斜拉索振动的模糊半主动控制研究

考虑拉索垂度及抗弯刚度的影响,得出了索-阻尼器系统振动偏微分方程;用中心差分法将偏微分方程在空间内离散,导出了系统的面内振动常微分方程组;提出了使用MR阻尼器(Magnetorheological Damper)作为控制设备,模糊集为基础的半主动控制算法,并运用提出的算法对索-阻尼器系统进行了振动控制分析。本文方法的优势在于算法自身的鲁棒性、处理非线性问题的能力强和不需要结构的精确数学模型,算法需要的输入变量少,可以解决实际工程中斜拉索的振动响应信息难以测量的困难。模糊算法的输出直接控制MR阻尼器的输入电压。与LQR-Clipped算法不同,MR阻尼器的输入电压可以是零与最大值之间的任意值。本文以实际斜拉桥拉索为例,分析了拉索的振动控制效果,结果表明本文提出的模糊半主动控制算法,使MR阻尼器的功能得到了更好的发挥,比MR被动控制效果好,且可以减小控制力。     

机械臂臂杆刚度主动控制下的末端振动特性研究

机械臂在运动过程中会因臂杆柔性引发结构变形和弹性振动,降低机械臂末端的定位精度和运动稳定性,将结构振动控制方法用于机械臂的振动抑制研究具有重要意义. 基于变刚度主动控制的设计思想,提出了臂杆刚度主动控制方法,通过改变机械臂臂杆的轴向受力状况来主动改变机械臂的刚度. 采用变形耦合法描述了机械臂的非线性变形,进而结合假设模态法和拉格朗日方程建立了臂杆的变刚度动力学模型,并进行了数值仿真. 在此基础上,设计了基于臂杆刚度主动控制方法的单自由度实验台,分析了不同预紧力下机械臂末端的振动特性. 数值仿真和实验结果表明,随着预紧力的增加,机械臂末端的振动幅值得到衰减,验证了臂杆刚度主动控制方法的有效性. 通过采用响应面法建立了机械臂末端的振动响应与预紧力的关系,并基于内部映射牛顿法的子空间置信域法优化算法对预紧力进行了优化分析,得到了最优预紧力. 该研究可为机械臂的精细动力学建模和振动抑制提供一定的理论依据,并为研究经济型低刚度材料的刚化问题提供了方向,以利用廉价低刚度材料取代目前所应用的昂贵高刚度材料.      

RESEARCH ON VIBRATION CHARACTERISTICS OF THE MANIPULATOR END UNDER ACTIVE CONTROL OF ARM STIFFNESS$^{\bf 1)}$

机械臂在运动过程中会因臂杆柔性引发结构变形和弹性振动,降低机械臂末端的定位精度和运动稳定性,将结构振动控制方法用于机械臂的振动抑制研究具有重要意义. 基于变刚度主动控制的设计思想,提出了臂杆刚度主动控制方法,通过改变机械臂臂杆的轴向受力状况来主动改变机械臂的刚度. 采用变形耦合法描述了机械臂的非线性变形,进而结合假设模态法和拉格朗日方程建立了臂杆的变刚度动力学模型,并进行了数值仿真. 在此基础上,设计了基于臂杆刚度主动控制方法的单自由度实验台,分析了不同预紧力下机械臂末端的振动特性. 数值仿真和实验结果表明,随着预紧力的增加,机械臂末端的振动幅值得到衰减,验证了臂杆刚度主动控制方法的有效性. 通过采用响应面法建立了机械臂末端的振动响应与预紧力的关系,并基于内部映射牛顿法的子空间置信域法优化算法对预紧力进行了优化分析,得到了最优预紧力. 该研究可为机械臂的精细动力学建模和振动抑制提供一定的理论依据,并为研究经济型低刚度材料的刚化问题提供了方向,以利用廉价低刚度材料取代目前所应用的昂贵高刚度材料.     

Force and displacement transmissibility of a quasi-zero stiffness vibration isolator with geometric nonlinear damping

A geometric nonlinear damping is proposed and applied to a quasi-zero stiffness (QZS) vibration isolator with the purpose of improving the performance of low-frequency vibration isolation. The force, stiffness and damping characteristics of the system are presented first. The steady-state solutions of the QZS system are obtained based on the averaging method for both force and base excitations and further verified by numerical simulation. The force and displacement transmissibility of the QZS vibration isolator are then analysed. The results indicate that increasing the nonlinear damping can effectively suppress the force transmissibility in resonant region with the isolation performance in higher frequencies unaffected. In addition, the application of the nonlinear damping in the QZS vibration isolator can essentially eliminate the unbounded response for the base excitation. Finally, the equivalent damping ratio is defined and discussed from the viewpoint of vibration control.     

