Piezoelectric Rectangular Plate Research Articles

Calculation of the Bottom Signal of a Direct Transducer with a Rectangular Piezoelectric Plate

The dependence of the bottom signal of a direct transducer with a rectangular piezoelectric plate on the distance to a reflective planar plate is calculated using a two-dimensional Fourier transform. The calculations for piezoelectric plates with different aspect ratios are made using numeric integration. Results for rectangular and circular piezoelectric plates are compared.

Exact three-dimensional solutions of laminated orthotropic piezoelectric rectangular plates featuring interlaminar bonding imperfections modeled by a general spring layer

The bending and free vibration of an imperfectly bonded orthotropic piezoelectric rectangular laminates are investigated using a three-dimensional state-space approach. The plate is assumed to have simple supports only, which enables us to obtain a solution in a completely exact form. A general spring layer is adopted to model the bonding imperfections. The laminated plate that is in a state of cylindrical bending is also considered as a particular case. Numerical results are presented and some particular issues are discussed.

Transient phenomenon of longitudinal flexural coupled vibrations in a small rectangular piezoelectric ceramic plate (8 mm×2.16 mm×1 mm)

The coupling between two vibration modes is usually fixed when the working frequency is determined. However, in this letter, we report a transient coupled vibration phenomenon occurring between second bending and first longitudinal resonant frequencies in a small rectangular piezoelectric ceramic plate (8 mm×2.16 mm×1 mm). At some frequencies, the transient coupled vibration amplitude may increase to a certain level, and at other frequencies, it decreases its vibration amplitude. These experimental results may be helpful to understand the real essence of piezoelectric phenomenon in piezoelectric ceramics and to find applications for small rectangular piezoelectric ceramic plates.

A `Center-Wobbling' Ultrasonic Rotary Motor Using a Metal Tube-Piezoelectric Plate Composite Stator

This paper demonstrates a new type of compact ultrasonic motor that operates using a wobbling mode of motion. The motor was driven by a piezoelectric composite stator that consisted of a hollow metal cylinder whose outside surface was flattened on two sides at 90° to each other, upon which two rectangular piezoelectric plates were bonded. A wobbling motion was generated at both ends and at the center of the stator upon application of a sinusoidal voltage to each piezoelectric plate (which were phase shifted by 90° with each other). Results showed that the flexural displacement at the stator's center was ∼ 4 × that at its ends. Consequently, the stator could drive a rotor using a center wobbling motion. Our prototype motor had a significantly higher driving force than conventional end driven stators. The prototype was 4.7 mm in diameter and 20 mm in length, having a rotor 20 mm in diameter. The prototype operated at 46 kHz, had a maximum torque output of ∼ 50 mNm, and had a no-load rotational speed of 70 rpm in both directions. The prototype was also found to be suitable for precision actuation applications.

On free vibration of a functionally graded piezoelectric rectangular plate

On the basis of three-dimensional theory equations of transversely isotropic piezoelasticity, two independent state equations with variable coefficients are derived. To this end, separation formulae for displacements and shear stresses are employed. A laminated approximation is used to transform the state equations to the ones with constant coefficients in each layer. The free vibration problem of a piezoelectric rectangular plate with a functionally graded property is then investigated. Discussion on the boundary conditions is presented.

A piezoelectric motor using two orthogonal bending modes of a hollow cylinder.

This paper proposes a compact ultrasonic motor with low manufacturing costs, a simpler driving circuit, and scalability. The stator of the motor presented in this paper consists of a hollow metal cylinder, whose outside surface was flattened on two sides at 90 degrees to each other, on which two rectangular piezoelectric plates were bonded. Because the cylinder has a partially square/partially circular outside surface, the stator has two degenerated bending modes that are orthogonal to each other. A wobbling motion is generated on the cylinder when only one piezoelectric plate is excited at a frequency between the two orthogonal bending modes. A rod through a pair of ferrules was used as the rotor of this motor. The prototype motor, whose stator was 2.4 mm in diameter and 10 mm in length, operated at 69.5 kHz, was experimentally characterized, and a maximum torque of 1.8 mNm was obtained.

Piezoelectric inverter using thin plate transformer

In order to apply a piezoelectric transformer to back lighting fluorescence lamp in a liquid crystal display, asymmetric extension vibration mode of a piezoelectric rectangular plate has been investigated with special reference to the power transfer efficiency upon electrically loaded by the fluorescence lamp. In spite of a simple and thin monolithic structure, the optimum transformer, 21.3 × 11 × 0.5 mm in size, indicated 96% power efficiency as well as up to 30 step-up ratio which corresponds to more than 4 times that of the conventional Rosen-type transformer. The transformer has been successfully incorporated into a small size inverter unit together with a newly developed IC element for controlling frequency to the resonance, with less than 2.2 mm total thickness.

