Application for generating characteristics of free and bonded systems

The present paper is the continuation of earlier publications with stack of piezoelectric plates. This work is an author's idea of application for generating characteristics of piezoelectric systems. The presented program, called Piezo3D, allows for generation a single piezoelectric plate graphs as well as complex, free and bonded systems. An additional advantage is the ability to obtain the 3D graphs, in which the characteristics of the test graph can be based not only on frequency, but also on other parameters such as the thickness of the plate. The application is written in the numerical software "Matlab". (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Two Degree-Of-Freedom Online Compensation of a Piezoelectric Micro-Positioning Unit

Due to their almost unlimited resolution and fast dynamics, piezoelectric actuators are a common choice for mechatronic systems targeting positioning tasks with high demands on precision. However, these piezoelectric actuators inherently suffer from nonlinear characteristics (mainly hysteresis and creep effects) which need to be addressed by appropriate control strategies. The operator-based modified Prandtl-Ishlinksii (mPI) approach does not only model hysteresis effects with asymmetries and creep effects but also provides an analytical solution for its inverse model. Online feedforward compensation of the aforementioned nonlinear effects can be realized by using the inverse model and additional weight adaptation. In this paper, online compensation via the mPI model is applied to a commercial micro-positioning unit driven by piezoelectric actuators with more than one degree of freedom (DOF). For validation of the proposed approach, two coupled trajectories in the X-Y plane are utilized. Subsequent tracking error analysis validates the efficacy of the stated approach. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Piezoelectric control of flexible vibrations in rotating beams: An experimental study

Active control of flexible vibrations by distributed piezoelectric actuators and sensors plays an increasing role in engineering, especially in light-weight structures. Exemplarily, in this contribution a rotating beam is studied which can be found in many practical applications, e.g. as robot arms or flexible manipulators in production processes. It has been intensively shown in the literature that it is possible to completely suppress the flexible vibrations by an appropriate distribution of piezoelectric actuation strains. In order to compensate the inertial forces in the considered rotating beam, a complex distribution is obtained, such that a practical realisation would be very extensive. To overcome the problem, a discrete approximation by piezoelectric patches is applied. In order to find an optimal configuration for an experimental setup, and to investigate several control strategies, a numerical simulation model has been implemented based on Bernoulli-Euler beam theory. The numerical results are verified by an experimental set-up, in which 48 piezoelectric patches have been attached on a beam with rectangular hollow cross-section. Each patch can be used either as an actuator or a sensor. Additionally, strain gauges can be used as sensors. For monitoring, acceleration sensors are used. The control system is implemented within a dSpace environment. The results show a significant reduction of the flexible vibrations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Finite deformations of thin shells with piezoelectric sensors and actuators

We treat coupled electromechanical problem of finite deformations of piezoelectric shells with the help of the direct approach. A shell is considered as a material surface with mechanical degrees of freedom of particles and with an additional field variable, namely electric potential on the electrodes. This results both in the nonlinear system of equations of piezoelectric shells and in the appropriate numerical scheme. Application of the direct approach is preceded with the three-dimensional asymptotic analysis of a linear electromechanical problem for a non-homogeneous piezoelectric plate, which provides the constitutive relations for the nonlinear theory. As a sample problem, we present finite element analysis of deformation and local buckling of cylindrical panel, equipped with piezoelectric sensors. The latter influence the mechanical behavior and produce signals, which can be interpreted in terms of structural entities. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonlinear dynamic characteristics of bi-graphene sheets/piezoelectric laminated films considering high order van der Walls force and scale effect

This paper presents an analytical method to investigate the nonlinear vibration characteristics of bi-graphene sheets/piezoelectric (BGP) laminated films subjected to electric loading based on a nonlocal continuum model, in which the two adjacent layers are coupled by van der Walls force. Utilizing von Kármán nonlinear geometric relation and nonlocal physical relation, the nonlinear dynamic equation of BGP laminated films under electric loading exerted on the piezoelectric layer is found, then the relation between the nonlinear resonant frequency and the nonlinear vibration amplitude for each layer of the BGP laminated films is obtained by using Galerkin method and harmonic-balance method. Results show that the nonlinear vibration amplitude for each layer of laminated films can be controlled by adjusting the electric potential exerted on piezoelectric layer, and the coupled effect of van der Walls force between graphene sheet and piezoelectric layer on the vibration amplitude of each layer depends on the order number of nonlinear resonant frequency and the mode shape.     

