Active aeroelastic flutter suppression of a supersonic plate with piezoelectric material

The active aeroelastic flutter properties of supersonic plates are investigated by using the piezoelectric material. The piezoelectric material has been extensively used for the active vibration control of engineering structures. In this paper, the piezoelectric material is further used to improve the flutter characteristics of the supersonic plates. The equation of motion of the plate and piezoelectric material system is obtained by Hamilton’s principle with the assumed mode method. The supersonic piston theory is used to evaluate the aerodynamic load. By applying an appropriate external control voltage to activate the piezoelectric material, a displacement and acceleration feedback control strategy is used to obtain the active stiffness and active mass. Solving the eigenvalue problem of the equation of motion, the natural frequencies and damping ratios of the structural system are obtained. Furthermore, the aeroelastic flutter bounds are calculated, and the effects of feedback control gains on the active aeroelastic flutter characteristics of the structure are analyzed in detail. From the numerical results it is seen that the active stiffness and active mass have prominent effects on the flutter characteristics of the supersonic plates. The aeroelastic flutter properties can be greatly improved by introducing the active stiffness and active mass into the supersonic plate with the piezoelectric patch. With the increase of the feedback control gains, the active aeroelastic flutter properties for the lower order modes of the supersonic plate are gradually improved.     

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.     

基于模态应变能分布的压电致动器/传感器位置优化遗传算法

本文由线弹性压电结构有限元动力方程,推导了压电智能结构的振动控制方程。建立了准确模拟层合压电结构动力行为的有限元模型。基于主结构模态应变能分布提出了一种新的优化目标函数,将压电致动器/传感器位置编号作为优化变量,建立了离散变量表示的智能结构优化问题,并通过二进制编码的遗传算法（GA）求解了该最优问题。以四边固支复合层合压电智能板为数值算例,采用比例反馈控制, 研究了最优位置配置致动器/传感器智能结构目标模态的控制效果。数值结果表明基于模态应变能分布的遗传算法所得优化解具有较好的振动控制效果。     

Optimal design in vibration control of adaptive structures using a simulated annealing algorithm

Advanced reinforced composite structures incorporating piezoelectric sensors and actuators are increasingly becoming important due to the development of smart structures. These structures offer potential benefits in a wide range of engineering applications such as vibration and noise suppression, shape control and precision positioning. This paper presents a finite element formulation based on the classical laminated plate theory for laminated structures with integrated piezoelectric layers or patches, acting as sensors and actuators. The finite element model is a single layer triangular nonconforming plate/shell element with 18 degrees of freedom for the generalized displacements, and one additional electrical potential degree of freedom for each surface bonded piezoelectric element layer or patch. The control is initialized through a previous optimization of the core of the laminated structure, in order to minimize the vibration amplitude and maximize the first natural frequency. Also the optimization of the patches position is performed to maximize the piezoelectric actuators efficiency. The simulated annealing algorithm is used for these purposes. To achieve a mechanism of active control of the structure dynamic response, a feedback control algorithm is used, coupling the sensor and active piezoelectric layers or patches, and to calculate the dynamic response of the laminated structures the Newmark method is considered. The model is applied in the optimization of an illustrative adaptive laminated plate case. The influence of the position and number of piezoelectric patches, as well as the control gain, are investigated and the results are presented and discussed.     

考虑静水压力的压电弹性层合圆柱壳动力响应的控制模型

基于经典的层合板理论和Navier解法,对静水压作用下压电弹性层合圆柱壳的动力问题的主动控制进行了研究。首先由Hamilton原理导出压电弹性层合壳的非线性动力基本方程。利用压电材料的正、逆压电效应,通过闭环方式,采用速度反馈控制方法得到了任意形式动载作用下带压电感测层/激励层的简支层合圆柱壳动力响应的主动控制模型。数值算例中对于三种不同的外载条件下该控制模型对圆柱壳的动力响应的控制效果进行了研究。结果表明本文中提出的控制模型能够有效抑制动载作用下结构的振动。     

Optimal shapes of PZT actuators for laminated structures subjected to displacement or eigenfrequency constraints

