Finite element analysis of cracks in piezoelectric materials taking into account the permittivity of the crack medium

In this paper, the influence of the electric boundary conditions on cracks in piezoelectric components shall be studied. Several electric boundary conditions have been proposed in the literature. Here, influence of the permeability of the crack on electric and mechanical fields near the crack tip is considered. Cracks of lower permeability lead to stronger electric singularities. Furthermore, the influence on the stress intensity factors and energy release rate will be discussed. Finally, an experiment with piezoceramic CT specimens, which was performed by Park and Sun, will be evaluated taking into account the permeability of the crack.     

Boundary element method taking into account external power source

A formulation for solving two-dimensional magnetic field problems making use of boundary integral equations to extend the application of T. Nakata and N. Takashi's (1982) finite-element method including the external power source has been developed. The development of the method of analysis has made it easy to calculate practical magnetic field problems using the boundary-element method. The same procedure of the boundary-element formulation may be applied to three-dimensional magnetic field problems by using this two-dimensional boundary-element method     

Finite element bending analysis of multilayer plates

The development of a general quadratic multilayer plate element is presented for the analysis of arbitrarily layered curved plates. In the formulation, each layer of the multilayer plate can have different orthotropic properties and can deform locally. Examples of bending problems are presented which demonstrate the applicability of the formulation.     

Finite element analysis of advanced multilayer capacitors

We establish a systematic methodology to design and analyse electromagnetic components such as advanced multilayer ceramic capacitors (MLCCs) using the finite element (FE) method. We employ a coupled formulation to compute the interaction between the electric and magnetic fields. Unlike a linear distribution of current assumed in the circuit model, an accurate electrostatic solution to model the entire advanced MLCCs (4 × 4 × 27 = 432 cells) is presented. The FE solution is used to compute the lumped parameters for a range of frequencies. These lumped parameters are then used to compute the parasitic elements of the MLCCs. We introduce two algorithms to efficiently analyse the behaviour of a capacitor with changing frequency. The lower frequency (much below the self‐resonant frequency of the capacitor) algorithm separates the effect of the electric and magnetic fields and reduces the computational effort required to solve the FE problem, whereas, the high‐frequency algorithm couples the effect between the electric and the magnetic fields. We use these algorithms in conjunction with a new multiple scale technique to effectively determine the small values of R, L and C in MLCCs. The formulation, the implementation, and the numerical results demonstrate the efficacy of the present FE formulation and establish a systematic methodology to design and analyse advanced electromagnetic components. Copyright © 2003 John Wiley & Sons, Ltd.     

Deflection characteristics of a trapezoidal multilayer in-plane bending piezoelectric actuator

A novel multilayer split-morph actuator has been designed and fabricated using the thick film screen-printing technology. Deflection characteristics of the split-morph actuator have been investigated by theoretical analysis and experimental measurement. The results indicate that the tip displacement is inversely proportional to the thickness of each piezoelectric layer, but is independent of the number of layers and the total thickness of the actuator. The displacement/voltage sensitivity of the trapezoidal actuator is larger than that of the rectangular design, assuming both have the same width of clamped end and the same thickness of the piezoelectric layers. The maximum displacement/voltage sensitivity of 0.157 micron/V was obtained with a split-morph actuator with 30-micron thick layers. The proposed actuator is a promising candidate for the secondary fine-tuning actuator of a dual stage head-positioning servo system in high density hard disk drives.     

Finite element analysis on piezoelectric ring transformer

The use of a piezoelectric ring as transformer is reported and studied in this paper. By using a concentric electrode pattern, a ring-shaped transformer can be designed to operate at its high order extensional modes. Lead zirconate titanate (PZT) ceramic rings with 12.7-mm outer diameter, 5.1-mm inner diameter and 1.2-mm thickness were used to fabricate the prototypes. Three-dimensional (3-D) finite element models are built to study and analyze the vibration characteristics of the piezoelectric transformers (PTs) using higher order modes (>3). The resonant frequencies, mean coupling effect, mode shapes, and other open-circuit characteristics are simulated and compared with experimental measurements. Prototypes of PTs using mode order three and four were fabricated and characterized. Good agreement can be obtained between experimental results and finite element model (FEM) simulations. The dimensions for the PTs using higher order symmetric extensional modes are optimized by FEM. To avoid mode coupling with the thickness mode, the ideal ring thickness has to be less than or equal to 0.6 mm. The ring PT offers advantages of simple structure and small size. It has a good potential in making low cost PT for low-voltage applications.     