Simulation Based Determination of Piezoelectric Material Parameters

The exact numerical simulation of piezoelectric transducers needs the knowledge of all material tensors that occur in the piezoelectric constitutive relations. The determination of these tensors is achieved by a simulation based algorithm which adjusts the 3D - FEM simulated data with electrical measurements of a piezoelectric transducer. Its advantage compared to the standards (see [1], [2]) lies in the fact that a determination of the complete set of material parameters from one arbitrarily shaped specimen with a high precision is possible. The reconstruction of the material tensors is formulated as a parameter identification problem for a system of PDEs. Since unique solvability of this inverse problem may hardly be verified, the system of equations we have to solve for recovering the material tensor entries can be rank deficient and therefore requires application of appropriate regularization strategies. For this purpose, we use inexact Newton methods. The material parameters are assumed to be complex-valued which allows to account for mechanical, dielectric and piezoelectric losses. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On some relations between different interface crack models

Exact analytical solutions for an interface crack with an artificial contact zone in isotropic, anisotropic and piezoelectric materials have been analyzed and their comparison with the correspondent classical results has been performed. This analysis showed the way of a presentation of the main results for an artificial contact zone model in the manner very similar to the classical model, and due to this phenomenon the essential simplification of the investigation of the contact zone model has been attained. The application of the obtained results to interface cracks in anisotropic and piezoelectric bimaterials can be demonstrated. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Cylindrical bending responses of angle-ply piezoelectric laminates with viscoelastic interfaces

The time-dependent behavior of a simply supported, angle-ply piezoelectric laminate in cylindrical bending with viscoelastic interfaces is investigated. The interfacial bonding in piezoelectric laminates is considered to be dielectrically weakly (or highly) conducting, and mechanically compliant characterized by the Kelvin–Voigt viscoelastic law. The state-space approach, which is directly based on the piezoelectricity equations and very effective in analyzing laminated structures, is employed. For exact analysis, a state equation of the relative sliding displacements with respect to the time variable is further presented. Comparison study shows that the numerical results by the present analysis agree well with those reported before. Numerical results also indicate that the electromechanical response of the piezoelectric laminates with viscoelastic interfaces changes remarkably with time elapsing. Thus, the bonding imperfection should be considered carefully in the practical design of piezoelectric laminates.     

Electro-mechanical shear buckling of piezoelectric nanoplate using modified couple stress theory based on simplified first order shear deformation theory

This paper studies the electro-mechanical shear buckling analysis of piezoelectric nanoplate using modified couple stress theory with various boundary conditions.In order to be taken electric effects into account, an external electric voltage is applied on the piezoelectric nanoplate. The simplified first order shear deformation theory (S-FSDT) has been employed and the governing differential equations have been obtained using Hamilton's principle and nonlinear strains of Von-Karman. The modified couple stress theory has been applied to considering small scale effects. An analytical approach was developing to obtain exact results with various boundary conditions. After all, results have been presented by change in some parameters, such as; aspect ratio, effect of various boundary conditions, electric voltage and length scale parameter influences. At the end, results showed that the effect of external electric voltage on the critical shear load occurring on the piezoelectric nanoplate is insignificant.     

Exact solutions of functionally graded piezoelectric material sandwich cylinders by a modified Pagano method

The three-dimensional (3D) coupled analysis of simply-supported, functionally graded piezoelectric material (FGPM) circular hollow sandwich cylinders under electro-mechanical loads is presented. The material properties of each FGPM layer are regarded as heterogeneous through the thickness coordinate, and obey an exponent-law dependent on this. The Pagano method is modified to be feasible for the study of FGPM sandwich cylinders. The modifications are as follows: a displacement-based formulation is replaced by a mixed formulation; a set of the complex-valued solutions of the system equations is transferred to the corresponding set of real-valued solutions; a successive approximation method is adopted to approximately transform each FGPM layer into a multilayered piezoelectric one with an equal and small thickness for each layer in comparison with the mid-surface radius, and with the homogeneous material properties determined in an average thickness sense; and a transfer matrix method is developed, so that the general solutions of the system equations can be obtained layer-by-layer, which is significantly less time-consuming than the usual approach. A parametric study is undertaken of the influence of the aspect ratio, open- and closed-circuit surface conditions, and material-property gradient index on the assorted field variables induced in the FGPM sandwich cylinders.     

含界面电极压电介质的Green函数

研究了由两个不同压电材料和一半无限长电极组成的复合材料系统的广义二维问题·　基于Stroh公式,提供了当一个线力、线电荷和一个线电偶极子施加在电极端附近时,精确的Green函数解·　进一步地,获得了相应的场强度系数·　这些结果可作为边界元的基本解,以分析更加复杂的压电复合材料断裂问题·     

Active Vibration Control of Roll Press System by Piezoelectric Actuators

A common treatment in manufacturing web-like thin materials like paper is to manipulate it between two cylinders under rolling contact. A roll press is sensitive to vibration, which is unwanted, because it marks the web by regular stripes. A piezoelectric actuator is an excellent device for vibration control applications because of its large force generation, very short response time and easy controllability. Control of piezoelectric actuator is straightforward by direct compensation of input voltage. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of laminated piezoelectric composite plates using an inverse hyperbolic coupled plate theory

