for developing and designing fluid sensors for measuring fluid viscosity or density.

The propagation of transverse surface waves in a functionally graded material carrying a piezoelectric layer is investigated analytically. The material properties in the substrate change gradually with the depth coordinate. We here assume that all material properties of the substrate have the same exponential function distribution along the depth direction. The dispersion equations relating phase velocity to the material gradient in the substrate for the existence of the waves are obtained in a simple mathematic form for class 6mm piezoelectric materials. It is demonstrated that the material gradient in the elastic substrate significantly affects the phase velocity and cut-off frequency of long waves but has only negligible effects on short waves. The effects of the material gradient on the penetration depth and electromechanical coupling factor, which are two parameters of practical interest, are also calculated and plotted. The significant influence of the material gradient on the wave propagation behavior provides a potential factor for designing acoustic wave devices.

The existence and propagation behavior of transverse surface waves in a layered structure concerning a piezoelectric substrate and a gradient metal layer are theoretically investigated in this paper. The Wentzel–Kramers–Brillouin (WKB) method is applied to obtain the analytical solutions in the gradient metal layer. The dispersion equation for transverse surface waves in such structure is obtained in a quite simple mathematical form, where the material gradient of the metal layer assumes arbitrary functions. Effects of material gradient on three types of dispersion behavior are discussed in detail based on a proper classification. Numerical results show that the material gradient in the metal layer evidently affects the fundamental mode shape of the transverse surface waves but has negligible effects on the higher order modes.

The propagation behavior of Love waves in a functionally graded material layered non-piezoelectric half-space with initial stress is taken into account. The Wentzel–Kramers–Brillouin (WKB) technique is adopted for the theoretical derivations. The analytical solutions are obtained for the dispersion relations and the distributions of the mechanical displacement and stress along the thickness direction in the layered structure. First, these solutions are used to study the effects of the initial stress on the dispersion relations and the group and phase velocities, then the influences of the initial stress on the distributions of the mechanical displacement and shear stresses along the thickness direction are discussed in detail. Numerical results obtained indicate that the phase velocity of the Love waves increases with the increase in the magnitude of the initial tensile stress, while decreases with the increase in the magnitude of the initial compression stress. The effects on the dispersion relations of the Love wave propagation are negligible as the magnitudes of the initial stress are less than 100 MPa. Some other results are obtained for the distributions of field quantities along thickness direction. The results obtained are not only meaningful for the design of functionally graded structures with high performance but also effective for the evaluation of residual stress distribution in the layered structures.

The existence and propagation behavior of Love waves in a functionally graded material (FGM) layered structure are theoretically investigated in this paper based on the three-dimensional equations of linear electricity. The Wentzel–Kramers–Brillouin (WKB) method is applied to obtain the analytical solutions in the FGM layer. The dispersion equation for a Love surface wave in this kind of structure is obtained in a simple mathematical form, where the material property variation of the FGM layer is arbitrary. First, the solution is used to study the effect of the gradient coefficients on the dispersion curves and the phase velocities of Love waves. Then, the influence of gradient coefficients on the stress and displacement fields is discussed in detail. The reported results are important in the design of surface acoustic wave (SAW) devices with high performance.

In this paper, we present results of full band structures for two-dimensional piezoelectric phononic crystals with {1–3} connectivity family. The plane-wave-expansion (PWE) method is applied to the theoretical derivation of secular equations of the two polarization modes: a transverse polarization mode and a mixed (longitudinal-transverse) polarization mode. And the band structures of the two modes for both the case of piezoelectric rods embedded in a polymer matrix and the case of polymer rods embedded in a piezoelectric matrix are calculated for two different cross-sections of the rods, i.e., circular and square, considering the practical fabrication of phononic crystals. We reveal the existence of several very large complete band gaps in a material of practical interest such as PZT rods reinforced polythene composite. The effects of shapes and filling fraction of the rods on band gaps are discussed in detail. The existence of these gaps in relation to the physical parameters of the constituent materials involved is studied. Understanding the band structures of piezoelectric phononic crystals can give some information for improvements in the design of acoustic transducers.

