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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

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.

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.

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 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.

In this paper, we analyze the propagation of Bleustein–Gulyaev waves in an unbounded piezoelectric half-space loaded with a viscous liquid layer of finite thickness within the linear elastic theories. Exact solutions of the phase velocity equations are obtained in the cases of both electrically open circuit and short circuit by solving the equilibrium equations of piezoelectric materials and the diffusion equation of viscous liquid. A PZT-5H/Glycerin system is selected to perform the numerical calculation. The results show that the mass density and the viscous coefficient have different effects on the propagation attenuation and phase velocity under different electrical boundary conditions. In particular, the penetration depth of the waves is of the same order as the wavelength in the case of electrically short circuit. These effects can be used to manipulate the behavior of the waves and have implications in the application of acoustic wave devices.