Vibration and damping analysis of a composite plate with active and passive damping layer

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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.     

主动约束层阻尼振动控制研究进展

主动约束层阻尼(Active Constrained Layer Damping, ACLD)是以可控的压电材料代替被动约束层中不可控的约束层,通过可控的约束层主动地控制黏弹性材料的剪切变形以进一步增大其对振动能量耗散的主动阻尼形式,它充分结合了主动控制与被动阻尼作用各自的优势,使得其在结构振动控制方面显示出极好的应用价值.本文首先解释了ACLD的基本结构和阻尼机理,然后综述了最近几年有关ACLD在结构建模,控制方案及结构优化等方面的最新研究进展,最后指出了应用前景并总结了进一步研究的问题.      

具损伤压电智能层合板的动力分析

基于应变能等效原理、高阶剪切变形理论和Hamilton变分原理,考虑复合材料铺设层内的损伤效应,建立了具损伤压电智能层合板的运动控制方程,并运用Galerkin方法进行求解.数值算例中,讨论了损伤效应、厚跨比及压电层厚度与层合板总厚度之比对四边简支压电智能层合板自由振动频率的影响和外部控制电压对其动力响应的影响.     

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.     

带压电层的混合层合板的自由振动和动力响应

基于Reddy高阶剪切变形理论和广义Kármán型方程,用双重Fourier级数展开法求得了四边简支带压电层的混合层合剪切板的自由振动及动力响应的解析解,分析中考虑了热/机/电荷载共同作用,并讨论了温度变化、控制电压、铺层方式对固有频率及动力响应的影响。     

等效刚度对非线性压电俘能系统性能影响研究

基于Hamilton原理，考虑几何非线性和梁的不可伸长条件，建立了五层压电双晶片叠合梁俘能器在直接和参数激励作用下的运动微分方程。利用Galerkin法和谐波平衡法获得了俘能器的位移、输出电压和输出功率的解析解。引入随时间变化的扰动，提出了非线性方程解的稳定性条件。为了对压电俘能器的结构-性能关系进行综合分析，研究了被动层的配置形式、被动层与主动层的厚度比和弹性模量对压电俘能系统性能的影响。结果表明，在叠合梁厚度不变的情况下，采用五层的压电双晶片叠合结构，选择合理的被动层与主动层厚度比、被动层弹性模量、被动层厚度比和负载电阻，可以有效提高能量俘获的效率。     

Dynamic characteristics of a cantilever beam with partial self-sensing active constrained layer damping treatment

The equations of motion governing the vibration of a cantilever beam with partially treated self-sensing active constrained layer damping treatment(SACLD) are derived by application of the extended Hamilton principle. The assumed-modes method and closed loop velocity feedback control law are used to analyze and control the flexural vibration of the beam. The influence of the bonding layer and piezoelectric layer thickness, material properties, placements of the piezoelectric patch and feedback control parameters on the actuation ability of the vibration suppression are investigated. Some design considerations for pure passive, pure active control, and self-sensing active constrained layer damping are discussed. The present work is supported by the National Natural Science Foundation of China (No. 59635140).     

有限长压电层合简支板自由振动的三维精确解

基于三维弹性理论和压电理论，导出了有限长矩形压电层合简支板的动力学方程及相应的边界条件，给出了一种求解压电层合板自由振动三维精确解的方法；分析了正、逆向压电效应对层合板振动频率的影响．本文所述的方法和结果对于求解其他三维动态问题，验证、比较其他简化模型、有限元计算结果以及工程应用都有指导意义．     

自感知主被动阻尼悬臂梁动态特性分析

由Ｈａｍｉｌｔｏｎ原理导出了压电层作约束层作约束层的自感知主被动阻尼控制结构的振动控制方程;由自感知电压引入速度负反馈闭环控制,并由假设模态法将位移按模态展开,求解了悬臂梁结构的动态特征;对被动控制、自感知主动控制、自感知主被动控制的控制效果进行了分析比较;分析了粘弹层厚度变化、材料参数变化以及压电层厚度、位置等结构参数变化对控制效果及模态频率的影响;并对自感知主被动阻尼控制结构的特点和设计中应注     