In this paper, dynamics, electromechanical couplings, and control of piezoelectric laminated cylindrical shells and rectangular plates are investigated. It is assumed that the piezoelectric layers are distributed on the top and bottom surfaces of the structures. First of all the governing equations and boundary conditions including elastic and piezoelectric couplings are formulated and solutions are derived. Then control of the plate/shells deflections and natural frequencies using high control voltages are studied in order to optimize the structural response. The present formulation of optimal design introduces boundaries of piezoelectric patches as new class of design variables. In addition, classical design variables in the form of ply orientation angles of orthotropic layers are also taken into account. For the actuator/actuator configuration, it was shown that the piezoelectric actuators can significantly reduce deformations/eigenfrequencies of the composite plate. Those effects were dependent on the value of the applied voltage. It was demonstrated that the proper choice of the actuator area is more efficient in reducing deflections/eigenfrequencies. The accuracy of optimal design are verified both with the aid of the FE package ABAQUS and using the standard Rayleigh-Ritz method. The results concerning active vibration control for axisymmetric cylindrical shells are also discussed.     

Vibration suppression of laminated composite beams with a piezo-electric damping layer

An analytical formulation is derived for modelling the behaviour of laminated composite beams with integrated piezoelectric sensor and actuator. The major difference in approach to the solution compared to previous studies is that the analytical solution for active vibration control and suppression of smart laminated composite beams is presented in this paper. The governing equation is based on the first-order shear deformation theory (Mindlin plate theory), which is applicable for both thin and moderately beams, and includes the coupling between mechanical and electrical deformations. The voltage generated by the sensor layer and response of the beam to the actuator voltage can be computed independently. In this study, the new assumption of harmonic vibration is introduced, which includes both of the sine and cosine terms. Another contribution of this paper is introducing the transformation method of complex numbers to reduce the order of the governing equation of smart laminated beams. Thus, the exact solution of the reduced governing equation can be obtained by using MATLAB and the entire numerical results are presented. The behaviour of the output voltage from the sensor layer and the input voltage acting on the actuator layer is also studied. Graphical results are presented to demonstrate the ability of closed-loop system to actively control the vibration of laminated beams and it shows a good control effect. The influence of stacking sequence on the controlled transient response of the laminated beam is examined. Finally, the experiential formulation of the amplitude of beam vibration varying with the negative velocity feedback control gain has also been evaluated. The present method has a general application in this field of study.     

Performance of piezoelectric fiber-reinforced composites for active structural-acoustic control of laminated composite plates

This paper deals with the active structural acoustic control of thin laminated composite plates using piezoelectric fiber-reinforced composite (PFRC) material for the constraining layer of active constrained layer damping (ACLD) treatment. A finite element model is developed for the laminated composite plates integrated with the patches of ACLD treatment to describe the coupled structural-acoustic behavior of the plates enclosing an acoustic cavity. The performance of the PFRC layers of the patches has been investigated for active control of sound radiated from thin symmetric and antisymmetric cross-ply and antisymmetric angle-ply laminated composite plates into the acoustic cavity. The significant effect of variation of piezoelectric fiber orientation in the PFRC layer on controlling the structure-borne sound radiated from thin laminated plates has been investigated to determine the fiber angle in the PFRC layer for which the structural-acoustic control authority of the patches becomes maximum.     

The effect of piezoelectrically induced stress stiffening on the aeroelastic stability of curved composite panels

This work investigates the aeroelastic stability boundary of flutter in aircraft composite panels, curved or flat, subject to the effect of stress stiffening caused by the piezoelectric actuator (PZT). Hamilton’s principle is used for the formulation of the energy functional and to obtain the equilibrium equations and boundary conditions of the problem. The finite element method is employed to numerically solve the equations. The aeroelastic behavior of panels manufactured in composite material (boron–epoxy) or conventional material (aluminum 2024-T3) are assessed. Two layers of piezoelectric material (ACX QP10N) are attached to the panels: one on the top surface one on the bottom surface of the panels. Prescribed voltages are statically applied to the piezoelectric actuators, inducing a prestress field which is responsible for the stress stiffening effects when coupled with the nonlinear strain components. Different geometric configuration, laminate stacking sequence, boundary conditions and curvatures are investigated. The study shows that mechanically strain-induced piezoelectric effect increases the rate of occurrence of flutter, stabilizing the plate. This stiffening of the structure is related to the voltage applied on the actuators and the geometrical parameters of the plate. Thus, one can control the occurrence of flutter speed by controlling the voltage applied and the proper design of the geometric properties of the panel and tailoring of the composite laminate.     