The propagation behavior of Love waves in a functionally graded material layered half-space with initial stress is taken into account. The Wentzel-Kramers-Brillouin (WKB) asymptotic technique is adopted for the theoretical derivations. The analytical solutions are obtained for the dispersion relations and the distributions of mechanical displacement and stress along thickness direction in the layered structure. Firstly, these solutions are used to study effects of the initial stress on the dispersion relations and phase velocities, then influences of the initial stress on the distributions of mechanical displacement and shear stresses along thickness direction are discussed in detail. Numerical results obtained indicate that the phase velocity of Love wave increases with the increase of the magnitude of the initial tensile stress, while decreases with the increase of the magnitude of the initial compression stress. The effects on the dispersion relations of the Love wave propagation are negligible as the magnitudes of the initial stress are less than 100MPa. Some other results are shown for distributions of field quantities along thickness direction. The results obtained are not only meaningful for the design of functionally graded structures with high performance but also effective for the evaluation of residual stress distribution in the layered structures.

The propagation behavior of transverse surface waves (Love waves) in a piezoelectric half space of polarized ceramics carrying a functionally graded material layer is studied from the three-dimensional equations of linear piezoelectricity. The Wentzel–Kramers–Brillouin (WKB) asymptotic technique is adopted for the theoretical derivations of analytical solutions in the functionally graded layer. The dispersion relations of Love wave in the structure are obtained for both electrically open and shorted cases. Firstly, these solutions are used to study effect of the gradient coefficients on the dispersive relations and phase velocities of Love wave propagation. Then influence of the gradient coefficients on the electromechanical coupling factor is discussed in detail. The results reported are meaningful for the design of surface acoustic wave (SAW) devices with high performance.

The diffraction of Lamb waves by a finite delamination situated on a random plane parallel to the symmetric plane of a laminated plate is taken into account. Two imaginary planes are introduced to solve the problem by adopting the method of mode matching. By taking an appropriate finite number of terms of the infinite expansion series and some selected points on the two imaginary planes through convergence and precision tests, a matrix equation is obtained to evaluate the expansion coefficients numerically. Reflection coefficients versus the normalized length a/h and the relative location h1/h of the delamination are calculated in the low-frequency domain, the relative errors are found to be less than 1%. Results obtained indicate that the theory developed in this paper is meaningful for the detection of both the size and the location of a delamination in a laminated plate by cooperating with experimental techniques for the non-destructive evaluation (NDE) technology.

This paper analyses free vibration frequencies and modes for thickness-shear and thickness-twist vibrations of centrally partially electroded circular AT-cut quartz plate by using 3-D finite element models of commercial package ANSYS. The analysis has been done with the 3-D Finite Element Analysis (FEA) for displacements and vibration frequency at the thickness-shear mode, which is important in the design of quartz crystal resonators. Trapped modes are found with vibrations mainly confined under the circular electrodes. The 3-D FEA solutions of displacement distribution can be used in the optimal selection of the structural parameters.

The wave function expansion method is engaged for the theoretical derivations to study the effect of material parameters perturbations on the resonance acoustic scattering behavior of 1-3 piezoelectric composites. Numerical examples are provided to verify the effectiveness of the analysis. Results obtained are meaningful for the non-destructive evaluation of 1-3 piezoelectric composites.

The scattering behavior of P-waves in piezoelectric composites with 1–3 connectivity is studied. The method of wave function expansion is adopted for the theoretical derivations. Analytical expressions are obtained for the distributions of mechanical displacement in z -direction along the circumferences of piezoelectric cylinders. These solutions are used to study the influence of each element of the stiffness matrix and the piezoelectric matrix on the various resonant modes of vibration. Numerical results obtained indicate that perturbations of the elements c 44 and e 15 significantly affect resonant frequencies and amplitudes, perturbations of c 11 and c 12 have pronounced effects on resonant modes of high frequencies also. However, the resonant modes are not so sensitive to the perturbations of c 13 , e 31 and e 33 . The dynamic characteristics of 1–3 connectivity piezoelectric composites exposed here are meaningful for the design and manufacture of sensor/actuator elements by this kind of composites as well as the on-line health monitoring of the mechanical properties variations of the composites itself.

For the piezoelectric layer/substrate structure with slowly varying inhomogeneous initial stress in the layer, the influence of the initial stress on the properties of Love wave propagation is studied. The Wentzel?Kramers?Brillouin?(WKB) approximate approach is adopted for analytical derivations. Numerical results obtained for the BaTiO3 layer/borosilicate glass substrate combination system indicate that, under certain conditions, initial stress in the layer can markedly affect the propagation of the Love wave. The analysis is meaningful for the theoretical analysis and engineering applications of Love waves.

