采用压电机敏元件进行结构振动控制Ⅲ：控制系统设计与实验研究

采用作者在上篇导出的压电耦合体动力学模型，给出了压电主动阻尼控制系统的设计方法；导出了压电耦合梁系统的作动方程和检测方程的显式表达式。以此为基础，以简单梁为对象，对压电检测器和作动器的性能、粘结层的影响、压电主动阻尼控制及压电主、被动阻尼双控制进行了实验研究     

空间结构耦合模态控制及实验研究

智能结构以主动元件为传感器和驱动器,根据结构的动态响应和控制要求,自适应地改变结构的动态性能,实现结构特性的自调节功能,以增强结构适应于外界环境变化的能力.结构振动主动控制方法中常用的模态空间控制方法,就是将系统方程转化到模态坐标下,从而得到内部解耦的以模态坐标表示的方程组,然后根据一定的控制方法,计算出模态控制力,实现实时控制.该方法计算简单,效率高,能满足实时控制的需要.本文根据一个三层智能结构主动控制实验,介绍了耦合模态控制理论及实现方法,设计并阐述了压电主元杆件的工作原理,根据Riccati方程得到了主元杆件的最优布置.通过对实验数据运用五点滑动平均平滑法进行处理分析及频谱分析可以看到,智能结构通过主动控制,对相应的控制模态位移及加速度有很大的抑制作用,对应的模态阻尼系数得到了不同程度的提高.     

运动柔性梁非线性振动主动控制的建模与分析

采用运动参考系方法,根据Ｊｏｕｒｄａｉｎ动力学普遍方程,导出了具有给定空间运动的弹性结构的有限元方程,进而得到其闭环振动控制方程,采用分段线性化的思想,由线性二次优化理论导出了有闭环反馈控制的以分段压电片作为执行器的运动柔性杆梁结构非线性振动的主动控制的分析方法,两个算例验证了所提方法的有效性。     

小变形轴力杆件的变形位移方程

从杆件变形量的定义出发,利用两点间距离公式,导出了小变形轴力杆件的变形位移方 程. 此方程形式简洁,计算方便,对线性和非线性材料的小变形问题都可应用,也不必区分静定 结构和超静定结构,还可以方便地处理支座沉陷问题,因而广泛适用于桁架结构的受力分析.     

一类网格结构模型的研究

提出了一类适用于大规模二维网格结构计算的离散模型。该模型以网格节点为研究对象，其控制方程仅与跟节点相连的杆件数目及几何形状有关；只要给出几种基本类型的节点控制方程，就可以对具有相应形式节点的各种规模的网格材料组合其控制方程而求解。这种离散模型形式简单，尤便于在计算机上实现。     

平稳随机激励下随机智能桁架结构振动主动控制中的优化

研究了平稳随机激励下随机智能桁架结构振动主动控制中主动杆的配置位置和闭环控制系统增益的优化问题。考虑结构物理参数、几何尺寸、阻尼同时具有随机性以及作用荷载为平稳随机激励，基于系统最小储存能，构建了具有位移响应均方值、应力响应均方值可靠性约束的主动杆配置和控制增益的优化模型；并对结构平稳随机动力响应的数字特征进行了推导。通过算例，验证了该优化配置模型的合理性和有效性，获得了若干有意义的结论。     

电磁约束阻尼层结构振动主动控制研究

基于弹性、粘弹性、电磁学理论,应用Hamilton原理,导出了覆盖电磁约束层阻尼(EMCLD)主动控制方式的梁的控制方程,并针对覆盖EMCLD的悬臂梁,进行了主动控制仿真模拟,得到了较好的控制效果,分析了控制电流和阻尼层厚度对控制效果的影响.结果表明电磁约束阻尼技术具有结构简单、作动方式合理、耗能低的优点,是一种有效的振动主动控制方式.     

