考虑可控性的压电作动器拓扑优化设计

压电作动器可以把电能转换成机械能,在结构主动振动控制中具有应用背景. 由于压电作动器的布局对振动控制效果影响很大,因此作动器布局优化一直是结构控制研究的关键之一. 为了提高压电结构控制能量的利用效率,本文提出了以提高结构可控性为目标的压电作动器的拓扑优化方法. 基于经典层合板理论对压电结构进行了有限元建模,并采用模态叠加法将动力控制方程映射到模态空间,推导了基于控制矩阵奇异值的可控性指标. 优化模型中,选取可控性指标指数形式为目标函数,将设计变量定义为作动器单元的相对密度,并基于人工密度惩罚模型构造了压电系数惩罚模型,给出了基于控制矩阵奇异值的可控性指标关于设计变量的灵敏度分析方法. 优化问题采用基于梯度的数学规划法求解. 数值算例验证了灵敏度分析方法和优化模型的有效性,并讨论了主要因素对优化结果的影响.      

考虑可控性的压电作动器拓扑优化设计

压电作动器可以把电能转换成机械能,在结构主动振动控制中具有应用背景.由于压电作动器的布局对振动控制效果影响很大,因此作动器布局优化一直是结构控制研究的关键之一.为了提高压电结构控制能量的利用效率,本文提出了以提高结构可控性为目标的压电作动器的拓扑优化方法.基于经典层合板理论对压电结构进行了有限元建模,并采用模态叠加法将动力控制方程映射到模态空间,推导了基于控制矩阵奇异值的可控性指标.优化模型中,选取可控性指标指数形式为目标函数,将设计变量定义为作动器单元的相对密度,并基于人工密度惩罚模型构造了压电系数惩罚模型,给出了基于控制矩阵奇异值的可控性指标关于设计变量的灵敏度分析方法.优化问题采用基于梯度的数学规划法求解.数值算例验证了灵敏度分析方法和优化模型的有效性,并讨论了主要因素对优化结果的影响.     

基于回传波射矩阵法的复合材料层合框架振动特性分析

将求解弹性杆系结构动态响应的回传波射矩阵法应用于层合框架的固有频率和模态的求解.用回传波射矩阵法得到单位脉冲载荷作用下层合框架的频响函数,然后由频响函数曲线的波峰确定层合框架结构的固有频率.最后通过回传波射矩阵法控制方程系数矩阵的伴随矩阵得到结构的振动模态.将对称铺层简支梁计算结果与用经典理论算得的解析解进行比较,验证了回传波射矩阵法计算结果具有很高的精度.然后对9根杆组成的平面层合框架进行计算,表明回传波射矩阵法可以有效地计算层合框架结构的固有频率和模态.     

简单周期结构波传播主动控制研究

研究了在梁结构插入压电材料的周期结构波传播的一般规律。以梁的弯曲波传播方程的解析解为基础，进一步分析了简单周期结构的波传播的一些固有特性。并在此基础上，以压电材料作为作动器，采用主动控制方法研究了调整结构传播波的带通、带阻的频率范围可行性和有效性。     

一种悬臂梁模态测试方法1)

基于欧拉-伯努利梁理论得到悬臂梁自由振动的振型函数。通过数值计算得出实验用的悬臂梁前五阶振型的节点位置及其与梁长的比值。考虑传感器对悬臂梁固有频率的影响,建立梁-传感器模型进行仿真分析并得出悬臂梁前五阶固有频率。基于节点位置和测点位置,在实验中选择激励点。将具体实验的结果与梁-传感器仿真模型结果进行对比,通过前五阶固有频率的误差分析,发现仿真分析结果与实验结果误差最高为 1.3%。研究完整地叙述了悬臂梁的模态测试流程,可为工程技术人员的模态测试起一定的指导作用。     

