压电层合板结构振动控制的有限元法

利用有限元方法模拟压电结构的振动控制，从Ｈａｍｉｌｔｏｎ理论出发推导出具有压电传感器及激励器的层合板的电耦合动力方程，应用Ｌｙａｐｕｎｏｖ及负速度反馈控制算来实现振动的控制。     

压电结构振动控制及压电片位置优化的遗传算法

采用比例反馈控制,由线弹性压电层合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.采用三维八节点实体耦合单元(Solid5)模拟压电致动器/感应器,三维实体单元(Solid45)模拟主结构,利用ANSYS中参数化语言(APDL)编写了压电层合智能结构的有限元程序.以零一最优问题来描述致动器/感应器的位置优化问题,用遗传算法(GA)求解.以压电智能悬臂板为数值算例,采用比例反馈控制,研究了瞬时荷载作用下,最优位置和一般位置配置致动器/感应器时智能结构的控制效果.为了进一步验证本文方法的正确性,研究了简谐荷载作用下系统的控制效果.数值结果表明采用遗传算法搜索压电智能结构振动控制中压电致动器/感应器的最优位置是十分有效的并具有较高的计算效率.     

挠性自适应结构振动控制的分析与实验研究

采用自适应结构的原理和方法,对压电元件用于挠性结构振动控制的一些问题进行了探讨。对压电驱动器与结构的匹配关系进行了理论分析,对模态传感/驱动器在挠性悬臂板结构中的布置方案进行了优化设计,并进行了结构的振动控制实验,从而验证了方法的有效性     

Analysis and active control of nonlinear vibration of composite lattice sandwich plates

This paper is devoted to investigate the nonlinear vibration characteristics and active control of composite lattice sandwich plates using piezoelectric actuator and sensor. Three types of the sandwich plates with pyramidal, tetrahedral and Kagome cores are considered. In the structural modeling, the von Kármán large deflection theory is applied to establish the strain–displacement relations. The nonlinear equations of motion of the structures are derived by Hamilton’s principle with the assumed mode method. The nonlinear free and forced vibration responses of the lattice sandwich plates are calculated. The velocity feedback control (VFC) and H_∞ control methods are applied to design the controller. The nonlinear vibration responses of the sandwich plates with pyramidal, tetrahedral and Kagome cores are compared. The influences of the ply angle of the laminated face sheets, the thicknesses of the lattice core and face sheets and the excitation amplitude on the nonlinear vibration behaviors of the sandwich plates are investigated. The correctness of the H_∞ control algorithm is verified by comparing with the experiment results reported in the literature. The controlled nonlinear vibration response of the sandwich plate is computed and compared with that of the uncontrolled structural system. Numerical results indicate that the VFC and H_∞ control methods can effectively suppress the large amplitude vibration of the composite lattice sandwich plates.

     

Finite element analysis of smart functionally graded plates

This paper deals with the derivation of a finite element model for the static analysis of functionally graded (FG) plates integrated with a layer of piezoelectric fiber reinforced composite (PFRC) material. The layer of PFRC material acts as the distributed actuator of the FG plates. The Young’s modulus of the FG plate is assumed to vary exponentially along the thickness of the plate while the Poisson’s ratio is assumed to be constant over the domain of the plate. The finite element model has been verified with the exact solutions for both thick and thin plates. Emphasis has been placed on investigating the effect of variation of piezoelectric fiber angle in the PFRC layer on its actuating capability of the FG plates. The finite element solutions also revealed that the activated PFRC layer is more effective in controlling the deformations of the FG plates when the layer is attached to the surface of the FG plate with minimum stiffness than when it is attached to the surface of the same with maximum stiffness.     

Nonlinear active control of damaged piezoelectric smart laminated plates and damage detection

Considering mass and stiffness of piezoelectric layers and damage effects of composite layers, nonlinear dynamic equations of damaged piezoelectric smart laminated plates are derived. The derivation is based on the Hamilton＇s principle, the higher- order shear deformation plate theory, von Karman type geometrically nonlinear straindisplacement relations, and the strain energy equivalence theory. A negative velocity feedback control algorithm coupling the direct and converse piezoelectric effects is used to realize the active control and damage detection with a closed control loop. Simply supported rectangular laminated plates with immovable edges are used in numerical computation. Influence of the piezoelectric layers＇ location on the vibration control is in- vestigated. In addition, effects of the degree and location of damage on the sensor output voltage are discussed. A method for damage detection is introduced.     