等截面圆弧杆件的转角位移方程

本用力法导出了等同圆弧杆件的转角位移方程,使某些带有圆弧杆件的复杂刚架适用位移法,从而使内力计算工作得到简化。     

压电套筒式拉压双向受力主动杆件设计及测试

压电堆具有体积小、频响快、能耗低以及集传感与驱动于一体等优点。结合二次驱动机械设计原理,开发了适应于结构振动控制的压电套筒式拉压双向受力主动杆件。本文介绍了主动杆件的设计方法及构成部件,并给出了详细的工作原理图,阐述了主动杆件为充分发挥压电堆良好受压性能而将拉力转化为压力的传力途径,并运用Hamilton原理,对主动杆件进行了有限元建模。通过对压电堆的性能测试,得到了压电堆的电压-位移输出关系以及动态性能曲线;通过对压电主动杆件的动力性能测试,得出压电主动杆件适宜于在20Hz～50Hz频段范围内工作;由驱动性能测试,得到了主动杆件的增益函数。本文结论可为进行结构抗振提供设计参考。     

杆件纵向振动中联接刚度的识别

以传递矩阵法为基础，用计算机代数系统编程，导出以联接刚度为未知量的方程，输入杆件纵向振动的第二阶固有频率，从而识别出杆件的联接刚度，并通过实验来验证该法的正确性。     

位移约束下智能桁架的强度最优控制

针对智能桁架结构，提出了在考虑多点位移约束的情况下，使结构工作应力处于最佳状态的规划法最优控制模型。当结构位移约束起主要作用时，模型可在保证位移约束的前提下，同时尽可能提高结构的承载能力；当结构位移并不重要时，仍可用该模型来提高结构的承戴能力。对于复杂结构，为了提高控制效果，可以调整为了满足位移条件而需要的作动器数目及布置方案。文中给出了数值算例，说明该方法的调控能力。     

Optimal placement of piezoelectric active bars in vibration control by topological optimization

A continuous variable optimization method and a topological optimization method are proposed for the vibration control of piezoelectric truss structures by means of the optimal placements of active bars. In this optimization model, a zero-one discrete variable is defined in order to solve the optimal placement of piezoelectric active bars. At the same time, the feedback gains are also optimized as continuous design variables. A two-phase procedure is proposed to solve the optimization problem. The sequential linear programming algorithm is used to solve optimization problem and the sensitivity analysis is carried out for objective and constraint functions to make linear approximations. On the basis of the Newmark time integration of structural transient dynamic responses, a new sensitivity analysis method is developed in this paper for the vibration control problem of piezoelectric truss structures with respect to various kinds of design variables. Numerical examples are given in the paper to demonstrate the effectiveness of the methods.     

Design optimization of truss-cored sandwiches with homogenization

Lightweight metallic sandwich plates comprising periodic truss cores and solid facesheets are optimally designed against minimum weights. Constitutive models of the truss core are developed using homogenization techniques which, together with effective single-layer sandwich approaches, form the basis of a two-dimensional (2D) single-layer sandwich model. The 2D model is employed to simulate the mechanical behaviors of truss-cored sandwich panels having a variety of core topologies. The types of loading considered include bending, transverse shear and in-plane compression. The validities of the 2D model predictions are checked against direct FE simulations on three-dimensional (3D) truss core sandwich structures. Optimizations using the 2D sandwich model are subsequently performed to determine the minimum weights of truss-cored sandwiches subjected to various failure constraints: overall and local buckling, yielding and facesheet wrinkling. The performances of the optimized truss core sandwiches with 4-rod unit cell and solid truss members and pyramidal unit cell with hollow truss members are compared with benchmark lightweight structures such as honeycomb-cored sandwiches, tetrahedral core sandwiches and hat-stiffened single layer plates.     