Active constrained layer damping of geometrically nonlinear vibrations of smart laminated composite sandwich plates using 1–3 piezoelectric composites

This paper deals with the analysis of active constrained layer damping (ACLD) of geometrically nonlinear vibrations of sandwich plate with orthotropic laminated composite faces separated by a flexible core. The constraining layer of the ACLD treatment is composed of the vertically/obliquely reinforced 1?C3 piezoelectric composites. The Golla?CHughes?CMcTavish method has been implemented to model the constrained viscoelastic layer of the ACLD treatment in time domain. The first-order shear deformation theory and the Von Kármán type nonlinear strain displacement relations are used for analyzing this coupled electro-elastic problem. A three dimensional finite element model of smart laminated composite sandwich plate integrated with ACLD patches has been developed to investigate the performance of these patches for controlling the geometrically nonlinear vibrations of the plates. The numerical results indicate that the ACLD patches significantly improve the damping characteristics of the sandwich plates with laminated cross-ply and angle-ply facings for suppressing their geometrically nonlinear vibrations. Particular emphasis has been placed on investigating the effect of the variation of piezoelectric fiber orientation angle on the performance of the ACLD treatment.     

Flutter stabilization of cantilevered plates using a bonded patch

In recent years, many researchers have studied active vibration suppression of fluttering plates using piezoelectric actuators. Lots of these researchers have focused on optimal placement of piezoelectric patches to obtain maximum controllability of the plate. Although mass and stiffness characteristics of bonded patches can alter the aeroelastic behavior of fluttering plates, few of the investigators have considered the effect of the mentioned parameters in the optimization process. This paper investigates the effect of a bonded patch on the aeroelastic behavior of cantilevered plates in supersonic flow and examines the optimal location of the patch for the best controllability performance. For mathematical simulation of the structure, linear von Karman plate theory along with first-order piston theory is employed. The results obtained through this study reveal that a bonded patch with a small mass ratio can change the system critical dynamic pressure significantly. The maximum raise of the critical dynamic pressure is acquired when the bonded patch is placed on the leading edge of the plate. A variation of the system??s aerodynamic characteristics, subsequently, influences the control performance of the bonded patch and alters the optimal patch location.     

Control of geometrically nonlinear vibrations of skew laminated composite plates using skew or rectangular 1–3 piezoelectric patches

This paper deals with the analysis of active constrained layer damping (ACLD) of geometrically nonlinear transient vibrations of skew laminated composite plates using skew or rectangular patches of the ACLD treatment. The constraining layer of the patch of the ACLD treatment is composed of the vertically/obliquely reinforced 1–3 piezoelectric composite material. The Golla–Hughes–McTavish method has been used to model the constrained viscoelastic layer of the ACLD treatment in the time domain. A coupled electromechanical nonlinear three dimensional finite element model of skew laminated thin composite plates integrated with the skew or rectangular patches of ACLD treatment has been derived. The performance of the patches is investigated for different configurations of their placements on the top surface of the skew substrate plates. The analysis reveals that the ACLD treatment significantly improves the active damping characteristics of the skew laminated composite plates over the passive damping for suppressing their geometrically nonlinear transient vibrations. It is found that even though the substrate laminated plates are skew, a rectangular patch of the ACLD treatment located at the centre of the top surface of the substrate should be used for optimum damping of geometrically nonlinear vibrations of skew laminated composite plates irrespective of their skew angles and boundary conditions. The effects of piezoelectric fiber orientation angle and the skew angles of the substrate plates on the control authority of the ACLD patches have been emphatically investigated.     

Active control of functionally graded laminated cylindrical shells

An analytical method on active vibration control of smart FG laminated cylindrical shells with thin piezoelectric layers is presented based on Hamilton’s principle. The thin piezoelectric layers embedded on inner and outer surfaces of the smart FG laminated cylindrical shell act as distributed sensor and actuator, which are used to control vibration of the smart FG laminated cylindrical shell under thermal and mechanical loads. Here, the modal analysis technique and Newmark’s integration method are used to calculate the dynamic response of the smart FG laminated cylindrical shell with thin piezoelectric layers. Constant-gain negative velocity feedback approach is used for active vibration control with the structures subjected to impact, step and harmonic excitations. The influences of different piezoelectric materials (PZT-4, BaTiO₃ and PZT-5A) and various loading forms on the active vibration control are described in the numerical results.     

