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.     

Finite element piezothermoelasticity analysis and the active control of FGM plates with integrated piezoelectric sensors and actuators

 An efficient finite element model is presented for the static and dynamic piezothermoelastic analysis and control of FGM plates under temperature gradient environments using integrated piezoelectric sensor/actuator layers. The properties of an FGM plate are functionally graded in the thickness direction according to a volume fraction power law distribution. A constant displacement-cum-velocity feedback control algorithm that couples the direct and inverse piezoelectric effects is applied to provide active feedback control of the integrated FGM plate in a closed loop system. Numerical results for the static and dynamic control are presented for the FGM plate, which consists of zirconia and aluminum. The effects of the constituent volume fractions and the influence of feedback control gain on the static and dynamic responses of the FGM plates are examined. Received: 13 March 2002 / Accepted: 5 March 2003 The work described in this paper was supported by a grant awarded by the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 1024/01E).     

Finite element modeling of active control of functionally graded shells in frequency domain via piezoelectric sensors and actuators

 A flat-shell element is presented for the active control of functionally graded material (FGM) shells through integrated piezoelectric sensor/actuator layers. The finite element formulation based on first-order shear deformation theory (FSDT) can be applied to shells ranging from relatively thin to moderately thick dimensions. A constant gain displacement and velocity feedback control algorithm coupling the direct and inverse piezoelectric effects is applied to provide active control of the integrated FGM shell in a self-monitoring and self-controlling system. Frequency response characteristics of the FGM shell containing the piezoelectric sensors/actuators are analyzed in the frequency domain. The effects of constituent volume fraction and the influence of feedback control gain values on the dynamic responses of the FGM shell system are examined in detail. Received 13 November 2000     

Reducing friction-induced vibration using intelligent active force control (AFC) with piezoelectric actuators

In this paper, a novel approach to reduce the effect of mode coupling that causes friction induced vibration (FIV) is proposed by applying an intelligent active force control (AFC)-based strategy employing piezoelectric actuators with hysteresis effect to a simplified two degree-of-freedom mathematical model of a friction-induced vibration system. At first, the model is simulated and analysed using a closed loop pure Proportional-Integral-Derivative (PID) controller. Later, it is integrated with the intelligent AFC with fuzzy logic (FL) estimator and simulated under similar operating condition. After running several tests with different sets of operating and loading conditions, the results both in time and frequency domains show that the PID controller with the intelligent AFC is much more effective in reducing the vibration, compared to the pure PID controller alone.     

Finite element method for piezoelectric vibration

A finite element formulation which includes the piezoelectric or electroelastic effect is given. A strong analogy is exhibited between electric and elastic variables, and a ‘stiffness’ finite element method is deduced. The dynamical matrix equation of electroelasticity is formulated and found to be reducible in form to the well-known equation of structural dynamics, A tetrahedral finite element is presented, implementing the theorem for application to problems of three-dimensional electroelasticity.     

Shape control of smart composite plate with non-rectangular piezoelectric actuators

Quasi-static shape control of a smart structure may be achieved through optimizing the applied electric fields, loci, shapes and sizes of piezoelectric actuators attached to the structure. In this paper, a finite element analysis (FEA) software has been developed for analyzing static deformation of smart composite plate structures with non-rectangular shaped PZT patches as actuators. The mechanical deformation of the smart composite plate is modeled using a 3rd order plate theory, while the electric field is simulated based on a layer-wise theory. The finite element formulation is verified by comparing with experimentally measured deformation. Numerical results are obtained for the optimum values of the electric field in the PZT actuators to achieve the desired shape using the linear least square (LLS) method. The numerical results demonstrate the influence of the shapes of actuators.     

The dynamic behaviour of surface-bonded piezoelectric actuators with debonded adhesive layers

The performance of smart structures depends on the electromechanical behaviour of piezoelectric actuators and the bonding condition along the interface, which connects the actuators and the host structures. This paper provides a theoretical study of the effect of partially debonded adhesive layers on the coupled electromechanical behaviour of piezoelectric actuators subjected to high-frequency electric loads. An actuator model with an imperfect adhesive bonding layer, which undergoes a shear deformation, is proposed to simulate the two-dimensional electromechanical behaviour of the integrated system. An analytical solution of the problem is provided by solving the resulting integral equations in terms of the interfacial stress. Numerical simulation is conducted to study the effect of the bonding layer upon the actuation process. The effect of interfacial debonding on the dynamic response of the layered structure and on the interlaminar strain and stress transfer mechanisms is discussed.     