弯曲波彩虹捕获效应及其在能量俘获中的应用

弹性波在色散关系经过设计的梯度结构中传播时会产生空间分频现象和波场能量增强现象,即不同频率的弹性波会在结构的不同位置停止向前传播并发生能量聚集,这就是弹性波彩虹捕获效应.其相关研究成果可以促进结构健康监测、振动控制以及能量俘获等领域的发展.本文通过所设计的梯度结构梁,系统地研究了弯曲波彩虹捕获效应及其在压电能量俘获中的应用.首先,利用传递矩阵法获得了梯度结构梁元胞能带结构的解析解,进而分析了弯曲波彩虹捕获效应的产生机理:不同频率的弯曲波会在不同元胞附近群速度减小到零,从而停止向前传播并发生反射;入射波和反射波的叠加,以及群速度减小带来的能量聚集,会显著增强反射处的波场能量.其次,通过有限元仿真和实验验证了弯曲波彩虹捕获效应的空间分频现象和波场能量增强现象.最后,通过有限元多物理场耦合仿真和实验,研究了粘贴PVDF压电薄膜的梯度结构梁相对于均匀梁的弯曲波能量俘获效果及其随入射波频率的变化规律.结果表明,在弯曲波彩虹捕获效应发生频带内,粘贴在梯度结构梁上的PVDF压电薄膜的输出电压约为粘贴在均匀梁相应位置处的PVDF压电薄膜的输出电压的2倍.     

一种新型压电作动器的设计及其特性研究

提出了一种新型压电作动器,这种作动器由一片压电片粘贴在一个弓型梁金属底座上构成.对其变形放大原理进行了理论分析,实验测定了这种压电作动器自由状态下输出变形随驱动电压变化曲线.推导了约束状态下该作动器的输出作动弯矩与驱动电压的关系式;实验测得了约束状态下其中点位移响应幅频特性曲线.实验结果表明本文设计的新型压电作动器与传统压电片作动器相比具有较大的变形输出,具有较宽的稳定工作频率范围,而所需的驱动能量与传统压电片作动器相同,同时在使用上具有可预制、安装方便、可拆卸、对结构表面适应性好等优点.     

旋转圆环动态特性的行波解

基于固体弹性介质中的行波理论,对旋转圆环的固有频率进行了计算.以扩张弯曲梁微元体的运动方程为基础,分析了运动条件下该波导中行波的色散关系.通过分离正行波数和负行波数,解决了行波法计算旋转圆环的固有频率问题.同时给出了波数分离的判断依据,并结合简谐波动的相位封闭原理和传递矩阵建立了旋转圆环的特征方程.数值模拟研究了旋转体...     

一种逆优化设计振动控制作动器的数目和位置的方法

在建立了悬臂梁上粘贴压电陶瓷片实现振动控制的动力学方程的基础上,研究了一种逆优化设计作动器/传感器的数目和位置的方法:用压电陶瓷作为自传感作动器,以悬臂梁的振动控制为研究对象,要求振动控制系统具有一定的模态阻尼比,并以作动器控制力最小为目标函数,优化设计作动器/传感器的数目和位置.最后通过数值算例证明了该方法的有效性.     

基于碰撞升频的MEMS压电振动能量采集系统

论文提出了一种基于碰撞升频机制的微型压电能量采集系统,由一对共振频率不同的悬臂梁平行叠放组成.在外界低频振动激励下,底部低频S形金属曲梁产生共振,在运动过程中碰撞顶部高频微型压电直梁,从而将低频环境振动转换为高频压电梁的振动,解决了压电直梁的固有频率与外界激励频率不匹配问题.论文建立了压电悬臂梁受迫振动、压电悬臂梁与金属悬臂梁碰撞耦合振动的动力学模型,讨论了压电悬臂梁的电压输出特性.通过实验测试了压电能量收集系统和单个压电悬臂梁的开路电压并计算了输出功率,结果表明当振动加速度为1.0g时,升频式压电能量采集系统在25 Hz的激振下输出功率达到8.6 μW,高于单个压电悬臂梁的最大输出功率.     