Following the advances in structural applications, composite structures are being used commonly in transducer applications to improve acoustic, mechanical and electrical performance of piezoelectric devices. Functional composite transducers for sensors and actuators generally consist of ceramics and polymers, the disadvantage of the brittleness nature of the piezoelectric ceramics can be overcome and the structures especially good for sensing can be allowed for building up. Propagation behavior of horizontally polarized shear waves (SH-waves) in piezoelectric ceramic-polymer composites with 2-2 connectivity is taken into account. The multilayer structures are consisted of piezoelectric thin films bonded perfectly with polymeric thin films alternately. The phase velocity equations of SH-waves propagation in the piezoelectric ceramic-polymer composites with 2-2 connectivity are obtained for the cases of wave propagation in the direction perpendicular to the layering and along the layering, respectively. Filter effect of this kind of structure and the effect of volume fraction and shear modulus ratio of piezoelectric layer to polymer layer on the phase velocity are discussed in detail, respectively. One practical combination of piezoelectric thin film-polymer thin film multilayer system is chosen to carry out the numerical simulation, some basic properties of SH-waves propagation in above multilayered structures are revealed.

Propagation behavior of horizontally polarized shear waves (SH-waves) in a periodic piezoelectric–polymeric layered structure is taken into account. The layered structures are consisted of piezoelectric thin films bonded perfectly with polymeric thin films alternately. The phase velocity equations of SH-waves propagation in the periodic layered piezoelectric structure are obtained for the cases of wave propagation in the direction normal to the interface and along the interface, respectively. Filter effect of this kind of structure and the effects of volume fraction and shear modulus ratio of piezoelectric layer to polymeric layer on the phase velocity are discussed in detail, respectively. One set of piezoelectric thin film––polymeric thin film multilayer system (PZT-5H piezoelectric ceramics––polythene) is chosen to show the numerical simulation, basic properties of SH-waves propagation in this particular structure are revealed.

In this paper, we analytically study the dispersion behavior of transverse surface waves in a piezoelectric coupled solid consisting of a transversely isotropic piezoelectric ceramic layer and an isotropic metal or dielectric substrate. This study is a revisit to the stiffened Love wave propagation done previously. Closed-form dispersion equations are obtained in a very simple mathematical form for both electrically open and shorted cases. From the viewpoint of physical situation, two transverse surface waves (i.e., the stiffened Love wave and the FDLW-type wave) are separately found in a PZT-4/steel system and a PZT-4/zinc system. All the observed dispersion curves are theoretically validated through the discussion on the limit values of phase velocity using the obtained dispersion equations. Those validation and discussion give rise to a deeper understanding on the existence of transverse surface waves in such piezoelectric coupled structures. The results can be used as a benchmark for the study of the wave propagation in the piezoelectric coupled structures and are significant in the design of wave propagation in the piezoelectric coupled structures as well.

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.

The propagation of the transverse surface waves in an unbounded piezoelectric half-space with a viscous liquid layer between the half-space surface and an unattached electrode is analyzed. An exact dispersion relation is obtained from the equations of the linear theory of piezoelectricity. Results show that the wave speed is sensitive to the viscous coefficient, the mass density and the dielectric permittivity of the fluid layer. Especially, the phase velocity changes linearly with the increasing mass density when other parameters keep constant, which can be used to manipulate the behavior of the waves and has implications in acoustic wave devices.

Theory of the propagation of transverse surface waves in piezoelectric ceramic/metal coupled media is developed. Dispersion equations relating phase velocity to material constants for the existence of various modes are obtained in simple mathematic form for a piezoelectric material of class 6mm. Piezoelectricity allows a nonleaky but dispersive wave of one or two modes to exist under conditions when the bulk-shear-wave velocity in the layer is greater than that in the substrate. The study extends the regime of transverse surface waves and may lead to potential applications to acoustic wave devices.

