复合材料层合板振动衰减主动控制力学模型

简要介绍了新兴的智能复合材料结构及其应用发展前景。对双压电元件复合材料层合板的振动衰减主动控制给出了有限元计算公式,导出了压电激振器、传感器的输入、输出方程,建立了结构振动主动控制的数学模型。     

复合材料层合板自由振动的谱切比雪夫解法EI北大核心CSCD

采用二维谱切比雪夫法(2D-ST),对一般边界条件下复合材料层合板的自由振动进行了分析。基于一阶剪切变形理论(FSDT),采用边界弹簧技术模拟任意边界条件,推导了复合材料层合板的能量方程表达式。利用二维谱切比雪夫法求解能量方程,得到了任意边界条件下复合材料层合板的自由振动特征方程。在数值算例中,通过与其它方法的计算结果进行对比,验证了所提出方法的收敛性和准确性,并在此基础上研究了弹性模量比和铺设角对复合材料层合板振动特性的影响。     

点式压电智能柔性板的振动主动控制的建模与仿真

基于有压电电层的层合板结构的二维传动方程与二维传感方程,导出了粘贴有点压电传感器与执行器的智能板结构的有限元模型的模态振动控制方程与传感方程。由此模态－状态方程,利用线性二次优化方法得到了智能板结构的最优控制输入。     

点式压电智能柔性板振动主动控制的建模与仿真

基于有压电层的层合板结构的二维传动方程与二维传感方程,导出了粘贴有点压电传感器与执行器的智能板结构的有限元模型的模态振动控制方程与传感方程。由此模态-状态方程,利用线性二次优化方法得到了智能板结构的最优控制输入。对在冲击与随机激励下的悬壁智能板的计算机仿真结果,证明了本有限元模型的可行性与有效性。     

温度变化下复合材料层合板的试验模态分析

通过动力测试试验研究了环境条件变化对复合材料层合板振动特性的影响 , 这对于复合材料结构基于动力响应健康监测和振动控制系统设计使用的安全性具有重要意义。在不同温度条件下利用锤击以及激振器实验方法测定复合材料层合板的动力响应 , 采用随机子空间法 (SSI) 识别了其固有频率、 阻尼以及模态振型。研究结果表明 , 复合材料层合板结构固有频率及阻尼比与温度变化存在逆相关关系 , 而所识别的模态振型变化并没有非常清晰的相关关系。分析结果进一步表明 , 复合材料结构振动控制和健康监测系统设计过程中需要考虑上述影响。      

用压电元件实现复合材料层合板振动控制的数值分析

采用板的一阶剪切变形理论，对含有压电材料层的复合材料层合板，从机电耦合的变分方程及Ｈａｍｉｌｔｏｎ原理出发，建立起求解其动态响应 的有限元方程。同时也给出了压电材料层作为传感元件时的传感方程及作为作动元件时的作动方程。并采用速度反馈控制实现了层合板的主动振动。最后给出了计算实例。     

基于灵敏度分析的复合材料层合板优化设计

工程结构中的复合材料层合板的几何参数往往具有随机性质.如何研究随机参数层合板的灵敏度,并对参数进行优化分析,这对正确估计结构设计的可靠性有着非常重要的意义.根据层合板的一阶剪切理论,采用样条有限元法,推导并建立了层合板的振动方程,刚度矩阵,质量矩阵,比例阻尼矩阵以及求解反对称层合板响应灵敏度的计算公式,在基于灵敏度分析的基础上,进行了复合材料层合板的基频分析和优化设计,并用网格法计算最佳铺层角.数值算例验证了算法的有效性.     

各向异性复合材料对称角铺设层合板非线性弯曲强迫振动

笔者曾经研究讨论了各向异性复合材料反对称角铺设层合板的非线性弯曲强迫振动问题[1]。本文是这一研究领域的继续和扩展。在这里,笔者详细研究了各向异性复合材料对称角铺设层合板在简谐激振力作用下的非线性弯曲强迫振动问题,做了包括算例的全解析过程分析,得到了各向异性对称角铺设层合板在各种量级载荷作用下的幅一频关系,分析了对称角铺设层合板结构的铺设方向角对非线性弯曲强迫振动的幅一频关系影响,所求得的解析形式结果保证了结果的可靠性。本文无疑是对复合材料层合板非线性强迫振动问题研究的一个有意义的深入扩展,它们对于探讨其它复合材料结构的非线性动力问题具有一定的意义。      

复合材料角铺设层合板非线性振动特性研究

本文运用渐进摄动法得到复合材料角铺设层合板系统的平均方程在此基础上研究了四边简支碳纤维增强复合材料角铺设层合板在外激励作用下的非线性振动和混沌运动。指出由于复合材料角铺设层合板的强耦合作用而引起该板系统运动控制方程的复杂性,系统平面的振动方程不仅与横向振动方程相耦合而且与中面法线的转角有关。考虑了复合材料角铺设层合板系统在1:1内共振和基本参数共振的情况下的动力学特性,数值模拟得到了复合材料角铺设层合板在参数激励和横向激励联合作用下的复杂周期和混沌运动。     

形状记忆合金纤维正交各向异性层合矩形板的非线性弯曲振动

研究了形状记忆合金(SMA)纤维混杂复合材料大挠度层合板的非线性自由与受迫振动特性。基于描述SMA力学行为的Brinson理论以及层合板材料性能预测的混合率, 建立了SMA纤维混杂复合材料大挠度层合板的本构方程, 基于对称层合各向异性弹性板的非线性理论, 建立了以横向挠度和应力函数表示的板的横向振动方程和相容方程。采用Galerkin近似解法将振动方程化为时间变量的含有三次非线性项的Duffing型常微分方程, 采用谐波平衡法(HBM)获得系统的固有频率方程和强迫振动稳态频率响应方程。数值计算表明: 非线性板自由振动频率比与激励温度的关系具有与线性板相同的特征, 马氏体相向奥氏体相转变阶段温度对板的振动频响特性曲线的影响最显著, 同时也讨论了SMA纤维含量、 板的纵横比以及自由振动幅值对板的非线性频率比的影响。      

