柔性梁内平衡模型降阶与主动控制的实验研究

内平衡降阶方法能够有效地解决柔性结构的模型降阶问题,尤其是对于频率密集结构．然而由于存在如何从物理传感器测量中提取内平衡模态坐标的问题,目前关于内平衡降阶方法的研究大多是在理论上进行探索,少有实验研究和工程应用报道．该文以柔性梁为对象,开展内平衡降阶方法的理论与实验研究,并且基于降阶模型进行主动控制的设计．文中介绍了一个基于DSP TMS320F2812芯片的实验系统,提出了一个从物理传感器测量中提取内平衡模态坐标的近似方法,并且通过仿真与实验验证了该方法的可行性和有效性,基于降阶模型的控制设计能够有效地抑制梁的弹性振动．     

基于Mori-Zwanzig格式和偏最小二乘的非线性模型降阶

本征正交分解及Galerkin投影是解决复杂非线性系统模型降阶问题常用的方法.然而,该方法在构造降阶系统过程中只截取基函数的部分模态,这通常会使得降阶系统不准确.针对该问题,提出了对降阶系统误差进行快速校正的方法.首先应用Mori-Zwanzig格式对降阶系统的误差进行分析,理论上得到误差模型的形式和有效预测变量.再通过偏最小二乘方法构造预测变量和系统误差的多元回归模型,建立误差预测模型.将所构造的误差预测模型直接嵌入到原降阶系统,得到新的降阶系统在形式上等价于对原模型的右端采用Petrov-Galerkin投影.最后给出了新的降阶系统的误差估计.数值结果进一步说明了所提方法能有效地提高降阶系统的稳定性和准确性,且具有较高计算效率.     

基于卷积神经网络气动力降阶模型的翼型优化方法

针对非线性大扰动翼型气动力优化问题,提出了基于卷积神经网络气动力降阶模型的优化方法.该方法用不同形状参数下翼型的气动力数据作为训练信号,训练卷积神经网络翼型气动力降阶模型.采用该气动力降阶模型,以最大升阻比为目标,对翼型进行优化,结果表明该方法可用于大扰动下翼型气动力的预测和优化.该文同时还讨论了池化法和径向基法的训练...     

径向基函数参数化翼型的气动力降阶模型优化

基于小扰动和弱非线性假设,提出了一种基于气动力降阶模型和径向基函数参数化的翼型优化方法.其主要方法是用径向基函数参数化翼型扰动;通过CFD辨识参数扰动对翼型气动力影响的降阶模型核函数;基于叠加法建立了参数变化对翼型气动力影响的降阶模型;最后基于该气动力降阶模型计算并优化翼型升阻特性.NACA0012翼型优化的结果表明基于气动力降阶模型的优化方法是可行的,可以极大地提高翼型优化速度.     

车路耦合非线性振动高阶Galerkin截断研究

将移动车辆模型化为运动的两自由度质量-弹簧-阻尼系统,道路模型化为立方非线性黏弹性地基上的弹性梁,并将路面不平度设定为简谐函数．通过受力分析,建立车路非线性耦合振动高阶偏微分方程．采用高阶Galerkin截断结合数值方法求解耦合系统的动态响应．首次研究不同截断阶数对车路耦合非线性振动动态响应的影响,确定Galerkin截断研究车路耦合振动的收敛性．研究结果表明,对于软土地基的沥青路面,耦合振动的动态响应,需要150阶以上的截断才能达到收敛效果．并通过高阶收敛的Galerkin截断研究了系统参数对车路耦合非线性振动动态响应的影响.     

基于谐波平衡法的尾流激励的叶片振动降阶模型方法

在航空发动机中下游叶片在上游尾流的作用下易发生受迫振动,严重影响叶片的颤振和疲劳性能.对于这种尾流作用下复杂的流固耦合情况需要一种有效的方法来分析.针对这一问题,提出了基于谐波平衡法的尾流激励的叶片振动降阶模型方法.该方法首先将上游尾流Fourier(傅立叶)分解为若干尾流谐波,并计算各尾流谐波下叶片气动力谐波的振幅,得到尾流引起的叶片气动力;再通过叶片的结构运动方程和气动力降阶模型的耦合分析尾流激励下叶片的振动.算例结果表明,该方法可以快速准确地分析尾流激励下叶片的振动特性.     

基于降阶模型和数据驱动的动态结构数字孪生方法北大核心CSCD

针对受动载荷作用的结构,提出了一种基于降阶模型库和机器学习数据驱动的数字孪生构建方法.首先根据物理结构服役过程中可能出现的损伤状态,采用有限单元法建立高保真有限元模型.其次采用Krylov子空间模型降阶方法对模型进行降阶,建立了物理结构各种状态下的降阶模型,形成模型库.最后利用随机森林机器学习算法训练获得模型选择器,通过物理结构上传感器的数据推断当前物理结构的状态,驱动数字孪生体跟随物理结构一同演化.设计制作了一个框架结构物理模型,模拟了结构不同位置损伤及不同损伤程度,验证了提出的数字孪生构建方法.     

