用三线摆测定物体对非质心轴的转动惯量

对三线摆的线性近似模型和转动惯量计算公式的由来作了简要说明. 分析了三线摆扭振系统 质心偏移对转动惯量测试的影响，给出了扭振系统质心与三线摆中心轴对齐的判别准则和用 三线摆测定物体对非质心轴转动惯量的工程实用方法. 通过工程实例说明了该方法的有效性 与可靠性. 最后讨论了提高转动惯量实测精度的几项具体措施.     

The influences of both offset and mass moment of inertia of a tip mass on the dynamics of a centrifugally stiffened visco-elastic beam

The present study is concerned with the out-of-plane vibrations of a rotating, internally damped (Kelvin-Voigt model) Bernoulli-Euler beam carrying a tip mass. The centroid of the tip mass, possessing also a mass moment of inertia is offset from the free end of the beam and is located along its extended axis. This system can be thought of as an extremely simplified model of a helicopter rotor blade or a blade of an auto-cooling fan. The differential eigenvalue problem is solved by using Frobenius method of solution in power series. The characteristic equation is then solved numerically. The simulation results are tabulated for a variety of the nondimensional rotational speeds, tip mass, tip mass offset, mass moment of inertia and internal damping parameters. These are compared with the results of a conventional finite element modeling as well, and excellent agreement is obtained. Some numerical results are given in graphical form. The numerical results obtained, indicate clearly that the tip mass offset and mass moment of inertia are important parameters on the eigencharacteristics of rotating beams so that they have to be included in the modeling process.     

有限单元质量质心集中方法的探讨

提出利用单元质量质心集中方法来优化单元惯性效应表征、改善单元力学效应匹配的 思想: 将单元质量质心集中能够建立精确描述单元质点系惯性效应的动力学方程, 进而达到 优化单元惯性效应表征以及改善单元惯性和变形两种力学效应匹配的目的. 本文通过一维问 题的频散效应分析等对该方法的有效性进行了详细的分析和验证.     

三线摆摆线质量对转动惯量精确测量的影响

三线摆法是测量转动惯量的常用方法, 理论上通常都是把摆线作理想处理(即摆线质量趋于0), 但在工程测量中, 被测工件往往较重, 摆线不再是轻质细线, 摆线质量势必会对空载悬盘的转动惯量测量产生影响. 本文应用哈密顿原理和变量替换, 导出三线摆摆线的变张力弦振动方程, 通过对摆线与悬盘连接点(x=0)的运动状态讨论, 推得摆线质量不能忽略情形下的对称式三线摆的转动惯量计算式, 并借助于MATLAB 软件快速便利地进行计算.     

广义协调厚薄通用板单元的动力特性分析

推导了板的有限元运动方程,构造了单元刚度矩阵和考虑转动惯量的单元质量矩阵,并采用 子空间迭代法计算了板的前几阶频率,分析了广义协调厚薄通用板单元ATF-PQ4a的动力特 性,并讨论了转动惯量和剪切变形对固有频率的影响. 结果表明：ATF-PQ4a单元计算结果和 理论解及有限元软件ABAQUS的结果比较吻合,说明在动力学范围内ATF-PQ4a单元能做到厚 薄通用,满足工程需要.     

Dynamic analysis of the variable stiffness support rotor system with elastic rings

Nonlinear Dynamics - Elastic rings are common rotor supporting structure, which have been widely used in aeroengine rotor support system. However, large inertia force and gyroscopic moment may...     

折叠翼飞行器的动力学建模与稳定控制

折叠翼飞行器在变形过程中,其动力学模型呈现多刚体、多自由度和强非线性特点,同时气动力/力矩、压心、质心和转动惯量等参数也会大幅度变化,严重影响飞行稳定性. 由此,本论文将对飞行器的多刚体动力学建模与变形稳定控制进行研究.基于凯恩方法建立了折叠翼飞行器的多刚体动力学模型,并从中得到了变形所产生的附加力和力矩表达式.通过气动计算拟合出气动参数与折叠角之间的函数关系,由此分析了不同折叠角速度下飞行器的纵向动态特性, 结果表明,折叠翼飞行器变形过程中速度、高度和俯仰角均会发生变化,飞行器无法保持稳定飞行.为此提出了一种基于自抗扰理论的飞行器变形过程中的稳定控制方法.将折叠翼飞行器纵向非线性动力学模型中存在的非线性项、耦合项以及参数时变项都视为系统内外总扰动,利用扩张状态观测器对总扰动进行实时估计和补偿, 针对补偿后的系统设计PD控制器,实现了速度通道和高度通道的解耦控制.通过Lyapunov稳定性原理证明了系统的稳定性, 并进行数学仿真验证. 仿真结果表明,基于自抗扰理论设计的稳定控制器能够解决飞行器变形所带来的强非线性和参数时变等问题,保证飞行器的高精度稳定控制.      

