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Two-dimensional equations for flexural motions of a lithium niobate piezoelectric plate are derived from three-dimensional equations. The plate has a ferroelectric inversion layer where the piezoelectric constants reverse signs. The equations show an unconventional behavior that a uniform electric field along the plate thickness can produce bending. This offers many possibilities for new designs of devices. Waves in unbounded plates are examined for the accuracy of the equations. A piezoelectric energy harvester based on such a plate is analyzed as an example of the application of the equations derived in vibrations of finite plates. [ABSTRACT FROM AUTHOR]

We study thickness-extensional vibration frequencies and modes in a thin ZnO or AlN film on a silicon layer with a circular ring driving electrode. It is shown that the vibration tends to be trapped in the annularly electroded area and decays away from the electrode edges. The convexity of the vibration distribution near the film center can be adjusted through design, and can be made nearly uniform for mass sensor application. The theoretical analysis presented can be used to optimize the design of the device. [ABSTRACT FROM AUTHOR]

We propose using a circular driving electrode on a conventional thin film bulk acoustic wave resonator with a square piezoelectric film on a square ground electrode and a square dielectric layer. The circular driving electrode has the advantage of avoiding the electric field concentration at the corners of a square driving electrode and the related negative effects. A circular driving electrode is also perfectly consistent with the in-plane material isotropy of common thin film resonator materials such as AlN and ZnO. A theoretical analysis on the proposed resonator was performed to obtain the basic vibration characteristics including resonant frequencies and mode shapes. [ABSTRACT FROM AUTHOR]

An analysis was performed on the vibration of a rectangular contoured quartz plate resonator. The surface of the resonator has different curvatures in the two in-plane directions. The analysis was based on the equation by Tiersten and Smythe, which has variable coefficients. The power series method was used. Thickness-shear and thickness-twist vibration frequencies and modes were obtained. The effects of the curvatures of the resonator surface were examined. Two types of boundary conditions were considered from which the proper size of the resonator was determined. The results are useful in the understanding of these resonators and their design. [ABSTRACT FROM AUTHOR]

The propagation of shear-horizontal waves in a piezoelectric film of aluminum nitride on a silicon substrate is studied. Three different electrode configurations are considered for thin film acoustic wave resonator application. A theoretical analysis is performed. The equations of linear piezoelectricity and anisotropic elasticity are used for the film and the substrate, respectively. Real and imaginary dispersion curves as well as electromechanical mode shapes are obtained. The effects of electrode configuration on the distribution of the electromechanical fields and the dispersion curves of long thickness-twist waves as well as energy trapping are examined. [ABSTRACT FROM PUBLISHER]

We studied thickness-shear vibration frequencies and modes in an inverted-mesa AT-cut quartz plate piezoelectric resonator thinner in the center and thicker near the edges. It is electroded in the central part and unelectroded near the edges. A theoretical analysis was performed using the scalar differential equations by Stevens and Tiersten for thickness-shear vibrations of electroded and unelectroded quartz plates. Based on the variational formulation of the scalar differential equations established in a previous paper and the variation-based Ritz method with trigonometric functions as basis functions, free vibration resonant frequencies and the corresponding thickness-shear modes were obtained. It was found that the electrodes tend to trap the vibration in the central part of the resonator (energy trapping) but the curvature of the resonator surface has an opposite effect. The trapping is sensitive to the electrode thickness, the electrode length, and the curvature of the resonator surface. Hence accurate design is needed to achieve proper energy trapping in inverted-mesa resonators. [ABSTRACT FROM AUTHOR]

The effects of the thickness variation and the material property variation of thin-film piezoelectric actuators on the actuation shear stress when the actuators are attached to an elastic plate are studied. A system of 2D equations for the flexure and shear of an elastic plate with symmetric piezoelectric actuators on the plate surfaces is derived. The equations are reduced to the case of elementary flexure without shear as a special case. The effects of the actuator thickness variation and material property variation on the actuation stress are examined using the equations obtained. It is shown that the distribution of the actuation stress depends on the thickness and material property variations of the actuators, and that actuators with varying thickness or varying material properties can be used to make modal actuators for producing a particular deformation or exciting a particular vibration mode. [ABSTRACT FROM PUBLISHER]

Highlights: [•] Equations are derived for thickness-stretch waves in piezoelectric plates. [•] The waves are classified into two types with opposite convexities. [•] The equations are useful for analyzing thickness-stretch mode resonators. [ABSTRACT FROM AUTHOR]

For time-harmonic motions, we generalize a 2-D scalar differential equation derived previously by Tiersten for slowly-varying thickness-shear vibrations of AT-cut quartz resonators. The purpose of the generalization is to include the effects of surface acoustic impedance from, e.g., mass layers or fluids for sensor applications. In addition to the variation of fields along the plate thickness, which is considered in the usual 1-D acoustic wave sensor models, the equation obtained also describes in-plane variations of the fields, and therefore can be used to study the vibrations of finite plate sensors with edge effects. The equation is compared with the theory of piezoelectricity in the special cases of acoustic waves and pure thickness vibrations in unbounded plates. An example of a finite rectangular plate is also given. [ABSTRACT FROM PUBLISHER]