Dynamic electromechanical response of piezoelectric plates as sensors or actuators

This study presents a simple and accurate approach to examine the dynamic electromechanical responses of piezoelectric actuators or sensors, which are modeled as a piezoelectric rectangular plate. Based on the three-dimensional linear piezoelectricity, the fundamental unknowns such as the displacements and the electric potential are assumed to be expandable through the plate thickness coordinate. The dynamic electromechanical responses of the plate are expressed in terms of Fourier coefficients. When the boundary conditions and electromechanical inputs are specified, the unknown Fourier coefficients can be determined explicitly. In terms of analyzing a vibrating PIC-151 piezoelectric plate, numerical results of the proposed formulation correlate well with results in previous literature regarding frequencies. Analysis results also indicate that the plate size, thickness, and electroelastic constants influence dynamic response.

Three-dimensional asymptotic approach to inhomogeneous and laminated piezoelectric plates

An asymptotic theory is developed for anisotropic inhomogeneous and laminated piezoelectric plates on the basis of three-dimensional linear piezoelectricity. The inhomogeneity is assumed in the thickness direction and includes the important piezoelectric laminates as a special case. Through asymptotic expansions, the resulting two-dimensional differential equations are of the same form for each order, with different nonhomogeneous terms being determined systematically by preceding-order solutions. The governing equations of the leading-order, when degenerated to pure elasticity, are shown to be the same as those for equivalent classical thin elastic plates. The proposed methodology is illustrated by considering a rectangular piezoelectric plate subject to both mechanical and electric loadings with its edges simply supported and grounded. A three-dimensional solution for the fully electromechanically coupled problem is obtained by successively solving the two-dimensional field equations from the leading order to higher orders. Excellent agreement is observed with established results and new results are presented, from which significant physical insights are discussed.

Three-Dimensional Analytical Solution for Hybrid Multilayered Piezoelectric Plates

Analytical solutions for the static three-dimensional deformations of multilayered piezoelectric rectangular plates are obtained by using the Eshelby-Stroh formalism. The laminated plate consists of homogeneous elastic or piezoelectric laminae of arbitrary thicknesses. The equations of static, linear, piezoelectricity are exactly satisfied at every point in the body. The analytical solution is in terms of an infinite series; the continuity conditions at the interfaces and boundary conditions at the edges are used to determine the coefficients. The formulation admits different boundary conditions at the edges and is applicable to thick and thin laminated plates. Results are presented for thick piezoelectric plates with two opposite edges simply supported and the other two subjected to various boundary conditions. [S0021-8936(00)01803-1]

Alternately poled piezoelectric transformers using rectangular ceramic plates

In order to apply a piezoelectric transformer to an LCD backlight inverter, piezoelectric transformers are investigated [1, 2]. The load is a cold cathode fluorescent lamp (CCFL), whose impedance is low, about 100 kΩ. But the step-up ratio of the conventional Rosen-type piezoelectric transformer is small and inadequate for this application. We have developed a new piezoelectric transformer structure which has an alternately poled structure in a rectangular single-layer piezoelectric ceramic plate. Its step-up ratio is twice that of the Rosen-type transformer. Two types of samples were fabricated and analyzed using equivalent circuits, and the vibration characteristics and the electrical characteristics were evaluated. © 1998 Scripta Technica, 81(12): 29–36, 1998

An Exact Three-Dimensional Solution for Simply Supported Rectangular Piezoelectric Plates

An exact three-dimensional solution for the problem of a simply supported rectangular homogeneous piezoelectric plate is obtained, in the framework of the linear theory of piezoelectricity. The plate is made of a transversely isotropic material, is earthed on the lateral boundary, and is subjected to prescribed surface charge and tractions on the end faces. The limit of this solution as the plate thickness aspect ratio approaches zero is explicitly carried out. The analytical results obtained may constitute a reference case when developing or applying two-dimensional plate theories for the analysis of more complex piezoelectric problems. A numerical investigation in the case of a square uniformly loaded plate is also performed, in order to evaluate the influence of the thickness-to-side ratio on the three-dimensional solution of the plate problem.

Rectangular piezoelectric plate loaded on each face: a three-dimensional approach

This paper deals with the vibration mode determination of a rectangular plate loaded on each face. The resonant frequencies, the mechanical displacement and the electrical impedance of the plate are calculated using a three-dimensional approach based on the plane wave propagation along each coordinate axis. Then, the constitutive piezoelectric equations reduce and by introducing the relevant boundary conditions — that is, the stresses and particle displacements are continuous — a 7 × 7 linear matrix system is obtained. Solving this system yields the particle displacements in terms of the load impedances located on the sample faces. The electrical impedance of the sample can also be easily computed. It is shown that due to lateral coupling, there is no nodal plane inside the sample and the material losses used are less than those introduced with the one-dimensional approach.