复合材料层合板智能结构主动振动控制的边界元法

利用边界元法模拟智能结构的振动控制，推导出具有压电传感器及致动器的复合材料层合板的边界积分方程，应用负速度反馈控制律，研究了复合材料层合板智能结构主动振动控制问题，算例分析证明该方程的正确性。     

Active damping of rotating composite thin-walled beams using MFC actuators and PVDF sensors

The object of this research is to enhance the damping performance for vibration suppression of rotating composite thin-walled beams using MFC actuators and PVDF sensors. The formulation is based on single cell composite beam including a warping function, centrifugal force, Coriolis acceleration and piezoelectric effect. Adaptive capability of the beam is acquired through the use of a negative velocity feedback control algorithm. Numerical analysis is performed using finite element method and Newmark time integration method is used to calculate the time response of the model. It is observed that the feedback control gain has an effect on damping performance. The paper continues with an investigation into influences of parameters such as the rotating speed and the fiber orientation in host structures. Also, it is confirmed that effective damping performance is achievable through the suitable arrangement and distributed size of sensor and actuator pair using case study.     

Active structural-acoustic control of laminated composite plates using vertically/obliquely reinforced 1–3 piezoelectric composite patch

This article deals with the active structural-acoustic control of thin laminated composite plates using vertically reinforced 1–3 piezoelectric fiber-reinforced composite (PFRC) material for constraining layer of active constrained layer damping (ACLD) treatment. A finite element model is developed for the laminated composite plates integrated with ACLD patches and coupled with acoustic cavity to describe the coupled structural-acoustic behavior of the plates enclosing the cavity. Both in-plane and out of plane actuation of the constraining layer of the ACLD treatment have been utilized for deriving the finite element model. The analysis revealed that the vertical actuation dominates over the in-plane actuation. The performance of PFRC layers of the patches has been investigated for active control of sound radiated from thin symmetric and antisymmetric cross-ply and antisymmetric angle-ply laminated composite plates into the acoustic cavity.     

A Viscoelastic Sandwich Finite Element Model for the Analysis of Passive,Active and Hybrid Structures

In this paper we present a finite element model for the analysis of active sandwich laminated plates with a viscoelastic core and laminated anisotropic face layers, as well as piezoelectric sensor and actuator layers. The model is formulated using a mixed layerwise approach, by considering a higher order shear deformation theory (HSDT) to represent the displacement field of the viscoelastic core and a first order shear deformation theory (FSDT) for the displacement field of the adjacent laminated anisotropic face layers and exterior piezoelectric layers. The dynamic problem is solved in the frequency domain with viscoelastic frequency dependent material properties for the core. Control laws are also implemented for the piezoelectric sensors and actuators. The model behaviour in dynamics is assessed with the few solutions found in the literature, including experimental data, and a laminated composite active sandwich application is proposed. In this numerical application, velocity feedback control law is implemented for active control, using co-located piezoelectric patch sensors and actuators.     

Vibration control of a simply supported cylindrical shell using a laminated piezoelectric actuator

Summary This paper develops a novel laminated piezoelectric actuator (LPA) to control the vibration of a cylindrical shell structure, which is fabricated through bonding multiple piezoelectric layers of the same property together. The electromechanically coupled equations of the system are derived based on the classic shell theory. A parametric study is then conducted to evaluate the effects of geometric and physical properties of the actuator on actuating forces. The results show that as the number of layers increases, the actuating forces per voltage produced by LPA in the axial, circumferential and radial directions of the shell all increase noticeably. The active vibration control of a simply supported cylindrical shell using LPA of different layer numbers is simulated as well under a velocity feedback scheme. It is indicated that with the same control voltage the LPA can obtain a better control performance than the conventional single layer piezoelectric actuator as expected and the targeted radial modal vibration of the shell is attenuated significantly.     

压电耦合板主动控制及稳定性分析

本文研究压电耦合板的主动控制及稳定性。压电耦合板在采用作为传感器和驱动器的压电片之间的速度负反馈时 ,能增大系统的阻尼性能。本文以闭环控制系统方法的特征值分析为基础 ,分析研究了其稳定性。研究表明主动控制在增加系统阻尼性能的同时 ,亦可能导致系统出现不稳定现象。文中指出当仅有对点之间的负反馈时 ,系统是渐近稳定的 ;当负反馈增益矩阵呈非对称或对称但非正定时 ,系统可能出现非稳定。文中以算例进一步给予证实。     

基于不同压电材料作动机制的压电层厚度研究

研究了压电材料复合板的3种作动机制,弯曲作动机制、剪切作动机制、混合作动机制,针对粘贴在纤维板上不同厚度的压电作动层,具体分析了复合板的端部位移,研究结果对噪声和振动的主动控制中的模态控制和智能结构静态形状控制提供了一定的参考。