Numerical analysis of ferroelectric/ferroelastic domain switching in ferroelectric ceramics

A numerical approach predicting the behavior of ferroelectric ceramics under electric field and mechanical loading is proposed in this paper. In the model, macroscopic properties of ferroelectric ceramics are determined by microscopic structures. Ferroelectric ceramics are seen to be composed of many domains with different orientations, and domain switching is the source of the nonlinear constitutive behavior of the ferroelectric ceramics. Numerical calculations based on the model were carried out, and the computational results are compared with the experimental results, which shows the two sets of results consist with each other. The calculation approach can provide a guidance for the ceramics component design.     

Design and fabrication of a high performance multilayer piezoelectric actuator with bending deformation

A new bending mode multimorph actuator was designed and fabricated successfully by a multiple screen printing process. Unlike the conventional bimorph actuator in which the bend occurs in the thickness direction, the bend in the multimorph actuator occurs in the widthwise direction because of synchronistical deformation of each single monolithic layer in the multilayer structure. The theoretical analysis and experimental measurements were conducted to study the performance of this type of actuator, and a comparison was made with the conventional bimorph actuator. Larger displacement, higher resonance frequency, and much larger blocking force could be achieved with the multimorph actuator than with a bimorph actuator of similar dimensions. The multimorph actuator presented in this paper provides a valuable alternative for actuator applications beyond those available with the popular bimorph and longitudinal multilayer actuators.     

Finite element analysis of piezoelectric thin film membrane structures

Thin film structures have found a wide variety of applications in electromechanical technologies. As the design flexibility for these structures increases, so does the demand for design software that can provide some good insights into the behavior of the structure before it is fabricated. In this study, a finite element code based on a combination of equivalent single-plate theory and classical laminated plate theory was used to predict the dynamic response of thin film structures in micro length scale. As a benchmark for the code development, thin film structures were also fabricated using MEMS technology, and their fundamental frequencies were characterized. It was demonstrated that the model predictions matched fairly well with the experimental data for the small membranes with widths less than 200 microm, but underestimated them for large ones with widths greater than 500 microm. The model also demonstrated that the fundamental frequencies increased with the thickness of the layers. The areas that need to be investigated further in order to improve the predicative capability of the calculations include effects of residual stress, dc bias voltage, parasitic capacitance, interaction of membrane vibration with the supports of the structure, and accurate measurement of the dimensions and material properties of the thin films.     

Finite element simulation of piezoelectric transformers

Piezoelectric transformers are nothing but ultrasonic resonators with two pairs of electrodes provided on the surface of a piezoelectric substrate in which electrical energy is carried in the mechanical form. The input and output electrodes are arranged to provide the impedance transformation, which results in the voltage transformation. As they are operated at a resonance, the electrical equivalent circuit approach has traditionally been developed in a rather empirical way and has been used for analysis and design. The present paper deals with the analysis of the piezoelectric transformers based on the three-dimensional finite element modelling. The PIEZO3D code that we have developed is modified to include the external loading conditions. The finite element approach is now available for a wide variety of the electrical boundary conditions. The equivalent circuit of lumped parameters can also be derived from the finite element method (FEM) solution if required. The simulation of the present transformers is made for the low intensity operation and compared with the experimental results. Demonstration is made for basic Rosen-type transformers in which the longitudinal mode of a plate plays an important role; in which the equivalent circuit of lumped constants has been used. However, there are many modes of vibration associated with the plate, the effect of which cannot always be ignored. In the experiment, the double resonances are sometimes observed in the vicinity of the operating frequency. The simulation demonstrates that this is due to the coupling of the longitudinal mode with the flexural mode. Thus, the simulation provides an invaluable guideline to the transformer design     

Finite element approximation of piezoelectric plates

A Reissner–Mindlin‐type modellization of piezoelectric plates is here considered in a suitable variational framework. Both the membranal and the bending behaviour are studied as the thickness of the structure tends to zero. A finite element scheme able to approximate the solution is then proposed and theoretically analysed. Some numerical results showing the performances of the scheme under consideration are discussed. Copyright © 2001 John Wiley & Sons, Ltd.     