Exact electroelastic analysis of piezoelectric laminae via state space approach

In an attempt to develop an efficient analytical approach for the electromechanical analysis of laminated piezoelectric structures, an exact transfer-matrix-based methodology is presented. The state space equations for a three-dimensional piezoelectric lamina are first derived by eliminating the in-plane stresses and electric displacements from the governing equations. The transfer matrix is rendered in block form by judiciously arranging the state variables and its property is then exploited to minimize the computational effort. Using the approach, an exact analysis of coupled electroelastic behavior of a rectangular piezoelectric plate of 6mm crystal symmetry subjected to a mechanical or electrical load is presented. A simply supported square plate made of barium titanate is analyzed as a numerical example and results are compared to those from the corresponding uncoupled analysis.

Operation Performance of Self-Oscillation Ultrasonic Vibrating Device for Liquid Atomization

An ultrasonic vibrating device, composed of a rectangular piezoelectric ceramic plate and a metal plate is described for liquid atomization. The resonance is used for the self-oscillation, which arises from the coupling between two vibration modes in the ceramic plate. The best operation occurs when one of the resonant frequencies of the vibrating device is equal to that of the piezoelectric ceramic plate without the metal plate. The ceramic plate has two electrodes on one of the two surfaces. A power feeding circuit is composed of the piezoelectric ceramic plate with three electrode terminals, which functions as a resonant element as well as a vibration source, and a power amplification transistor. The metal plate with minute holes functions effectively for liquid atomization.

Ultrasonic Rotary Motor Using Longitudinal and Bending Multimode Vibrator with Mode Coupling Caused by External Additional Asymmetry

The present paper deals with the ultrasonic rotary motor using a longitudinal and bending multimode vibrator constructed so that the mode coupling is caused by external additional asymmetry. It is well known that on a rectangular piezoelectric plate vibrator with its two corners cut diagonally or a parallelogram-shaped piezoelectric plate vibrator, the first longitudinal and second bending vibration modes are coupled under a certain dimensional condition. The motor mentioned above is to use this phenomenon; that is, a one-channel drive, reversible rotary motor can be achieved. From results of measurement and calculation of such a trial vibrator, it was found that there were two new resonance vibration modes in the neighborhood of degenerate resonance frequencies of original longitudinal and bending vibrations; hence, the directions of rotor revolution were different at both new modes when the mode-coupled vibrator was used to construct an ultrasonic rotary motor. The trial motor has proven that a simple ultrasonic motor could be easily constructed and it was suitable for light-load use because of its small contact area to the rotor.

Analysis of piezoelectric ceramic length‐expansion‐mode resonators using interdigital electrodes for both poling treatment and ac excitation

AbstractWhen interdigital electrodes set on the surface of a rectangular piezoelectric plate are used for poling and ac excitation, a length‐expansion‐mode resonance in the Lamé‐mode system alone is emphasized. However, this does not occur easily in conventional length‐expansion‐mode resonators having a uniform poling across the thickness and electrodes on the entire surface. The proposed method offers a resonator with very little spurious oscillation in this mode. To obtain a guideline for designing interdigital electrodes, the relationships between the width of electrodes, the period of electrodes and the capacitance ratios were analyzed theoretically in detail by using conformal mapping. The strength and direction of the dc electric field of this type of resonator at a poling state vary with positions, since the poling treatment is also carried out with interdigital electrodes, i.e., its dielectric constant, piezoelectric constant, and elastic constant vary significantly with positions. In this analysis, the distributions of these constants in various positions were considered by using the dependence of the poling electric field obtained experimentally, and they are not averaged. The results of the analysis agree well with the experimental values. The characteristics of two configurations were compared: a piezoelectric longitudinal coupling with electrodes set rectangularly to the direction of vibrations; and piezoelectric transverse coupling with electrodes set in parallel to it.

Application of the finite element method to the vibration analysis of a piezoelectric rectangular plate.

Application of the finite element method to the vibration analysis of a piezoelectric rectangular plate.

A note on pure bending of a piezoelectric rectangular plate

The problem of pure bending of a piezoelectric rectangular plate is considered in this paper by using the electromagnetic equations of Maxwell and equations of elasticity along with the constitutive equations of a piezoelectric quartz.

Contour extensional resonant properties of rectangular piezoelectric plates

This paper describes the results of an extensive theoretical study on the elastic contour extensional modes of planarly isotropic, rectangular piezoelectric plates. Results include numerical data on the resonant frequency, displacement pattern, and dynamic capacitance or dynamic coupling coefficient of the first fifty modes as a function of the length-to-width ratio. It is found that the resonances of this type of plate may be divided into four distinct and decoup1ed symmetry families. Calculated values for the resonant frequency vary in accuracy from about 0.2% for the first mode of each family to 1% for the twelfth mode. Dynamic coupling coefficient calculations are accurate to about 10%.