Optimal location of piezoelectric actuators for active vibration control of thin axially functionally graded beams

Up to now, optimal location for active control studies concern principally multilayers or homogeneous structures. In the case of functionally graded materials, very few papers exist and they only concern cross section variations. In this way, this paper deals with the optimization of piezoelectric actuators locations on axially functionally graded beams for active vibration control. For this kind of structures, the free vibration problem is more complicated as the governing equations have variable coefficients. Here, the eigenproblem is solved using Fredholm integral equations. The optimal locations of actuators are determined using an optimization criterion, ensuring good controllability of each eigenmode of the structure. The linear quadratic regulator, including a state observer, is used for active control simulations. Two numerical examples are presented for two kinds of boundary conditions.     

Improved finite element modeling of piezoelectric beam with edge debonded actuator for actuation authority and vibration behaviour

The main emphasis of the present work is to model a piezoelectric beam with edge debonded actuator by employing finite element method based layerwise shear deformation theory, to improve the accuracy with which the actuation authority and natural frequencies are computed. The surface-bonded piezoelectric actuators and the host beam are considered to rotate individually due to shear deformation, while they are assumed to undergo the same flexural deflection and slope. These modeling aspects have improved the accuracy of the computed results. Edge debonding of actuator is accounted in the model by modeling healthy and debonded regions of the beam individually and subsequently applying the displacement continuity conditions at the interfaces of different regions. The investigations are carried out to find the effect of different extents of edge debonding on the actuation authority and natural frequencies of the debonded piezoelectric beam. It is found from the numerical results that the behaviour of the beam with edge debonded actuator is affected considerably as regards to the actuation authority and marginally with respect to natural frequencies. Further it has been shown that, when an actuator is edge debonded it introduces the local modes besides displaying significant reduction in its actuation authority.     

Optimal placement of piezoelectric actuators on plate structures for active vibration control via modified control matrix and singular value decomposition approach using modified heuristic genetic algorithm

The present work deals with the optimal placement of piezoelectric actuators on a thin plate using modified control matrix and singular value decomposition (MCSVD) approach. The MCSVD is considered as the fitness function and optimal positions of the actuators are obtained by maximizing it with MHGA (modified heuristic genetic algorithm). Vibration suppression has been studied for simply supported plate with piezoelectric patches in optimal positions to suppress first specified modes using LQR (linear quadratic regulator) controller. It is observed that the positions of patches obtained with this approach give greater vibration suppression, reduced computational requirements, and provide global optimum solution only.     

超声换能器激励的板声源振动特性的有限元分析

为了解超声清洗等应用中常用超声换能器激励的板声源的振动特性,使用有限元方法对其进行了研究,并通过实验验证了仿真结果。结果表明使用有限元法对超声换能器激励的板声源的振动分析是可行的,超声换能器激励的板声源的振动并非活塞式振动,而具有复杂的振动分布。     

Optimal solid shell element for large deformable composite structures with piezoelectric layers and active vibration control

In this paper, we present an optimal low‐order accurate piezoelectric solid‐shell element formulation to model active composite shell structures that can undergo large deformation and large overall motion. This element has only displacement and electric degrees of freedom (dofs), with no rotational dofs, and an optimal number of enhancing assumed strain (EAS) parameters to pass the patch tests (both membrane and out‐of‐plane bending). The combination of the present optimal piezoelectric solid‐shell element and the optimal solid‐shell element previously developed allows for efficient and accurate analyses of large deformable composite multilayer shell structures with piezoelectric layers. To make the 3‐D analysis of active composite shells containing discrete piezoelectric sensors and actuators even more efficient, the composite solid‐shell element is further developed here. Based on the mixed Fraeijs de Veubeke–Hu–Washizu (FHW) variational principle, the in‐plane and out‐of‐plane bending behaviours are improved via a new and efficient enhancement of the strain tensor. Shear‐locking and curvature thickness locking are resolved effectively by using the assumed natural strain (ANS) method. We also present an optimal‐control design for vibration suppression of a large deformable structure based on the general finite element approach. The linear‐quadratic regulator control scheme with output feedback is used as a control law on the basis of the state space model of the system. Numerical examples involving static analyses and dynamic analyses of active shell structures having a large range of element aspect ratios are presented. Active vibration control of a composite multilayer shell with distributed piezoelectric sensors and actuators is performed to test the present element and the control design procedure. Copyright © 2005 John Wiley & Sons, Ltd.     