旋转运动柔性梁的时滞主动控制实验研究

对旋转运动柔性梁的时滞主动控制进行实验研究,验证时滞反馈控制的有效性. 实验中采用交流伺服电机带动柔性梁旋转运动,柔性梁上粘贴有压电作动器,用于控制梁的弹性振动. 实验研究考虑如下3种情况:(1)仅使用电机扭矩进行控制,电机扭矩存在时滞;(2)使用电机扭矩和压电作动器同时控制,仅压电作动器存在时滞;(3)使用电机扭矩和压电作动器同时控制,电机和压电作动器存在不同的时滞量. 重点通过实验验证时滞反馈控制的可行性和有效性.      

可控约束阻尼层板的控制实验研究

对具有可控约束阻尼层的板进行了振动控制实验研究． 以压电片作为作动器,根据测量的结构振动信号,反馈控制约束层的变形,抑制板的振动． 对试验件进行了试验模态分析,讨论了压电片的附加位置;采用比例反馈对试验件进行了控制试验;试验给出了控制效果和压电片面积的关系． 研究结果证明,这种利用粘弹性阻尼抑制结构的高频振动,利用压电材料的逆压电效应控制结构的低频振动的主被动杂交控制方式对薄壁结构的振动抑制效果显著,控制频率范围宽,可靠性高．     

压电智能梁振动控制的优化设计

本文研究了压电智能梁振动控制中压电传感作动元件的优化设计,并考虑了控制增益和结构阻尼的影响。采用负速度反馈控制策略及等效阻尼比优化准则。对简支梁和悬臂梁采用遍历搜索的方法计算了不同增益和结构阻尼下的优化,结果对进一步研究优化设计和振动控制有一定的参考价值。     

Infinite-Dimensional Control of Nonlinear Beam Vibrations by Piezoelectric Actuator and Sensor Layers

An infinite-dimensional approach for the active vibration control of a multilayered straight composite piezoelectric beam is presented. In order to control the excited beam vibrations, distributed piezoelectric actuator and sensor layers are spatially shaped to achieve a sensor/actuator collocation which fits the control problem. In the sense of von Kármán a nonlinear formulation for the axial strain is used and a nonlinear initial boundary-value problem for the deflection is derived by means of the Hamilton formalism. Three different control strategies are proposed. The first one is an extension of the nonlinear H-design to the infinite-dimensional case. It will be shown that an exact solution of the corresponding Hamilton–Jacobi–Isaacs equation can be found for the beam under investigation and this leads to a control law with optimal damping properties. The second approach is a PD-controller for infinite-dimensional systems and the third strategy makes use of the disturbance compensation idea. Under certain observability assumptions of the free system, the closed loop is asymptotically stable in the sense of Lyapunov. In this way, flexural vibrations which are excited by an axial support motion or by different time varying lateral loadings, can be suppressed in an optimal manner. A numerical example serves both to illustrate the design process and to demonstrate the feasibility of the proposed methods.     

Multi-pulse chaotic motions of high-dimension nonlinear system for a laminated composite piezoelectric rectangular plate

This paper investigates the multi-pulse global bifurcations and chaotic dynamics of the high-dimension nonlinear system for a laminated composite piezoelectric rectangular plate by using an extended Melnikov method in the resonant case. Using the von Karman type equations, Reddy’s third-order shear deformation plate theory and Hamilton’s principle, the equations of motion are derived for the laminated composite piezoelectric rectangular plate with combined parametric excitations and transverse excitation. Applying the method of multiple scales and Galerkin’s approach to the partial differential governing equation, the four-dimensional averaged equation is obtained for the case of 1:2 internal resonance and primary parametric resonance. From the averaged equations obtained, the theory of normal form is used to derive the explicit expressions of normal form with a double zero and a pair of pure imaginary eigenvalues. Based on the explicit expressions of normal form, the extended Melnikov method is used for the first time to investigate the Shilnikov type multi-pulse homoclinic bifurcations and chaotic dynamics of the laminated composite piezoelectric rectangular plate. The necessary conditions of the existence for the Shilnikov type multi-pulse chaotic dynamics of the laminated composite piezoelectric rectangular plate are analytically obtained. Numerical simulations also illustrate that the Shilnikov type multi-pulse chaotic motions can also occur in the laminated composite piezoelectric rectangular plate. Overall, both theoretical and numerical studies demonstrate that the chaos in the Smale horseshoe sense exists for the laminated composite piezoelectric rectangular plate.     