Analysis and design of the force and displacement transmissibility of nonlinear viscous damper based vibration isolation systems

This study is concerned with the analysis and design of the force and displacement transmissibility of nonlinear viscous damper based vibration isolation systems. Analytical algorithms are derived using the Ritz–Galerkin method to evaluate the transmissibility of SDOF displacement vibration isolation and force vibration isolation systems where a nonlinear viscous damper is used as an energy dissipating device. The results reveal that compared to linear dampers, nonlinear viscous dampers can more significantly improve the system vibration isolation performance in a wider frequency range. A procedure is then proposed based on the analysis results to facilitate the design of nonlinear viscous dampers for system vibration isolation purposes. These results have significant implications for the design of vibration isolation systems in many engineering applications.     

DYNAMIC CHARACTERISTICS OF VIBRATION ISOLATION SYSTEM WITH CUBIC STIFFNESS AND HYSTERESIS 1)

包含立方刚度和Bouc-Wen 型滞回的隔振系统具有复杂的非线性动力学特性。系统无阻尼响应模型可基于无滞回恢复力建立,利用谐波平衡法和泰勒展开求得近似解析解。系统有阻尼响应模型可利用解析/数值联合方法求解,该方法基于谐波平衡法和Levenberg-Marquardt 迭代算法,对于滞回产生的多值非光滑函数项,先计算时域响应再通过快速傅里叶变换求解谐波项系数。上述方法在含水平绞制梁的非线性隔振系统分析中得到有效应用。分析表明,在Bouc-Wen 型滞回和立方刚度的综合影响下,隔振系统呈现渐软–渐硬特性,滞回阻尼和线性阻尼都可以有效抑制共振,但前者高频隔振效果优于后者。     

Restoring force and dynamic loadings identification for a nonlinear chain-like structure with partially unknown excitations

Most of the currently employed vibration-based identification approaches for structural damage detection are based on eigenvalues and/or eigenvectors extracted from dynamic response measurements, and strictly speaking, are only suitable for linear system. However, the inception and growth of damage in engineering structures under severe dynamic loadings are typical nonlinear procedures. Consequently, it is crucial to develop general structural restoring force and excitation identification approaches for nonlinear dynamic systems because the restoring force rather than equivalent stiffness can act as a direct indicator of the extent of the nonlinearity and be used to quantitatively evaluate the absorbed energy during vibration, and the dynamic loading is an important factor for structural remaining life forecast. In this study, based on the instantaneous state vectors and partially unknown excitation, a power series polynomial model (PSPM) was utilized to model the nonlinear restoring force (NRF) of a chain-like nonlinear multi-degree-of-freedom (MDOF) structure. To improve the efficiency and accuracy of the proposed approach, an iterative approach, namely weighted adaptive iterative least-squares estimation with incomplete measured excitations (WAILSE-IME), where a weight coefficient and a learning coefficient were involved, was proposed to identify the restoring force of the structure as well as the unknown dynamic loadings simultaneously. The response measurements of the structure, i.e., the acceleration, velocity, and displacement, and partially known excitations were utilized for identification. The feasibility and robustness of the proposed approach was verified by numerical simulation with a 4 degree-of-freedom (DOF) numerical model incorporating a nonlinear structural member, and by experimental measurements with a four-story frame model equipped with two magneto-rheological (MR) dampers mimicking nonlinear behavior. The results show the proposed approach by combining the PSPM and WAILSE-IME algorithm is capable of effectively representing and identifying the NRF of the chain-like MDOF nonlinear system with partially unknown external excitations, and provide a potential way for damage prognosis and condition evaluation of engineering structures under dynamic loadings which should be regarded as a nonlinear system.     