基于复模态的控制力矩陀螺配置优化

由于陀螺耦合效应,系统动力学方程的特征值和特征向量皆为复数形式,不便于进行控制力矩陀螺的配置优化和控制律设计。本文基于复模态理论,构造出一种实数域上的伪模态矩阵,从而实现方程解耦。综合考虑结构模态、控制输入能量和传感器接收能量的复合优化准则,获得了控制力矩陀螺的最优配置。结果表明,采用线性二次型最优控制,能够快速将结构的响应振幅降至5%以内,验证了使用伪模态矩阵进行方程解耦的可行性及控制的有效性。     

Minimum weights of pressurized hollow sandwich cylinders with ultralight cellular cores

Long, open-ended, hollow sandwich cylinders with ultralightweight cellular cores are optimized under uniform internal pressure for minimum weight design. Five different core topologies are considered: Kagomé truss, single-layered pyramidal truss, double-layered pyramidal truss, single-layered corrugated core and double-layered corrugated core. The highly porous cellular materials are homogenized to obtain effective constitutive relations. Close-formed solutions are presented for the forces and stresses in individual structural members of the sandwich, which are then validated by finite element calculations. Optimization of the sandwich-walled hollow cylinder is achieved using a quadratic optimizer, subjected to the constraints that none of the following failure modes occurs: facesheet yielding; facesheet punch shearing (active only for truss-cored sandwiches); core member buckling; core member yielding. In comparison with hollow cylinders having solid walls, truss-core sandwich cylinders and single-layer corrugated core sandwich cylinders are found to have superior weight advantages, especially for more heavily loaded cases. With the consideration of both weight efficiency and failure modes, sandwich-walled hollow cylinders having Kagomé truss core with pyramidal sub-geometry have the best overall performance in comparison with other core topologies.     

大挠性航天桁架结构动力学及其主动控制研究进展

针对大挠性桁架结构在航天领域的工程应用背景, 对大挠性航天桁架结构进 行系统分类, 综述了几种常见的大挠性桁架结构(桁架式空间站/空间承载结构、网状反射天 线的支撑结构、环形张紧桁架可展开天线、变几何桁架结构)的研究进展、结构动力学建模 进展、主动杆建模进展以及主动控制理论和实验研究进展, 并结合大挠性航天桁架动力学和 主动控制的现状, 对这一领域的研究进行展望.     

Topological sensitivity to diagonal member flips of two-layered statically determinate trusses under worst loading

The paper deals with the topological sensitivity of free, unsupported, statically determinate plane trusses whose horizontal and vertical members form two horizontal layers of square cells and two or more vertical layers. The topology of a truss is decomposed into a form vector – the placement of cells containing diagonal members – and a binary vector describing the slopes of the diagonals. The construction of complete form and slope spaces is provided for any number of vertical layers. Using exhaustive search, forms with minimum and maximum sensitivity to slope change are found for trusses with 2 × 2 through 2 × 8 layers under worst static load condition, represented by the lowest eigenvalue of the least-squares equilibrium matrix. Typical features of the least and most sensitive forms and associated loads and internal forces are shown. Changes of absolute and relative topological sensitivities with increasing number of vertical layers are discussed.     

粘弹性复合桁架动态特性温度影响的实验研究

通过实验研究了一种可用于桁架结构阻尼控制的粘弹性阻尼构件的动力学特性和温度特性。在此基础上,进一步就环境温度变化对粘弹性复合结构动力学特性的影响作了实验分析。实验结果表明：粘弹性阻尼构件对结构阻尼控制的效果明显,环境温度的变化直接影响粘弹性阻尼担构件的动力学特性,并通过阻尼构件引真情整体结构动力学特性的改变。     

压电桁架作动器/传感器优化配置算法研究

针对自适应压电桁架结构振动控制,建立了作动器/传感器优化配置数学模型,并提出一种优化配置的新方法。为了减少结构分析次数,该方法将近似概念、对偶法和遗传算法相结合,首先采用多点近似技术建立原问题的序列近似问题,再对近似问题中的作动器/传感器位置离散变量和控制增益连续变量采用遗传算法和对偶方法分别寻优的分层优化策略。为了提高近似问题对原问题的逼近程度,本文提出一种适于离散变量结构优化的分段多点近似函数。算例表明本文方法能够以很少的结构分析次数得到最优解。