This paper presents a non-polynomial coupled plate theory for smart composite structures employing inverse hyperbolic displacement and electric potential functions. The theory is utilized towards analysis of composite piezoelectric plates operating in sensor and actuator modes. Particularly, the following three cases are studied: (i) passive laminated composite structure, (ii) composite piezoelectric plate actuator and (iii) unimorph and bimorph piezoelectric plate sensors. Analytical solutions are obtained for simply supported plates under static electrical and mechanical loads. These results are validated with existing 3D elasticity solutions and compared with other plate theory solutions. Furthermore, parametric studies are performed to determine the effect of loading, span-to-thickness ratio and lamination sequence on the response of the piezoelectric plate. Finally, the theory is applied to a transverse shear sensing device which utilizes transverse shear-electric field coupling in piezoelectric materials. This effect is often ignored in literature.It is observed that the maximum percentage error of the present theory, when compared with 3D results, is less than 3%, which is lower than other higher order plate theories.     

A Four-node Finite Element for Piezoelectric Shell Structures in Convective Co-ordinates

In this contribution, an isoparametric piezoelectric shell element is presented which is based on convective coordinates and which allows for the analysis of arbitrary shell geometries. A two-field variation formulation [1, 2] is used in which the displacements and the electric potentials serve as independent variables. Especially, for thin-walled structures under certain boundary conditions and load cases, the displacement based element tend to shear and membrane locking. In order to avoid this poor behaviour, the Assumed Natural Strain (ANS) method [3] is introduced into the piezoelectric shell element. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bending of sinusoidal functionally graded piezoelectric plate under an in-plane magnetic field

This work investigates the bending of a simply supported functionally graded piezoelectric plate under an in-plane magnetic field. The extended sinusoidal plate theory for piezoelectric plate is adopted. The governing equations are derived by the principle of the virtual work considering the Lorentz magnetic force obtained from the Maxwell's relation. The effect of magnetic field, electric loading and gradient index on the displacement, electric potential, stress and electric displacement are numerically presented and discussed in detail. These conclusions will be of particular interest to the future analysis of piezoelectric plate in magnetic field.     

On the piezoelectric shear effect in ultrasonic motors

A new actuator for piezoelectric ultrasonic motors (USM) using the d₁₅ effect was conceived. Whereas the piezoelectric d₃₃ and d₃₁ effects are normally used in commercial motors, there exist hardly any USM based on shear actuation. The actuator is a piezoelectric block polarized in axial direction and electroded circumferentially with four electrodes. The suitable superposition of two standing waves generates ultrasonic traveling waves in the actuator, which drives the rotor. The dimensions of the actuator are optimized with respect to the dynamic piezoelectric coupling factor. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

压电压磁复合材料中二维散射问题的解析研究

用极化方法分析了含一二维夹杂的无限压电压磁基体中的波动散射问题．以此为目的,首先构建了二维压电压磁“相对体”的极化方法．当一般性波动退减为简谐振动时,极化方法的核心函数退减为二维谐波Green函数．利用氡变换的解析方法,首次求得了二维谐波Green函数的积分表达式,该表达式在低频初始波与小尺度椭圆柱夹杂物的假设下可得到进一步的简化,并最终求得解析解．推导针对同时具有压电以及压磁效应的一般性各向异性材料进行,然后将所得的结果简化到仅针对压电复合材料的情况．以此简化解析解为基础,提供了两个算例,讨论了影响含一二维椭圆柱夹杂的PZT-5H压电陶瓷复合材料的散射截面的各种不同因素（包括夹杂的尺寸、形状效应,材料常数的影响,以及压电效应等）．     

A Finite Element Formulation for the Nonlinear Analysis of Piezoelectric Three-Dimensional Beam Structures

A finite element formulation for a three-dimensional piezoelectric beam which includes geometrical and material nonlinearities is presented. To account for the piezoelectric effect, the coupling between the mechanical stress and the electrical displacement is considered. Based on the Timoshenko theory, an eccentric beam formulation is introduced which provides an efficient model to analyze piezoelectric structures. The geometrically nonlinear assumption allows the calculation of large deformations including buckling analysis. A quadratic approximation of the electric potential through the cross section of the beam ensures the fulfilment of the charge conservation law exactly. This assumption leads to a finite element formulation with six mechanical and five electrical degrees of freedom per node. To take into account the typical ferroelectric hysteresis phenomena, a nonlinear material model is essential. For this purpose, the phenomenological Preisach model is implemented into the beam formulation which provides an efficient determination of the remanent part of the polarization. The applicability of the introduced beam formulation is discussed with respect to available data from literature. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)