非线性振动一种稳定的模糊控制方法研究

由于非线性振动系统的非线性本质,在于传统控制理论的线性控制器用于非线性振动控制效果不佳。本文针对非线性振动系统提出了一种模糊自适应滑模控制方案。     

A comparison of different semi-analytical techniques to determine the nonlinear oscillations of a slender microbeam

The purpose of this work is to investigate the dynamic behaviour of an electrically-actuated microbeam. The electromechanical model is based on the strain-gradient elasticity theory and it gives proper account of the nonlinear geometric term due to the mid-plane stretching and of an applied axial load. The free nonlinear vibrations are studied with the energy balance method and the homotopy analysis method Liao (Commun Nonlinear Sci Numer Simul 14(4):983, 2009), thus carrying out a thorough analysis with regard to the nonlinear terms. The analysis is based on a single-degree-of-freedom model, where the nonlinear electric force acting on the beam is approximated by the Chebyshev method and a fringing field correction term is considered as well. A numerical solution, obtained by a 4th order Runge Kutta algorithm, is also proposed as a benchmark for all the semi-analytical results. Major attention is paid to verify the agreement between the different methods and the their accuracy in the pull-in regime.     

含剪力销(锥)螺栓法兰连接结构非线性特性

连接结构广泛应用于航空航天、化工装备和核电站等大型工业装备中。对于轴弯剪组合作用下的连接结构,需要螺栓、法兰和剪力销的联合工作以抵抗外力。本文针对含剪力销(锥)的螺栓法兰连接结构的动力学问题开展研究,将该类结构抽象为三自由度的质量-双线性弹簧系统,建立非线性动力学模型的数学列式,并进行数值求解。重点研究该系统在横向冲击(剪力)下的动力学特性。通过理论分析与数值计算,指出该非线性系统存在3个方向自由度全耦合的振动现象,并阐述该系统自由度的解耦条件;对纵向振动与横向错动的耦合振动频率关系进行讨论并分析其相互联系;研究剪力销倾角对螺栓最大轴向拉力的影响规律并给出关系曲线,指出其最佳设计角度区间。     

DYNAMICS AND CONTROL OF RIGID-FLEXIBLE COUPLING FLEXIBLE SPACECRAFT WITH JOINT CLEARANCE1)

大型柔性航天器展开锁定后,运动副中仍存在大量无法消除的间隙. 铰链间隙直接影响柔性航天器的姿态 运动和有效载荷的指向精度及稳定度,会对航天器的动力学特性造成较大的影响. 针对这一问题, 提出一种含间隙铰 接的航天器刚柔耦合动力学建模与控制方法. 首先建立含间隙的铰链精确动力学模型,从而构建含间隙铰接的柔性结构 动力学模型. 然后利用哈密顿原理和模态离散方法,建立含间隙铰接柔性航天器离散形式的刚柔耦合非线性动力学 模型,采用 Newmark 算法对非线性动力学方程进行求解. 基于压电纤维复合材料 (macro fiber composite, MFC) 驱动器 构建航天器的刚-柔-电耦合动力学方程,采用最优控制设计控制律. 分析了铰链参数、中心刚体转动惯量、间隙尺寸和间隙数目对航天器动力学特性的影响,着重研究了铰链间隙对航天器姿态运动和结构振动的影响作用. 最后采用 MFC 驱动器对航天器施加主动控制. 结果表明,铰链参数和中心刚体转动惯量影响航天器的固有频率;随着铰链间隙尺寸的增大及间隙数目的增多,航天器的整体刚度逐渐减小,而航天器的姿态角和振动位移响应不断增大;通过基于 MFC 的主动控制,能够实现含间隙铰接航天器姿态运动与结构振动的协同控制,并缓解间隙对系统动态特性造成的影响.     

基于机械振动理论的垂直侵彻弹靶作用模型

为了给侵彻引信抗高过载优化设计提供准确的力学输入，将机械振动理论引入侵彻过程建模领域，提出了一种侵彻战斗部刚体运动与一阶轴向振动相结合的垂直侵彻弹靶作用模型。在垂直侵彻过程受力分析的基础上，基于牛顿第二定律建立了战斗部刚体运动模型，基于单自由度弹簧-质量-阻尼系统建立了战斗部一阶轴向振动模型，并采用数值积分的方法获得了垂直侵彻过程中各物理量的变化规律。和火炮试验实测加速度信号的对比分析结果表明:考虑战斗部一阶轴向振动后的垂直侵彻弹靶作用模型能更准确地描述侵彻过程，能更有效地指导侵彻引信的抗高过载优化设计。     