Active aeroelastic flutter analysis and vibration control of supersonic composite laminated plate

The active aeroelastic flutter analysis and vibration control at the flutter bounds of the supersonic composite laminated plates with the piezoelectric patches are studied. The piezoelectric patches are bonded on the top and bottom surfaces of the composite laminated plate to act as the sensor and actuator so that the active aeroelastic flutter suppression and vibration control for the supersonic laminated plate can be conducted. The unsteady aerodynamic pressure in supersonic flow is computed by using the supersonic piston theory. Hamilton’s principle with the assumed mode method is used to develop the governing equation of the structural system. The controller is designed by the velocity feedback and proportional feedback control algorithm, and the active damping and stiffness are obtained. The solutions for the complex eigenvalue problem are obtained by using the generalized eigenvalue methodology. The natural frequencies and damping ratios are also gotten. The aeroelastic flutter bounds of the supersonic composite laminated plate are calculated to investigate the characteristics of the aeroelastic flutter. The impulse responses of the structural system are calculated by using the Houbolt numerical algorithm to study the active aeroelastic vibration control. The influences of ply angle of the laminated plate and the control method on the characteristic of flutter and active vibration control are analyzed. From the numerical results it is observed that the aeroelastic flutter characteristics of the supersonic composite laminated plate can be improved and that the aeroelastic vibration response amplitudes can be reduced, especially at the flutter points, by the proportional feedback or the velocity feedback control algorithm using the piezoelectric actuator/sensor pairs. The effectiveness of the flutter control by the two control algorithms is also compared. The results of this study are of great significance to the flutter analysis and aeroelastic design of the aircraft.     

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.     

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。     

对称层合折板结构自由振动分析的移动最小二乘无网格法

提出了一种求解对称层合折板结构自由振动问题的移动最小二乘无网格法。以作者提出的折板无网格模型为基础,将对称层合折板结构视为由不同平面上对称层合板组成的复合结构。先基于一阶剪切变形理论,由移动最小二乘近似推导出各对称层合板的刚度和质量矩阵,再利用板与板间的位移协调条件,将各板的刚度和质量矩阵叠加得到整个结构的刚度和质量矩阵,推导出描述层合折板结构自由振动行为的控制方程。文末算例表明由本文方法得到的解与采用壳单元得到的ANSYS有限元解吻合良好,证明了本文方法的准确性。     

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。     

基于新修正偶应力理论的Mindlin层合板自由振动分析

该文基于各向异性修正偶应力理论建立一个Mindlin层合板（跨厚比10~20的中厚板）自由振动模型。该理论偶应力曲率张量不对称,但偶应力弯矩对称。利用Hamilton原理推导振动微分方程和边界条件。新模型可退化为修正偶应力层合薄板振动模型和经典Mindlin层合板振动模型。以正交铺设简支方板为例计算了偶应力模型的自振频率,分析偶应力Mindlin层合板的自由振动尺度效应。算例表明,该文建立的新修正偶应力层合板模型能够用于分析细观尺度下Mindlin层合板的自由振动及尺度效应。     

基于遗传算法和复合二次径向基函数的复合材料层合板自由振动分析

为了提高复合材料层合板自由振动分析的精度,采用无网格径向基配点法分析复合材料材料层合板的自由振动问题,径向基函数的形状参数对计算精度有很大影响。利用遗传算法对复合二次径向基函数的形状参数进行优化,用优化后的形状参数的复合二次径向基函数计算复合材料层合板的固有频率,计算结果与文献中的结果具有较好的一致性。遗传算法在形状参数优化方面具有很大的潜力,所提出的方法具有较高的计算精度。     

Elastic stability of skew laminated composite plates subjected to biaxial follower forces

The present study investigates the elastic stability of skew laminated composite plates subjected to biaxial inplane follower forces by the finite element method. The plate is assumed to follow first-order shear deformation plate theory (FSDPT). The kinetic and strain energies of skew laminated composite plate and the work done by the biaxial inplane follower forces are derived by using tensor theory. Then, by Hamilton's principle, the dynamic mathematical model to describe the free vibration of this problem is formed. The finite element method and the isoparametric element are utilized to discretize the continuous system and to obtain the characteristic equations of the present problem. Finally, natural vibration frequencies, buckling loads (also the instability types) and their corresponding mode shapes are found by solving the characteristic equations. Numerical results are presented to demonstrate the effects of those parameters, such as various inplane force combinations, skew angle and lamination scheme, on the elastic stability of skew laminated composite plates subjected to biaxial inplane follower forces.     

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.     

Vibration analysis of laminated composite plates with damage using the perturbation method

The present work focuses on vibration characteristics of damaged laminated composite plates. Damage is considered as a local reduction of anisotropic plate stiffness, and three damage factors (representing the damage severity, damage anisotropy, and damage location/area, respectively) are defined to describe damage status in the laminated composite plates. The analytical solutions are obtained by the perturbation method. A numerical analysis is conducted on the vibration of damaged laminated composited plates, and the effect of damage factors on the vibration characteristics is discussed. Results indicate that three damage factors have different influences on the vibration characteristics. Also, the modal curvatures and strain energy show higher damage sensitivity than the natural frequencies and displacement mode shapes. The perturbation-based vibration analysis developed in this study can be used to effectively evaluate the effect of damage on the vibration behavior of anisotropic plates and potentially identify the damage in the laminated plates.