输液曲管平面内振动的波动方法研究

采用Flügge曲粱模拟弯曲管道,推导了管内流体的加速度,在总体轴线不可伸长假定的基础上建立了曲管平面内振动的动力学方程;采用波动方法,获得了曲管内振动波的传播和反射矩阵,提出了计算曲管平面内振动固有频率的数值方法.算例分析中,通过计算两端固定半圆形曲管的临界流速并与已有文献结果对比,验证了论文方法的正确性.最后,计算了两端固定半圆形曲管在四种不同流速下的前四阶固有频率,结果表明,管内流速的增大会降低管道的固有频率,当流速增大到某一特定值时,管道的一阶固有频率消失.     

Free vibration of axially loaded,rotating Timoshenko shaft systems by the wave-train closure principle

A systematic approach for the free vibration analysis of a rotating Timoshenko shaft system subjected to axial forces is presented in this paper. The system has multiple point discontinuities such as elastic supports, rotor masses, and cross-sectional changes. Wave reflection and transmission matrices are employed to characterize the wave motions between the sub-spans of the shaft system. These matrices are combined with the field transfer matrices expressed in wave forms to obtain the characteristic equation in a straightforward manner. The solutions are exact since effects of attenuating wave components are included in the formulation. The wave propagation-based matrix algebra leads to recursive algorithms which are suitable for computer coding. Three examples are presented to illustrate the numerical procedure.     

Exact static solutions to piezoelectric smart beams including peel stresses. II. Numerical results,comparison and discussion

This part presents the numerical results, comparisons and discussion for the exact static solutions of smart beams with piezoelectric (PZT) actuators and sensors including peel stresses presented in Part I. (International Journal of Solids and Structures, 39, 4677–4695) The actuated stress distributions in the adhesive and the adhesive edge stresses varying with the thickness ratios are firstly obtained and presented. The actuated internal stress resultants and displacements in the host beam are then calculated and compared with those predicted by using the shear lag model. The stresses in the adhesive caused by an applied axial force, bending moment and shear force are calculated, and then used to compute the sensing electric charges for comparison with those predicted using the shear lag model. The numerical results are given for the smart beam with (a) one bonded PZT and (b) two symmetrically bonded PZTs, with a comparison to those predicted using the shear lag model. Novel, simple and more accurate formulas for the equivalent force and bending moment induced by applied electric field are also derived for the host beam with one PZT or two symmetrically bonded PZTs. The symmetric shear stress and the anti-symmetric peel stress components caused by a shear force are discussed. In addition, in the case of PZT edge debonding, the stress redistribution in the adhesive and the self-arresting mechanism are also investigated.     

Active control of flexural waves in a phononic crystal beam with staggered periodic properties

The band gaps of a phononic crystal beam with staggered periodic structure are investigated. The periodic system consists of a pure elastic (i.e. PMMA) matrix beam and some piezoelectric (i.e. PZT) patches with coupling between the mechanical–electrical components. The PZT patches connected by negative capacitance circuits are applied to function as the active control system. Based on the condition at the interface between adjacent unit cells, the transfer matrix and localization factor are derived. The influence of the degree of interlacing and negative capacitance circuits are discussed. The numerical results show that another band gap can be generated by the staggered periodic structure of PZT patches. The widths and locations of the band gaps can be changed by the degree of interlacing.     

Piezoelectric effect on transversal vibrations and buckling of a beam with varying cross section

In this study, the static and dynamic response of a system composed of an Euler-Bernoulli beam with axially restrained ends and a pair of piezo patches symmetrically bonded at a specified localization is investigated. The system is kinematically loaded as a result of the prescribed displacement of one or both supports. By applying an electric field to the piezo patches a residual in-plane stress is generated in the system. The residual force, depending on the direction of the electric field vector, may diminish or enhance the system buckling capacity as well as affecting its natural vibration frequency. In order to acquire approximate solutions to the non-linear dynamic equilibrium equation, a version of the Lindstedt-Poincare method is utilized. With this in mind, the transversal displacements, vibration frequency and axial dynamic force are expanded into exponential series with respect to the small amplitude parameter. The numerical results show the effect of the structural parameters and induced axial piezoelectric force on the stability of the system and its vibration frequency. The amplitude-frequency relationship of the actuated system is also investigated.     