Tracking control of a multilayer piezoelectric actuator using a fiber bragg grating displacement sensor system

This paper provides a fiber Bragg grating (FBG) sensor system which can measure the point-wise, out-of-plane displacement to examine the position-tracking control problem of a multilayer piezoelectric actuator (MPA). An FBG filter-based wavelength-optical intensity modulation technique is used in this study. A nominal system model is identified experimentally from the responses excited by random signals measured by an FBG displacement sensor that are simultaneously compared with those obtained from a laser Doppler vibrometer. To further investigate the sensing ability of the proposed system in a feedback control problem, control strategies including robust Hα control, proportional-integralderivative control, and pseudoderivative feedback control are implemented. The characteristics of the step responses for each controller are examined. The experimental results show that the proposed sensor system is capable of performing the system identification and can serve as a feedback control sensor which has a displacement sensitivity of 5 mV/nm.     

Finite element analysis on deflection control of plates with piezoelectric actuators

A finite element model for the deflection control of plates with piezoelectric actuators is presented. This model contains an actuator element, an adhesive interface element and an eight-node isoparametric plate element. The actuator element developed here is based on first-order shear deformation theory. An analytical solution is also derived in comparison with results using the finite element model. The analyses articulate separate response of the plate; actuators and the adhesive give the flexible meshing advantage of solving the- smart structure problem with any type of boundary conditions and geometry configuration.     

Model of diffusion taking into account sorption

The problem of the diffusion of a material in an adsorbing porous medium is considered. In the equation for the concentrations in the porous medium and the sorption layer a delay time is introduced.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 30, No. 3, pp. 453–455, March, 1976.     

Oscillations of a viscoelastic rod taking thermomechanical coupling into account

The effect of thermomechanical coupling on the forced longitudinal oscillations of a viscoelastic rod is investigated.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 35, No. 4, pp. 692–697, October, 1978.     

Finite element simulation of piezoelectric vibrator gyroscopes

A finite element approach to the simulation of piezoelectric vibrator gyroscopes is presented for characteristic prediction. The formulation is given including the effect of Coriolis force due to rotation for a piezoelectric thin plate, which is considered to be two-dimensional in plane vibration. For numerical examples, the gyroscopes of a thin square plate, and a cross-bar and a ring built in the plate are considered, which pave the way for the development of the gyroscopes of monolithic configuration. The effect of the rotation on the modal shapes, the resonant frequencies, and the transmission characteristics are discussed demonstrating the sensing capability against the rotation     

Vibration analysis of cubic rotary-linear piezoelectric actuator

Cubic design of a stator in a rotary-linear piezoelectric actuator is sophisticated and interesting, but the vibration theory of the cubic stator remains unclear when using the finite element method (FEM). In this paper, we analyze the vibration behavior of the cubic stator by applying the energy method, which distinguishes the component of mechanical energy. By changing the design of the stator (especially the length in the direction of the through-hole axis), we clarify how the vibration modes are in accordance at one equal frequency in cubic shape. The behavior of the vibration modes is discussed using conventional vibration theory of a beam and a plate.     

Finite element modelling of hybrid active–passive vibration damping of multilayer piezoelectric sandwich beams—part II: System analysis

An electromechanically coupled finite element model has been presented in Part 1 of this paper in order to handle active–passive damped multilayer sandwich beams, consisting of a viscoelastic core sandwiched between layered piezoelectric faces. Its validation is achieved, in the present part, through modal analysis comparisons with numerical and experimental results found in the literature. After its validation, the new finite element is applied to the constrained optimal control of a sandwich cantilever beam with viscoelastic core through a pair of attached piezoelectric actuators. The hybrid damping performance of this five‐layer configuration is studied under viscoelastic layer thickness and actuator length variations. It is shown that hybrid active–passive damping allows to increase damping of some selected modes while preventing instability of uncontrolled ones and that modal damping distribution can be optimized by proper choice of the viscoelastic material thickness. Copyright © 2001 John Wiley & Sons, Ltd.