振动控制中压电作动器非线性的补偿方法研究

在周期振动的自适应控制中,压电作动器的非线性特性会产生高次谐波,激发高阶模态振动。为抑制压电作动器的高次谐波激励,同时结合自适应振动控制的特点,提出一种新的作动器非线性补偿方法。该方法将作动器的非线性与结构的动态特性部分融合,用正交多项式从输入输出信号中拟合静态非线性及其逆变换,计算过程简单,数值稳定性高。在控制通道中,通过逆变换对控制信号进行预处理,使得补偿后的输入输出具有线性系统的特征,而输入输出之间的相位差完全由自适应算法进行补偿。实验结果表明,所给出的补偿方法能够抑制高次谐波,并改善了振动控制效果。     

Finite element modelling of nanostructured piezoelectric resonators (NAPIERs)

A new modification to the traditional piezoelectric thin film bulk acoustic wave resonator (FBAR) and solidly mounted acoustic wave resonator (SMR) is proven to significantly improve their performances. The proposed design involves the surface micro/nano structuring of planar piezoelectric thin films to realize an array of a large number of rod-like structures. In contrast to the plate-like thickness extensional resonance in traditional FBAR and SMR devices, the rod-like structures can be excited in their length extensional resonance, yielding a higher electromechanical coupling factor and effectively eliminating the spurious resonances from lateral modes of vibration. The designs have been investigated by two and three-dimensional finite element analyses and one-dimensional transmissionline modelling. The results show that significant increases in the electromechanical coupling factor of ca. 40% can be achieved by using the rod-like length extensional resonances as compared with the plate-like thickness extensional resonances in traditional devices. Simulations show that rod width-to-thickness aspect ratios of less than 0.5 could result in an electromechanical coupling factor (k2eff) of over 10% for a zinc oxide device, compared with approximately 7% for a conventional design.     

简支板振动无线主动控制及驱动器优化布置研究

推导光电层合简支板结构动力学方程及模态控制方程,以规格化后模态控制力指数作为遗传算法的适应度函数,基于二进制编码的遗传算法对用于简支板振动控制的单对、双对光致伸缩驱动器布局进行优化,计算机仿真结果表明优化后的驱动器布局方案可有效提高板结构振动控制的有效性。在此基础上进一步对板结构多模态振动控制进行探讨,提出适用于板结构多模态振动控制的驱动器布局优化方法及振动控制方案,仿真算例表明该方法可有效地对简支板前二阶模态进行振动无线控制。     

Active vibration control of composite plate with optimal placement of piezoelectric patches

The active vibration control of a composite plate using discrete piezoelectric patches has been investigated. Based on first order shear deformation theory, a finite element model with the contributions of piezoelectric sensor and actuator patches to the mass and stiffness of the plate was used to derive the state space equation. A global optimization based on LQR performance is developed to find the optimal location of the piezoelectric patches. Genetic algorithm is adopted and implemented to evaluate the optimal configuration. The piezoelectric actuator provides a damping effect on the composite plate by means of LQR control algorithm. A correlation between the patches number and the closed loop damping coefficient is established.     

Numerical modelling of piezoelectric actuators exposed to hydrogen

Modern fuel injectors have been developed based on piezoelectric stack actuators. Performance and durability of actuators in a hydrogen environment are important considerations in the development of hydrogen injectors. 2D plane stress and 3D models for analysis of coupled diffusion and thermo-electromechanical response of actuators are presented. Chemical potential, electric field and temperature gradients are taken as driving forces for hydrogen transport. The explicit Euler finite difference method is used to solve the nonlinear diffusion governing equation. The finite element method is used for time-dependent analysis of fully coupled mechanical, electric and thermal fields. The diffusion process and thermo-electromechanical deformations are coupled through the dependence of piezoelectric properties on hydrogen concentration. Experimental results for the piezoelectric coefficient d ₃₃ of PZT ceramics exposed to different hydrogen concentrations are used. A comparison of a fully coupled 2D model with 2D and 3D models with reduced coupling is made to examine the significance of coupling and computational efficiency. Selected numerical results are presented for time histories of hydrogen concentration, temperature and stroke of an idealized actuator unit cell to obtain a preliminary understanding of the performance of actuators exposed to hydrogen.     

压电材料在薄板振动抑制中的应用研究

对于热机电耦合压电智能薄板结构,鉴于包含了机电耦合、热释电效应和热力耦合的完整系统的阶数往往很高而不利于控制器求解,研究了基于平衡降阶法的H∞振动控制问题。对于直接关系到振动控制能否得以顺利实施的诸多问题,如系统的不可观性、温度的不可控性、降阶后系统状态变量的物理含义、评价信号的构建方法及其权矩阵的选取方法等,细腻地研究了它们对实现控制的影响机理,并在此基础上提出了相应的解决方法或技巧。数值算例表明这些研究工作有益于H∞振动控制的顺利实施。     

柔性板压电作动器的优化位置与主动控制实验研究

对柔性悬臂板主动控制中作动器的优化位置进行研究,其中作动器采用压电形式,优化算法采用粒子群方法,指标函数采用基于能量的可控Gramian优化配置准则。仿真和实验结果显示,粒子群优化算法能够有效地对作动器的优化位置进行计算,尤其适用于多个作动器的位置优化问题,基于作动器最优位置的控制设计能够取得良好的控制效果。