Active vibration control of thin constrained composite damping plates with double piezoelectric layers

Vibrations and the damping behaviour of thin constrained composite plates with double piezoelectric layers are analytically explored by using Fourier transformation and classical laminated plate theory. Electric potential equations in the double piezoelectric layers are solved with respect to closed and open circuit boundary conditions, an exterior dielectric slab and active control. The natural frequencies and loss factors of the constrained smart composite plates with passive control methods are not notably changed in comparison with those of the constrained composite plates without piezoelectric effects since vibrational energy does not efficiently convert to electrical energy. The loss factors of the composite plates with active constrained damping increase and the natural frequencies have significant variations as the proportional derivative gains increase. Transverse displacement power spectra of the piezoelectric composite plates with active control are compared with those of the piezoelectric composite plates with passive control showing that active control has the best suppression performance of vibrations for the constrained laminated plates with double piezoelectric layers. Radial power spectral density, phase angles and cylindrical-wave power spectral density are calculated. Interesting patterns of wave propagation are explained when plane wave expansion is used to obtain Bessel cylindrical waves.     

A Combined Static/Dynamic Technique for Damage Detection of Laminated Composite Plates

There is a growing demand to develop viable techniques for effective damage detection of composite structures, and the dynamics-based approach has been broadly used in structural health monitoring. A new combined static/dynamic technique for improved damage detection of laminated composite plates is presented. The promise of the technique is that under the sustaining static load, the abnormality of dynamic response due to damage may become more pronounced and easy to be detected. The experimental program consists of testing an E-glass/epoxy composite plate with an embedded delamination under a pre-set static compressive force, and the dynamic response of laminated composite plates is measured using two different actuator–sensor systems: (1) PZT (lead–zirconate–titanate) actuators and scanning laser vibrometer (SLV) sensing system (PZT–SLV), and (2) PZT actuators and Polyvinylidenefluoride (PVDF) sensors (PZT–PVDF). The influence of sustaining static forces to dynamic response of delaminated composite plates is evaluated. The numerical finite element (FE) analysis is also conducted to verify the effectiveness of this technique. The experimental and numerical mode shapes are used to detect the presence, location, and size of the delamination and to study the effect of static load on dynamic response. Two relatively new damage detection algorithms (i.e., Simplified Gapped Smoothing Method (GSM) and Generalized Fractal Dimension (GFD)) are employed to analyze the Uniform Load Surface (ULS) calculated from the experimental and numerical data. From the dynamic response and analysis results using the damage detection algorithms, it is observed that as the sustaining static load increases, the delamination is much easier to be identified through the enlarged damage parameters. The present combined static/dynamic technique is capable of magnifying the effect of damage, thus improving the effectiveness of damage detection.     

智能板模态传感与控制的数值分析

智能结构技术对空间大型柔性结构 振动控制问题具有重要意义,采用独立模态空间控制技术对压电智能板进行主动振动控制是一种常用方法,以前对这一问题的研究仅限于解析的方法,本文采用有限单元法,设计了新的压电模态传感器与致动器,该方法能够适用于形状及边界条件较为复杂的智能板,算例分析证明了该方法的正确性。     

压电薄板屈曲有限元分析及DKQ单元

在机电耦合本构方程基础上,利用Hamilton原理推导了压电薄板屈曲分析的有限元特征方程和机电耦合的内力计算公式,在有限元实现中选择了基于Kirchhoff薄板假定的四边形薄板单元（DKQ单元）,并给出该单元的几何刚度阵及其数值积分方法。在大型通用有限元分析和优化设计软件系统JIFEX中实现了该方法。给出的数值验证了DKQ单元在屈曲分析和压电薄板静力分析中具有较高精度和收敛性,通过机械荷载和电荷载联合作用下的临界荷载计算,表明压电耦合效应能够影响结构的稳定性,可以通过改变外加电压对结构稳定性进行控制。     