In this paper we analyze the existence of complete band gaps in periodic binary two-dimensional piezoelectric phononic crystals with {1-3} connectivity family from a point view of connectivity. For this structure and no wave-vector components parallel to the cylinders, there are two independent modes of vibration. One of them is the transverse polarization mode (Z mode) with the elastic displacement vector parallel to the cylinders. And the other one is the longitudinal-transverse polarization mode (XY mode) with the elastic displacement vector perpendicular to the cylinders. The plane-wave-expansion (PWE) method is applied to the theoretical derivation of secular equations of the two polarization modes. Band structures for the two modes are calculated to look for complete band gaps in piezoelectric phononic crystals with both 1-3 connectivity and 3-1 connectivity, which will be used to analyze the effect of connectivity on the existence of band gaps in piezoelectric phonic crystals. Numerical results reveal that the strong difference of physical properties between the constituents in piezoelectric phononic crystals can't dominate the existence of complete band gaps and the connectivity of the constituents plays an important role in the existence mechanism.

We analyze the propagation of thickness-twist waves in an unbounded piezoelectric ceramic plate with air gaps between the plate surfaces and two electrodes. These waves are also called anti-plane or shear-horizontal waves with one displacement component only. An exact solution is obtained from the equations of the linear theory of piezoelectricity. Dispersion relations of the waves are obtained and plotted. Results show that the wave frequency or speed is sensitive to the air gap thickness. This effect can be used to manipulate the behavior of the waves and has implications in acoustic wave devices.

The effect of initial stress on the propagation behavior of Love waves in a piezoelectric half-space of polarized ceramics carrying a functionally graded material (FGM) layer is analytically investigated in this paper from the three-dimensional equations of linear piezoelectricity. The analytical solutions are obtained for the dispersion relations of Love wave propagating in this kind of structure with initial stress for both electrical open case and electrical short case, respectively. One numerical example is given to graphically illustrate the effect of initial stress on dispersive curve, phase velocity and electromechanical coupling factor of the Love wave propagation. The results reported here are meaningful for the design of surface acoustic wave (SAW) devices with high performance.

The existence and propagation of Bleustein-Gulyaev (B-G) waves in a functionally graded piezoelectric substrate with exponential variation is studied by analytical technique. The dispersion equations for the existence of the B-G waves with respect to phase velocity are obtained for both electrically open and short conditions. A detailed investigation of the effect of the gradient coefficient on dispersion relation, phase velocity, electromechanical coupling factor is carried out. It is found by numerical examples that adjusting gradient coefficient makes the electromechanical coupling factor of the B-G waves achieve quite high values at some appropriate wave number. Because of the negligible initial stress in functionally graded piezoelectric materials, this model could serve as an excellent substitute for the typical layered piezoelectric structures used in surface acoustic wave (SAW) devices, which provides with a theoretical foundation for designing SAW devices with high performance.

From a practical point of view, a complete band gap can be engineered to provide a vibration insulation environment for high-precision mechanical systems in a given frequency range. Understanding the band structure of piezoelectric phononic crystals can lead to improvements in the design of high performance transducers. The band structures for the transverse mode of 2D phononic crystals consisting of piezoelectric cylinders distributed periodically in a polymer matrix (1-3 connectivity), and vice versa (3-1 connectivity) are investigated in this paper, respectively. We give a brief derivation of the secular equation for the transverse vibration mode (Z mode) in which the mechanical displacements and the cylinders are parallel and perpendicular to Bloch wave vectors. Band structures are calculated to find the band gaps for both types of piezoelectric phononic crystals, which will be used to analyze the effect of connectivity of piezoelectric phonic crystals on the existence of band gaps. Numerical results reveal that the strong difference of physical properties between the constituents in piezoelectric phononic crystals can't dominate the existence of band gaps and the connectivity of the constituents plays an important role in the mechanism. Finally the influences of cross-sectional shape and filling fraction of filling cylinders upon the existence of band gaps are studied as well.

As to an ideally layered structure with a functionally graded piezoelectric substrate and a hard dielectric layer, the existence and propagation behavior of transverse surface waves is studied by analytical technique. The dispersion equations for the existence of the transverse surface waves with respect to phase velocity are obtained for electrically open and short circuit conditions, respectively. A detailed investigation of the effect of gradient coefficient on dispersion relation, electromechanical coupling factor is carried out. It is found by numerical examples that adjusting gradient coefficient makes the electromechanical coupling factor of the transverse surface waves achieve quite high values at some appropriate ratio values of the layer thickness to the wavelength.