Measurements of dynamic properties of concrete structures using flexural wave propagation characteristics

Flexural wave propagation characteristics influence the impact noise generation of concrete structures that are found in building floors, railroads, bridges, and many other engineering structures. The flexural vibration of the structure is affected by concrete dynamic properties. The purpose of this study is to measure the concrete dynamic characteristics using a wave propagation approach. The flexural wave speeds, bending stiffness and their loss factors were measured. The measured characteristics are essential for understanding sound radiation and vibration dissipation capabilities of the concrete structures. Various concrete beam structures were made and tested. The dynamic stiffness and loss factor were influenced by its components and showed frequency-dependent variation, especially for the measured loss factor.     

轴向力作用任意不连续梁自由振动分析的广义函数解

摘要：首先运用分布理论建立了轴向力作用下含多个不连续点的欧拉梁的自由振动的统一微分方程。不连续点的影响由广义函数（Dirac delta函数）引入梁的振动方程。微分方程运用Laplace变换方法求解;与传统方法不同的是,本文方法适用于含任意类型的不连续点和多种不连续点组合情况的梁,求得的模态函数为整个不连续梁的一般解。由于模态函数的统一化以及连续条件的退化,特征值的求解得到了极大的简化。最后,以轴向力作用下多跨梁—弹簧质量块系统模型为例验证了本文方法的正确性与有效性。     

Lamb波理论及层合板冲击损伤的实验研究

从理论上分析了板中Lamb波信号的传播特性,并给出Lamb波在板中传播的频散方程。理论分析及实验均表明,Lamb波的频散特性与复合材料结构损伤有着直接的联系,而且最低阶的对称和反对称Lamb波模态对层合板的损伤比较敏感,但应用Lamb波的频散效应监测结构的损伤在检测技术上还难以实现。根据板中导波形成Lamb波的共振原理,板中应力波的幅频特性很大程度上反映了Lamb波的谐振特征。因此,利用压电元件的压电阻抗谱分析应力波的各阶模态频率及振幅对结构损伤的变化,能够反映材料内部损伤与Lamb波的频散特性。文中针对表面粘贴压电元件的层合板智能结构,建立了包含Lamb波谐振模式的压电阻抗计算模型。冲击损伤试件的实验表明,由于结构损伤的出现压电阻抗谱中的模态频率及其阻抗幅值等特征信息将发生变化。因此,引入应力波损伤因子可以对结构冲击损伤的存在和程度进行初步评价。该方法基于结构的机-电动态阻抗特性,不受结构的几何形状限制,测试用的压电元件成本低,方法简单可行,有望在智能结构的健康诊断方面获得应用。     

非均匀吸收介质中地震波的广义传播矩阵解法

本文在复频域内,通过应用混合变量粘弹性波方程和线性常微分方程组的指数矩阵解法,给出了一种计算非均匀吸收介质中地震波传播的广义传播矩阵解法。该方法适用于各种粘弹性模型,可模拟任意震源及所产生的各种体波、面波,数值结果表明具有很高的计算精度。     

基于传递函数法的兰姆波解析模拟

论文研究了兰姆波传播的解析模型.薄压电传感器(PZT)被用于兰姆波的激发.为模拟PZT的激励,采用PZT边缘的分布式点源等效PZT的激励,建立了解析模型的边界条件.结合三维傅里叶变换,在频率波数域求解了三维波动方程,得到了在单位周期激励下兰姆波的频域响应.结合传递函数法,可以得到任意激励下兰姆波的频域响应.利用傅里叶逆变换,进一步求解了兰姆波在时间-空间域的全局波场.为了验证解析模型,将解析模拟与实验进行了比对.试验测量值与解析模拟结果相吻合.