矩阵构造法在动力模型物理参数识别中的应用

通过矩阵奇异值分解得到矩阵构造的表达式,并将其应用于动力模型物理参数识别问题.根据矩阵构造表达式的特点,可以使参数识别模型降阶,降阶后的模型与原模型之间的数学和物理性质有明确的对应关系,避免了为忽略高阶频率而采用缩聚方法造成的误差.最后,数值算例获得满意的结果.     

基于等价输入扰动的空间桁架振动控制的研究(英文)

基于等价输入扰动(EID)的方法,通过对抑制外界未知扰动(匹配的或者非匹配的),实现了对空间桁架的振动控制.首先利用有限元分析(FEA),计算空间桁架的质量矩阵,阻尼矩阵,刚度矩阵及输入矩阵,进而建立空间桁架的模型.为了便于分析和设计,利用模态降阶的方法对模型进行降阶处理.在降阶的模型的基础上,设计等价输入扰动观测器观测外部未知扰动.基于观测的结果,进一步地设计了空间桁架的振动控制方法.最后给出数值仿真,以证实所提方法的有效性.     

二阶系统基于奇异值的保结构模型降阶方法（英文）

本文提出了一种二阶系统基于奇异值的保结构模型降阶方法.该方法通过脉冲响应的移位勒让德多项式展开系数直接计算得到二阶系统的可控和可观格拉姆矩阵的低秩因子.然后基于二阶系统的奇异值结构,构造相应的平衡系统,进而通过截断较小奇异值对应的状态得到保结构的降阶系统.最后,通过两个数值实验展示了所提方法的有效性.     

Modelling and analysis of the nonlinear string-mass structure of the vibration absorber

ABSTRACT

In this paper a nonlinear string-mass structure of the vibration absorber is analyzed. This structure is convenient to be installed in vibration damping systems of high buildings for their protection in the case of earthquake. The considered string-mass structure contains a translator movable mass connected with two strings. Due to nonlinear geometric properties of the system the motion of the mass is described with a strong nonlinear second order differential equation. In the paper the approximate procedure for solving of the nonlinear equation of motion is developed. Based on the solution the influence of the string preloading force, slider mass and friction force on the vibration property of the string-mass system is investigated. It is concluded that variation of the preloading string force may be applied as a control parameter for vibration absorption and as the regulator of vibration decay time.     

Nonlinear dynamic characteristics of bi-graphene sheets/piezoelectric laminated films considering high order van der Walls force and scale effect

This paper presents an analytical method to investigate the nonlinear vibration characteristics of bi-graphene sheets/piezoelectric (BGP) laminated films subjected to electric loading based on a nonlocal continuum model, in which the two adjacent layers are coupled by van der Walls force. Utilizing von Kármán nonlinear geometric relation and nonlocal physical relation, the nonlinear dynamic equation of BGP laminated films under electric loading exerted on the piezoelectric layer is found, then the relation between the nonlinear resonant frequency and the nonlinear vibration amplitude for each layer of the BGP laminated films is obtained by using Galerkin method and harmonic-balance method. Results show that the nonlinear vibration amplitude for each layer of laminated films can be controlled by adjusting the electric potential exerted on piezoelectric layer, and the coupled effect of van der Walls force between graphene sheet and piezoelectric layer on the vibration amplitude of each layer depends on the order number of nonlinear resonant frequency and the mode shape.     

转子动力学横向振动基本方程

针对转子动力学系统横向振动基本方程进行研究.将Euler（欧拉）角表示引入转子动力学系统,可以建立描述转子的非线性旋转运动的精细数学模型.并将该精细模型线性化,建立了描述转子动力的基本方程,通过数值算例分析验证了该方程的正确性和有效性.     

惯容器非线性减振与能量采集一体化模型动力学分析

为了解决航天工程中减振和能源供应的问题，构建了一种应用于航天工程的整星减振和能量采集一体化装置，设计并考察了一种基于非线性能量汇(nonlinear energy sink, NES)的新型非线性减振装置，通过以惯容器(inerter)替代传统的惯性元件以减少负载质量，并在该装置中整合了基于超磁致伸缩材料(giant magnetostrictive material, GMM)的能量采集器.在整星减振的实际背景下对其进行了建模、仿真和分析，同时通过数值计算，考察分析了能量采集器采集振动能量的效果，研究结果表明，在合理选择的参数下，该NES-inerter-GMM(NES-I-GMM)装置能够很好地起到减振作用，同时收集一定的振动能量.     