含间隙铰接的柔性航天器刚柔耦合动力学与控制研究

大型柔性航天器展开锁定后,运动副中仍存在大量无法消除的间隙. 铰链间隙直接影响柔性航天器的姿态 运动和有效载荷的指向精度及稳定度,会对航天器的动力学特性造成较大的影响. 针对这一问题, 提出一种含间隙铰 接的航天器刚柔耦合动力学建模与控制方法. 首先建立含间隙的铰链精确动力学模型,从而构建含间隙铰接的柔性结构 动力学模型. 然后利用哈密顿原理和模态离散方法,建立含间隙铰接柔性航天器离散形式的刚柔耦合非线性动力学 模型,采用 Newmark 算法对非线性动力学方程进行求解. 基于压电纤维复合材料 (macro fiber composite, MFC) 驱动器 构建航天器的刚-柔-电耦合动力学方程,采用最优控制设计控制律. 分析了铰链参数、中心刚体转动惯量、间隙尺寸和间隙数目对航天器动力学特性的影响,着重研究了铰链间隙对航天器姿态运动和结构振动的影响作用. 最后采用 MFC 驱动器对航天器施加主动控制. 结果表明,铰链参数和中心刚体转动惯量影响航天器的固有频率;随着铰链间隙尺寸的增大及间隙数目的增多,航天器的整体刚度逐渐减小,而航天器的姿态角和振动位移响应不断增大;通过基于 MFC 的主动控制,能够实现含间隙铰接航天器姿态运动与结构振动的协同控制,并缓解间隙对系统动态特性造成的影响.      

介电弹性作动器主动隔振模糊控制试验研究

采用模糊控制策略,开展介电弹性作动器的主动隔振性能试验研究。基于介电弹性材料的Maxwell应力模型建立了作动器的力电耦合模型,分析了作动器的非线性特性;针对隔振系统设计了Mamdani型模糊控制器,建立了控制电压信号与振动响应之间的关系;在此基础上,开展了介电弹性作动器主动隔振试验研究,并与加速度反馈控制进行了对比。试验结果表明,在相同驱动电压的情况下,基于模糊控制策略的主动隔振性能要优于加速度反馈控制,且能够显著降低由于非线性驱动力导致的倍频响应幅值,有助于提高隔振系统的稳定性。     

Modeling vortex-shedding effects for the stochastic response of tall buildings in non-synoptic winds

This study derives a model for the vortex-induced vibration and the stochastic response of a tall building in strong non-synoptic wind regimes. The vortex-induced stochastic dynamics is obtained by combining turbulent-induced buffeting force, aeroelastic force and vortex-induced force. The governing equations of motion in non-synoptic winds account for the coupled motion with nonlinear aerodynamic damping and non-stationary wind loading. An engineering model, replicating the features of thunderstorm downbursts, is employed to simulate strong non-synoptic winds and non-stationary wind loading. This study also aims to examine the effectiveness of the wavelet-Galerkin (WG) approximation method to numerically solve the vortex-induced stochastic dynamics of a tall building with complex wind loading and coupled equations of motions. In the WG approximation method, the compactly supported Daubechies wavelets are used as orthonormal basis functions for the Galerkin projection, which transforms the time-dependent coupled, nonlinear, non-stationary stochastic dynamic equations into random algebraic equations in the wavelet space. An equivalent single-degree-of-freedom building model and a multi-degree-of-freedom model of the benchmark Commonwealth Advisory Aeronautical Research Council (CAARC) tall building are employed for the formulation and numerical analyses. Preliminary parametric investigations on the vortex-shedding effects and the stochastic dynamics of the two building models in non-synoptic downburst winds are discussed. The proposed WG approximation method proves to be very powerful and promising to approximately solve various cases of stochastic dynamics and the associated equations of motion accounting for vortex shedding effects, complex wind loads, coupling, nonlinearity and non-stationarity.     

基于非线性吸能机理的涡激振动减振理论与实验研究

流致振动现象广泛存在于机械、航空、土木和石油等重要工程领域, 为防止工程结构因流致振动行为而造成疲劳破坏, 有必要对稳定性、动力学响应及其振动控制做深入研究. 本文提出了一种由弹簧和质量块构成的非线性吸能器(nonlinear targeted energy transfer, NTET), 研究了该非线性吸能器对弹性支承圆柱体涡激振动的被动控制影响机制. 基于能量法推导了圆柱体涡激振动非线性被动控制的耦合动力学方程, 通过设计非线性弹簧?质量块构型的NTET, 进一步开展了涡激振动控制的实验研究, 并与理论预测结果进行了较好的对比, 获得提升涡激振动控制效果的最佳参数值. 研究发现, NTET的质量、弹簧刚度以及弹簧预应力等参数会对涡激振动控制效果产生显著的影响. 本文研究结果表明, 该耦合系统中圆柱体和NTET均表现出周期性的稳态振动响应, NTET质量的改变会显著影响系统的耦合频率. 在无预应力状态下, NTET质量越大、刚度越小时, 有更好的减振效果. 当弹簧预应力逐渐增大时, NTET的非线性刚度逐渐变弱, 会降低涡激振动控制性能. 参数分析表明: 随着涡激振动控制性能的提升, 圆柱体的振幅逐渐较小, NTET的振幅逐渐增大, 能量传递效率逐渐提高. 研究结果可为工程中涡激振动控制策略的高效设计提供有用的理论支撑和实验数据.      