Active transient elasto-acoustic response damping of a thick-walled liquid-coupled piezolaminated cylindrical vessel

The linear 3D piezoelasticity theory in conjunction with the versatile transfer matrix approach and the wave equation for the internal acoustic domain are employed for active non-stationary vibroacoustic response control of an arbitrarily thick, tri-laminate, fluid-filled, simply supported, piezocomposite cylindrical tank, excited by arbitrary (non-axisymmetric) time-dependent on-surface mechanical loads. The smart structure is composed of a supporting core layer of functionally graded orthotropic material perfectly bonded to inner and outer spatially distributed radially polarized functionally graded piezoceramic sensor and uniform force actuator (FGPM) layers. Active vibration damping is implemented by transferring the accumulated voltage on the sensor layer to the piezoelectric actuator layer in context of proportional and derivative control laws. Durbin's numerical inverse Laplace transform scheme is utilized to calculate the time response histories of the relevant interface displacement/stress components, center-point acoustic pressure, and actuator voltage, for selected loading configurations (i.e., concentrated step, impulse, and moving external loads). Numerical simulations demonstrate the effectiveness of the adopted distributed sensing/actuation configuration together with the active damping control strategy in suppressing the vibroacoustic response of a three-layered (Ba₂NaNb₅O₁₅/Al/PZT4) water-filled piezoelastic cylindrical tank. Limiting cases are considered and the validity of results is established by comparison with the available data as well as with the aid of a commercial finite element package.     

三跨点阵桁架夹芯梁结构主动振动控制

利用压电作动器/传感器,对三跨沙漏型点阵桁架夹芯梁进行主动振动控制。基于哈密顿原理建立三跨点阵夹芯梁理论模型,采用假设模态法和标准特征值法完成夹芯梁的动力学分析;并利用有限元法建立仿真模型,验证理论结果的有效性和正确性。此外,用压电材料研究主动振动控制方法对多跨夹芯梁的有效性,其中传感器和作动器分别粘贴在夹芯梁上下表面处。该方法对多跨夹芯梁结构的振动控制有一定指导意义。

     

A refined finite element method for bending analysis of laminated plates integrated with piezoelectric fiber-reinforced composite actuators

This research presents a finite element formulation based on four-variable refined plate theory for bending analysis of cross-ply and angle-ply laminated composite plates integrated with a piezoelectric fiber-reinforced composite actuator under electromechanical loading. The four-variable refined plate theory is a simple and efficient higher-order shear deformation theory, which predicts parabolic variation of transverse shear stresses across the plate thickness and satisfies zero traction conditions on the plate free surfaces. The weak form of governing equations is derived using the principle of minimum potential energy, and a 4-node non-conforming rectangular plate element with 8 degrees of freedom per node is introduced for discretizing the domain. Several benchmark problems are solved by the developed MATLAB code and the obtained results are compared with those from exact and other numerical solutions, showing good agreement.     

柔性结构作动器／传感器优化配置研究

从有效衰减振动能量的角度出发,在对位配置作动器／传感器的情况下,通过最小化系统总储能积分,对柔性结构振动主动控制中的作动器／传感器位置及反馈增益进行了优化。在优化方法上,作者提出了一种快速收敛的遗传算法,即“适应度缩放” 加引入“有偏外来移民”的遗传算法。实验结果表明了该方法的有效性和控制系统的良好减振效果。     

Random Vibration Control of Laminated Composite Plates with Piezoelectric Fiber Reinforced Composites

This paper presents an analysis of the active control of random vibration for laminated composite plates using piezoelectric fiber reinforced composites(PFRC). With Hamilton's principle and the Rayleigh-Ritz method, the equation of motion for the resulting electromechanical coupling system is derived. A velocity feedback control rule is employed to obtain an effective active damping in the suppression of random vibration. The power spectral density and meansquare displacements of the random vibration for laminated plates under different control gains are simulated and the validity of the present control strategy is confirmed. The effect of piezoelectric fiber orientation in the PFRC layer on the random vibration suppression is also investigated.The analytical methodology can be expanded to other kinds of random vibration.