基于导纳方法的大型空间结构被动减振研究

以导纳方法研究空间桁架或框架结构的振动,建立了适合分析各种边界条件下均匀梁的机械导纳的通用计算方法,然后通过导纳函数求解各结构单元传递或损耗的功率,通过对损耗功率较大的单元来增加结构的阻尼特征。根据导纳分析结果,可以寻找阻尼单元的最优位置,对结构进行局修改。     

A numerical approach to design control invariant sets for constrained nonlinear discrete-time systems with guaranteed optimality

A numerical approach to design control invariant sets for constrained nonlinear discrete-time systems with guaranteed optimality is proposed in this paper. The addressed approach is based on the fact that zonotopes are more flexible for representing sets than boxes in interval analysis. Then the solver of set inversion via interval analysis is extended to set inversion via zonotope geometry by introducing the novel idea of bisecting zonotopes. The main feature of the extended solver of set inversion is the bisection and the evolution of a zonotope rather than a box. Thus the shape of admissible domains for set inversion can be broadened from boxes to zonotopes and the wrapping effect can be reduced as well by using the zonotope evolution instead of the interval evolution. Combined with global optimization via interval analysis, the extended solver of set inversion via zonotope geometry is further applied to design control invariant sets for constrained nonlinear discrete-time systems in a numerical way. Finally, the numerical design of a control invariant set and its application to the terminal control of the dual-mode model predictive control are fulfilled on a benchmark Continuous-Stirred Tank Reactor example.     

时滞影响下受控斜拉索的参数振动稳定性

研究了轴向激励作用下受控斜拉索系统主参数共振的时滞效应,考虑了拉索垂度和几何非线性的影响,基于Hamilton变分原理建立了受控斜拉索系统轴向激励下的非线性参数振动方程,利用Galerkin方法得到时滞动力系统,运用多尺度法对受控系统的主参数共振进行了分析,得到了不同时滞值、控制增益时参数振动稳定域和受控拉索的时程曲线.研究表明,时滞影响下斜拉索振动控制系统的效果变差,参数共振的稳定域发生偏移,对受控斜拉索系统的控制效果随着时滞的增大而变差,从而对控制系统的参数设计起到指导作用.     

含间隙非线性弹性超材料的低频宽带机理北大核心CSCD

揭示了基于非线性混沌理论含间隙的非线性局域共振结构的低频宽带形成机理,提出了一类含间隙非线性局域共振结构设计的新理念.在该间隙非线性局域共振系统中,产生了非线性混沌现象,且这种非线性运动可以成功地改变振动噪声中的频谱结构,当系统运动进入混沌状态时,线性谱能量大大削弱,变成了一个连续的宽频谱,进而有效隔离低频线谱.有限元计算结果表明,正是这个间隙引起的非线性混沌现象导致了低频宽带的产生,且理论分析和有限元分析结果高度一致.因此,这类含间隙非线性局域共振弹性超材料结构的设计新思想为局域共振弹性超材料的发展开辟了新天地,且基于非线性混沌理论的低频带隙的形成机理为减振降噪应用研究奠定了非常重要的理论基础.     

Nonlinear vibration analysis of double-walled carbon nanotubes based on nonlocal elasticity theory

The nonlinear free vibration of double-walled carbon nanotubes based on the nonlocal elasticity theory is studied in this paper. The nonlinear equations of motion of the double-walled carbon nanotubes are derived by using Euler beam theory and Hamilton principle, with considering the von Kármán type geometric nonlinearity and the nonlinear van der Waals forces. The surrounding elastic medium is formulated as the Winkler model. The harmonic balance method and Davidon–Fletcher–Powell method are utilized for the analysis and simulation of the nonlinear vibration. The simulation results show that the nonlocal parameter, aspect ratio and surrounding elastic medium play more important roles in the nonlinear noncoaxial vibration than those in the coaxial vibration of the double-walled carbon nanotubes. The noncoaxial vibration amplitudes of only considering nonlinear van der Waals forces are larger than those of considering both geometric nonlinearity and nonlinear van der Waals forces.     

Nonlinear dynamic analysis of a complex dual rotor-bearing system based on a novel model reduction method

In this paper, a dynamic model of a complex dual rotor-bearing system of an aero-engine is established based on the finite element method with three types of beam elements (rigid disc, cylindrical beam element and conical beam element), as well as taking into account the nonlinearities of all of the supporting rolling element bearings. To rapidly and accurately analyze dynamic behaviors of the complex dual rotor-bearing system, a two-level model order reduction (MOR) method is proposed by combining component mode synthesis (CMS) method and proper orthogonal decomposition (POD) technique. The first-level reduced-order model (ROM) of the dual rotors is obtained by CMS method with a high precision for the original system. Then, the POD method is applied to second-level model order reduction to further decrease the degrees of freedom (DOFs) of first-level ROM. Second-level ROM with mode expansion and direct second-level ROM are obtained, and the nonlinear displacement responses of the two ROMs are compared with the first-level ROM. The numerical results demonstrate that the proposed method has a higher computational efficiency and accuracy in terms of mode expansion than the direct model reduction by using POD method. In addition, the nonlinear vibration responses of the dual rotor-bearing system are studied by this second-level ROM in the case of different clearances of the inter-shaft bearing. The results indicate that the dynamic characteristics of the dual rotor-bearing system are very complicated for a large clearance.