半主动TLCD对偏心结构的离散模糊变结构控制

采用在结构水平双向设置TLCD半主动控制装置的方法,对偏心结构在多维地震作用下的离散模糊变结构控制问题进行了研究.首先建立了结构-TLCD扭转耦联控制系统微分方程及其离散化状态空间表达,然后阐述了基于模糊逻辑的变结构控制的基本策略,最后应用该模糊变结构控制策略对一个五层偏心结构的TLCD半主动控制问题进行了仿真分析.仿真分析的结果表明,该方法在对结构的平动反应和扭转反应都能起到较好的减震效果的同时,还具有对结构固有参数不确定性的较强的鲁棒性.     

几何非线性摩擦阻尼隔振系统动力学行为研究

非线性隔振系统由于具有较线性系统更优的隔振性能,因此在工程中应用广泛.本文通过配置与被隔振对象的运动方向相垂直的库伦摩擦阻尼器,构建了几何非线性摩擦阻尼模型.由于引入了几何非线性,因此其摩擦力与位移正相关,这与传统与位移无关摩擦力模型有显著不同.首先,建立了具有几何非线性摩擦阻尼的数学模型以及隔振系统的受迫振动方程;然后,使用谐波平衡法求解了动力学方程,并使用数值仿真方法验证了谐波平衡法求解的准确性;最后,研究了几何非线性摩擦阻尼隔振器的绝对位移传递率和相对位移传递率.研究结果表明,在库伦摩擦阻尼选择适当,非线性摩擦阻尼系统可以在保持高频振动衰减效果的前提下,显著降低系统共振峰,其性能优于传统的恒定摩擦阻尼隔振模型.同时,几何非线性摩擦阻尼系统能够避免传统摩擦阻尼系统中的“锁定”现象,从传递率角度来说,不利于共振峰控制;但从激励环境改变引发隔振系统失效的角度来看,几何非线性摩擦阻尼系统可以拓宽系统对激励幅值的适应范围,避免隔振系统失效.本文的研究结果对此类隔振系统的设计和摩擦阻尼参数的选择具有通用的指导意义.      

Stabilization of a 1/3-order subharmonic resonance using nonlinear dynamic vibration absorber

The paper proposes a stabilization method for a 1/3-order subharmonic resonance with a new type of nonlinear vibration absorber using nonlinear coupling between a main system and the absorber. The main system with nonlinear restoring force and harmonic excitation, i.e., subjected to a sinusoidally changed magnetic force, is introduced as a model which produces a 1/3-order subharmonic resonance. A damped pendulum, whose natural frequency is tuned to be in the neighborhood of twice that of the main system, is connected through a link to the main system as a nonlinear vibration absorber. Theoretical results using the method of multiple scales show that only a stable nontrivial steady state is changed into an unstable one due to the effect of absorber. In addition, we numerically confirm the validity of the proposed absorber using Runge–Kutta method.     

Piecewise constrained optimization harmonic balance method for predicting the limit cycle oscillations of an airfoil with various nonlinear structures

A method is proposed to calculate the periodic solutions of piecewise nonlinear systems. The method is based on analytical derivation of nonlinear multi-harmonic equations of motion. Since periodic variations of nonlinear forces are characterized by different states, the vibration cycle is broken into sequential transition intervals according to the instant sets of state transitions. Analytical formulations of the harmonic coefficients of the nonlinear forces and its derivatives with respect to the harmonic coefficients of displacements are developed. Sensitivities of the harmonic coefficients of periodic solutions are determined for constructing explicit expressions for vibration amplitude levels as a function of structural parameters. Numerical investigations of the limit cycle oscillations and its sensitivities of an airfoil with different piecewise nonlinearities have been performed. The results show that the developed method is capable of determining the periodic solutions and its sensitivities with respect to the structural parameters. In order to guarantee time continuity of the nonlinear force, for the hysteresis model it is not right to track the periodic solutions by using the preload or freeplay as the continuation parameters.