We derive two-dimensional equations for high-frequency vibrations of piezoelectric plates from a semi-mixed variational principle with the mechanical displacement vector, the electric potential, and the electric displacement vector as independent fields. This variational formulation allows independent expansions of the three fields into power series of the plate thickness coordinate. Similar to the shear correction factors used in Mindlin's equations for piezoelectric plates to adjust the thickness-shear frequencies predicted by the plate equations slightly so that they become the same as the exact frequencies from the three-dimensional equations, a charge correction factor is conveniently introduced in the plate equations in the present paper so that the inaccuracy of the plate equations in the literature in predicting the charge or current on the electrodes of an electroded plate is corrected. The final equations obtained are convenient and accurate to use for both electroded and unelectroded plates, and for calculating both the voltage and the charge on the electrodes at the plate surfaces in the case of an electroded plate. [ABSTRACT FROM AUTHOR]

We study the effects of the nonuniform thickness of a thin mass layer on a quartz crystal microbalance. A theoretical analysis is performed on thickness-shear vibration of an AT-cut quartz plate with a nonuniform mass layer. Mindlin's two-dimensional equation for thickness-shear vibration of a quartz plate is used. Free vibration frequencies and modes are obtained. The effects of the mass layer nonuniformity are examined. It is shown that resonant frequencies and energy trapping of thickness-shear modes are sensitive to mass layer nonuniformity. [ABSTRACT FROM PUBLISHER]

We perform a theoretical analysis on a ceramic plate piezoelectric transformer operating with thickness-twist modes. Mindlin's first order theory of piezoelectric plates is employed. Forced vibration solution is obtained. Transforming ratio and vibration mode shapes are calculated. The effects of plate thickness, electrode dimension and inertia are examined. The results are useful to the understanding of the operating principle and the design optimization of the transformer. [ABSTRACT FROM AUTHOR]

Abstract: We study thickness–shear and thickness–twist vibrations of a finite, monolithic, AT-cut quartz plate crystal filter with two pairs of electrodes. The equations of anisotropic elasticity are used with the omission of the small elastic constant c 56. An analytical solution is obtained using Fourier series from which the resonant frequencies, mode shapes, and the vibration confinement due to the electrode inertia are calculated and examined. [Copyright &y& Elsevier]

Abstract: We study the effects of electrodes of nonuniform thickness on thickness-shear vibration frequencies and mode shapes of quartz resonators. This paper extends a previous paper from electrodes of stepped thickness to continuously varying thickness. Numerical results for electrodes of linearly varying thickness are presented. The results show that strong energy trapping can be achieved and adjusted using electrodes with variable thickness. [Copyright &y& Elsevier]

Abstract: We analyze the effect of mass layer stiffness on thickness-twist waves propagating in a rotated Y-cut quartz crystal plate with thin mass layers on its surfaces. An equation that determines the dispersion relation of the waves is given and is solved numerically. Quantitative results of the effect of the mass layer stiffness on wave frequencies are presented. These results are important to the understanding and design of resonators and mass sensors. [Copyright &y& Elsevier]

Highlights • A systematic derivation is presented for imperfect interface conditions with coupled fields. • The derivation is from a unique angle providing deep insight into the interface conditions. • The derivation also shows the conditions and limitations of the interface conditions. Abstract We show systematically that when an interface between two materials is treated as a thin layer modelled by the first-order plate theory, the conventional mechanically, electrically and magnetically imperfect interface conditions can be derived from the plate theory. Specifically, the continuity of those components of the stress tensor, electric displacement vector and magnetic induction vector related to the normal of the interface are continuous at the interface as a consequence of the zero-order plate equations, but the displacement vector, electric potential and magnetic potential may have discontinuities across the interface as a consequence of the first-order plate equations. This procedure also shows the conditions or limitations of the conventional imperfect interface conditions. [ABSTRACT FROM AUTHOR]

We studied thickness-shear and thickness-twist vibrations of a monolithic, two-pole crystal filter made from a plate of AT-cut quartz. The scalar differential equations derived by Tiersten and Smythe for electroded and unelectroded quartz plates were employed which are valid for both the fundamental and the overtone modes. Exact solutions for the free vibration resonant frequencies and modes were obtained from the equations. For a structurally symmetric filter, the modes can be separated into symmetric and antisymmetric ones. Trapped modes with vibrations mainly under the electrodes were found. The effect of the distance between the two pairs of electrodes was examined. [ABSTRACT FROM AUTHOR]

Abstract: We study coupled face-shear (FS) and thickness-twist (TT) motions of a piezoelectric plate of monoclinic crystals with mass layers on the central parts of the plate surfaces. The plate is driven by a lateral electric field. Mindlin’s first-order theory of piezoelectric plates is used. An analytical solution is obtained. Numerical results are presented for an AT-cut quartz plate, including the motional capacitance of the plate as a resonator and the vibration modes trapped under the mass layers in the central portion of the plate. The relationship between the dimension of the mass layers and the number of trapped modes is examined. [ABSTRACT FROM AUTHOR]

Abstract: We perform a theoretical analysis of thickness vibrations in piezoelectric plates of crystals with 6mm symmetry. The six-fold axis is tilted with respect to the plate surfaces. The major surfaces of the plate are covered with two layers of electrodes of different metals. The equations of linear piezoelectricity are used for the crystal plate. The electrodes are modeled by the equations of elasticity. Thickness vibrations frequencies and modes as well as impedance are calculated and examined. [Copyright &y& Elsevier]