APPROXIMATE SOLUTIONS FOR TRANSIENT RESPONSE OF CONSTRAINED DAMPING LAMINATED CANTILEVER PLATE

The series composed by beam mode function is used to approximate the displacement function of constrained damping of laminated cantilever plates, and the transverse deformation of the plate on which a concentrated force is acted is calculated using the principle of virtual work.By solving Lagrange＇s equation, the frequencies and model loss factors of free vibration of the plate are obtained, then the transient response of constrained damping of laminated cantilever plate is obtained, when the concentrated force is withdrawn suddenly.The theoretical calculations are compared with the experimental data, the results show：both the frequencies and the response time of theoretical calculation and its variational law with the parameters of the damping layer are identical with experimental results.Also, the response time of steel cantilever plate, unconstrained damping cantilever plate and constrained damping cantilever plate are brought into comparison, which shows that the constrained damping structure can effectively suppress the vibration.     

约束阻尼层合板的稳态响应

基于Reddy分层理论推导出约束阻尼层合板的稳态振动方程,得到了约束阻尼层合板的振动频率和损耗因子;分别分析了约束阻尼层合板的粘弹性夹层厚度、模量对固有频率和损耗因子的影响;得到了稳态振动时振幅和频率曲线以及横向应力与面内应力。数值计算结果表明所采用的算法是可靠的。     

Smart damping of laminated thin cylindrical panels using piezoelectric fiber reinforced composites

In this paper performance of a new piezoelectric fiber reinforced composite (PFRC) material has been investigated for active constrained layer damping (ACLD) of laminated thin simply supported composite cylindrical panels. The constraining layer of the ACLD treatment has been considered to be made of this PFRC material. A finite element model of smart composite panels integrated with the patches of such ACLD treatment has been developed to demonstrate the performance of these patches on enhancing the damping characteristics of thin cross-ply and angle-ply laminated composite cylindrical panels. Particular emphasis has been placed on studying the effect of variation of the piezoelectric fiber orientation in the constraining PFRC layer and the shallowness angle of the panels on the control authority of the patches.     

Assessment of shunted piezoelectric devices for simultaneous noise and vibration reduction: comparison of passive,active and hybrid networks

Structural vibration and noise control of a cavity-backed three-layered smart piezo-coupled rectangular panel system under harmonic or transient loads is achieved by using purely active, passive, and hybrid active/passive piezoelectric shunt networks. Problem formulation is based on the classical lamination plate theory, Maxwell’s equation for piezoelectric materials, linear circuit theory, and wave equation for the enclosed acoustic domain. The orthogonal mode expansions along with the modal coupling theory are employed to obtain the coupled differential equations of the electro-mechanical-acoustic system, which are then put into the convenient state-space form, and subsequently solved numerically in both frequency and time domains. A triple-mode hybrid RLC shunt circuit, in series with an external active voltage source and connected to a single electroded piezoelectric segment, is tuned to the dominant resonance frequencies of the composite structure. The linear quadratic optimal control (LQR) theory is adopted for obtaining the active control gains. The frequency and time domain performances of the passive, active and hybrid multi-modal piezoelectric systems are calculated and discussed in terms of sensor output voltage, local sound pressure, and control effort. It is found that the hybrid control methodology with properly tuned circuit parameters can be an excellent candidate for simultaneous vibration and structure-borne noise control of the cavity-coupled smart panel with decreased control effort. Also, the active control strategy integrated in the hybrid control system is demonstrated to enhance the overall system damping characteristics and improve the control authority at frequencies where the passive shunt network performs weakly. Limiting cases are considered and correctness of the mathematical model is verified by using a commercial finite element software as well as by comparisons with the literature.     