DYNAMIC MODELING AND STABILITY CONTROL OF FOLDING WING AIRCRAFT 1)

折叠翼飞行器在变形过程中,其动力学模型呈现多刚体、多自由度和强非线性特点,同时气动力/力矩、压心、质心和转动惯量等参数也会大幅度变化,严重影响飞行稳定性. 由此,本论文将对飞行器的多刚体动力学建模与变形稳定控制进行研究.基于凯恩方法建立了折叠翼飞行器的多刚体动力学模型,并从中得到了变形所产生的附加力和力矩表达式.通过气动计算拟合出气动参数与折叠角之间的函数关系,由此分析了不同折叠角速度下飞行器的纵向动态特性, 结果表明,折叠翼飞行器变形过程中速度、高度和俯仰角均会发生变化,飞行器无法保持稳定飞行.为此提出了一种基于自抗扰理论的飞行器变形过程中的稳定控制方法.将折叠翼飞行器纵向非线性动力学模型中存在的非线性项、耦合项以及参数时变项都视为系统内外总扰动,利用扩张状态观测器对总扰动进行实时估计和补偿, 针对补偿后的系统设计PD控制器,实现了速度通道和高度通道的解耦控制.通过Lyapunov稳定性原理证明了系统的稳定性, 并进行数学仿真验证. 仿真结果表明,基于自抗扰理论设计的稳定控制器能够解决飞行器变形所带来的强非线性和参数时变等问题,保证飞行器的高精度稳定控制.     

Areal moments of inertia revisited: on the distinction between the principal directions

Three commonly used methods to determine the principal moments of inertia of a plane area and their directions are based on: (i) the stationarity condition for the axial moment of inertia, (ii) the eigenvalue analysis, and (iii) Mohr’s circle. In this paper we provide two new derivations, which are based on: (a) the matrix diagonalization and the invariant tensor properties, and (b) the conjugacy property of the moment of inertia vectors. A new general expression is derived which specifies the principal directions of inertia, as well as the directions of the maximum and minimum product of inertia. A comparative study of the five presented approaches is given, which is of interest from both conceptual and methodological points of view. The connection between the deviatoric part of the moment of inertia tensor and Land’s circle of inertia is also given. The presented analysis applies to any two-by-two symmetric second order tensor.     

铁木辛柯梁中的卸载弯曲波及二次断裂

半无限长梁承受恒定弯矩作用后, 如果自由端的初始弯矩突然释放, 将在梁中激发出一列卸载弯曲应力波. 采用铁木辛柯梁和瑞利梁来研究突然卸载所激发出的弯曲波的传播特征. 利用拉普拉斯变换方法进行分析, 首先推导出铁木辛柯梁和瑞利梁中的卸载弯曲波的像函数解析解, 采用数值反变换方法给出了时域上波传播的响应解, 并研究了梁中各点的横向位移、弯矩和剪力随时间的变化规律. 计算结果表明: 与简化的欧拉梁不同, 旋转惯性的引入使铁木辛柯梁和瑞利梁中的弯曲波传播具有强烈的局部化效应, 特别是梁中各点经历的弯矩变化, 和其距离自由端的位置相关, 不同时刻的弯矩峰值大小不同;瑞利梁中离自由端不同距离各点的峰值弯矩先增大后降低, 最后达到一个渐近值;铁木辛柯梁中各点的峰值弯矩总体上随着时间单调增大到同一个渐近值, 该渐近值与欧拉梁中的峰值弯矩值相同, 均为1.43.切应力效应的引入进一步降低了铁木辛柯梁中卸载弯曲波的波速, 同时也使得铁木辛柯梁中弯矩峰值的最大值小于瑞利梁中的最大值. 对于脆性细长梁的纯弯曲断裂, 铁木辛柯梁可以较好地预测二次断裂的发生位置, 相应的碎片尺寸约为7倍梁横截面厚度.      

FORMULATION AND EVALUATION OF AN ANALYTICAL STUDY FOR CYLINDRICAL HELICAL SPRINGS

The free vibration analysis of cylindrical helical springs is carried out by means of an analytical study.In the governing equations of the motion of the springs,all displacement functions are defined at the centroid axis and also the effects of the rotational inertia,axial and shear deformations are included in the proposed model.Explicit analytical expressions which give the vibrating mode shapes are derived by rigorous application of the symbolic computing package MATHEMATICA and a process of searching is used to determine the exact natural frequencies.Numerical examples are provided for fixed-fixed boundary conditions.The free vibrational parameters are chosen as the number of coils(n=4 ～ 14),the helix pitch angle(α=5 ～ 30?) and as the ratio of the diameters of the cylinder and the wire(D/d=4 ～ 18) in a wide range.Validation of the proposed model has been achieved through comparison with a finite element model using two-node standard beam elements and the results available in published literature,which in these cases indicates a very good correlation.     