Power transmission through double-walled laminated composite panels considering porous layer-air gap insulation

The acoustic behavior of double-walled laminated composite panels consisting of two porous and air gap middle layers is studied within the classical laminated plate theory （CLPT）. Thus, viscous and inertia coupling in a dynamic equation, as well as stress transfer, thermal and elastic coupling of porous material ave based on the Biot theory. In addition, the wave equations are extracted according to the vibration equation of composite layers. The transmission loss （TL） of the structure is then calculated by solving these equations simultaneously. Statistical energy analysis （SEA） is developed to divide the structure into specific subsystems, and power transmission is extracted with balancing power flow equations of the subsystems. Comparison between the present work and the results reported elsewhere shows excellent agreement. The results also indicate that, although favorable enhancement is seen in noise control particularly at high frequencies, the corresponding parameters associated with fluid phase and solid phase of the porous layer are important on TL according to the boundary condition interfaces. Finally, the influence of composite material and stacking sequence on power transmission is discussed.     

Sound transmission from stiffened double laminated composite plates

An analytical model is developed to investigate the sound transmission loss from orthogonally rib-stiffened double laminated composite plates structure under a plane sound wave excitation, in which first order shear deformation theory is presented for laminated composite plates. By using the space harmonic approach and virtual work principle, the sound transmission loss is described analytically. The validity and feasibility of the model are verified by comparing the present theoretical predictions with numerical results published previously. The influences of structure geometrical parameters on sound transmission loss are subsequently presented. Through numerical results, it can be concluded that the proposed analytical model is accurate and simple in solving the vibroacoustic behavior of an orthogonally rib-stiffened double laminated composite plates.     

复合材料层合板在动集中力作用下的结构声强特性

本文研究了复合材料正交异性层合板在动集中力作用下的结构声强特性。应用MSC/-NASTRAN商业软件计算了复合材料正交异性层合板在动集中力作用下各单元的内力和速度,再应用MATLAB软件得出复合材料层合板的结构声强。算例表明,复合材料正交异性层合板的结构声强流线图与各向同性板存在明显不同的特性。复合材料正交异性层合板的结构声强流线图受边界条件、层合板叠层顺序和层数的影响。从结构声强向量图和流线图可获得关于能量传递路径、源位置和能量汇合点的许多信息。进一步,结构振动产生的噪声可根据上述信息加以控制。     

Amplification of acoustic waves in laminated piezoelectric semiconductor plates

Summary Two-dimensional equations for coupled extensional, flexural and thickness-shear motions of laminated plates of piezoelectric semiconductors are obtained systematically from the three-dimensional equations by retaining lower order terms in power series expansions in the plate thickness coordinate. The equations are used to analyze extensional waves in a composite plate of piezoelectric ceramics and semiconductors. Dispersion and dissipation due to semiconduction as well as wave amplification by a dc electric field are discussed.     

MODELING AND DYNAMICS ANALYSIS OF SHELLS OF REVOLUTION BY PARTIALLY ACTIVE CONSTRAINED LAYER DAMPING TREATMENT

A new model for a smart shell of revolution treated with active constrained layer damping （ACLD） is developed, and the damping effects of the ACLD treatment are discussed. The motion and electric analytical formulation of the piezoelectric constrained layer are presented first. Based on the authors~ recent research on shells of revolution treated with passive constrained layer damping （PCLD）, the integrated first-order differential matrix equation of a shell of revolution partially treated with ring ACLD blocks is derived in the frequency domain. By virtue of the extended homogeneous capacity precision integration technology, a stable and simple numerical method is further proposed to solve the above equation. Then, the vibration responses of an ACLD shell of revolution are measured by using the present model and method. The results show that the control performance of the ACLD treatment is complicated and frequency-dependent. In a certain frequency range, the ACLD treatment can achieve better damping characteristics compared with the conventional PCLD treatment.     

具有叉指式电极的1-3型压电复合材料层合板力电耦合行为的三维精确分析

基于三维弹性理论和压电理论,导出了含有1-3型压电复合材料层的有限长矩形层合简支板的静力平衡方程和边界条件,给出了该层合板在叉指式电极和外力共同作用下力电耦合特性的三维精确解.数值算例的计算结果与有限元解进行了对比,取得了很好的一致性.研究了压电矩阵各向异性和刚度矩阵各向异性以及电势等因素对其挠曲面扭率最大值的影响.数值结果表明层合板扭率最大值的绝对值随压电矩阵各向异性系数Rd的增大而增大并随刚度矩阵各向异性系数Rc的减小而增加.