Random responses of a two-degree-of-freedom structure with strongly nonlinear coupling and parametric interaction

This paper investigates the random responses of a TDOF structure with strongly nonlinear coupling and parametric vibration. With the nonlinear coupling of inertia in the equations of motion of the system being removed by successive elimination, the non-Gaussian moment equation method (NGM) is applied and 69 moment equations are integrated with central cumulative truncation technique. The stochastic central difference-cum-statistical linearization method(SCD-SL) and the digital simulation method(DSM) are also used. A comparison of results by different methods are given and the SCD-SL method is the most efficient method. The project supported by National Natural Science Foundation of China     

EXPERIMENTAL MEASUREMENT OF A MONKEY TOY THAT CAN STAND STEADILY AFTER A 360° SOMERSAULT1)

对一种能空翻360°站稳的猴子玩具进行了实验测量。在实验测量中,用悬挂法测量了质心位置,复摆法测量了转动惯量,拉伸法测量了弹簧刚度。此外,还用数字图像相关法对猴子玩具的运动过程进行了测量。结果表明,通过实验测量结果与理论分析的相互印证,能更好地阐 述猴子玩具运动的力学机理。该实验项目的开展有助于培养学生的实验和科研兴趣。     

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.      

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.     

Quasi-Euler-Poinsot motion of a rigid body

The phase-plane method of nonlinear oscillation is used to discuss the influence of the small dissipation upon the Euler-Poinsot motion of a rigid body about a fixed point. The equations of phase coordinates are applied instead of Eulerian equations, and the global characteristics of the motion of rigid body are analysed according to the distribution and the type of the singular points. A Chaplygin's sphere on a rough plane, a rigid body in viscous medium and one with a cavity filled with viscous fluid are discussed as examples. It is shown that the motions of rigid bodies dissipated by various physical factors have a common qualitative character. The rigid body tends to make a permanent rotation about the principal axis of the largest moment of inertia. The transitive process can change from oscillatory to aperiodic with the decrease in dissipation.     

变刚度可瘪乳胶管的参数激振

当脉动流经过乳胶管时,如果跨壁压力为负,则乳胶管就被压瘪,其截面积和截面惯距都将减小。本文首先导出了上述问题的控制方程——有阻尼 Mathieu 方程,然后再用摄动法求解。证实了截面积和截面惯距的周期变化加强了脉动流的激励、容易使乳胶管发生位移振荡,这与实验结果在定性上是吻合的。     

在微粗糙平面上滚动的Chaplygin球的稳定性

本文利用文献[1]的结果,继续讨论 Chaplygin 球在微粗糙平面上滚动的稳定性。严格证明了在粘性和库仓两种磨擦条件下球绕最大惯量主轴滚动的一致稳定性,和在粘性摩擦条件及球的最大与中间主惯量矩十分接近的前提下球绕最小惯量主轴滚动的不稳定性。     

PrandtlPlane Joined Wing: Body freedom flutter,limit cycle oscillation and freeplay studies

Dynamic aeroelastic behavior of a joined-wing PrandtlPlane configuration is investigated herein. The baseline model is obtained from a configuration previously designed by partner universities through several multidisciplinary optimizations and ad hoc analyses, including detailed studies on the layout of control architecture. An equivalent structural model has then been adopted to qualitatively retain similar aeroelastic properties.Flutter and post-flutter regimes, including limit cycle oscillations (LCOs), are studied. A detailed analysis of the energy transfer between fluid and structure is carried out; the areas in which energy is extracted from the fluid are identified to gain insights on the mechanism leading to the aeroelastic instability. Starting from an existing design of control surfaces on the baseline configuration, freeplay is also considered and its effects on the aeroelastic stability properties of the joined-wing system are investigated for the first time.Both cantilever and free flying configurations are analyzed. Fuselage inertial effects are modeled and the aeroelastic properties are studied considering plunging and pitching rigid body modes. For this configuration a positive interaction between elastic and rigid body modes yields a flutter-free design (within the range of considered airspeeds).To understand the sensitivity of the system and gain insight, fuselage mass and moment of inertia are selectively varied. For a fixed pitching moment of inertia, larger fuselage mass favors body freedom flutter. When the moment of inertia is varied, a change of critical properties is observed. For smaller values the pitching mode becomes unstable, and coalescence is observed between pitching and the first elastic mode. Increasing pitching inertia, the above criticality is postponed; meanwhile, the second elastic mode becomes unstable at progressively lower speeds. For larger inertial values “cantilever” flutter properties, having coalescence of first and second elastic modes, are recovered.     

Particle displacement tracking technique and Cramer-Rao lower bound error in centroid estimates from CCD imagery

An efficient video based, multi-frame particle displacement tracking technique is presented. The technique is demonstrated on a thermocapillary flow. The Cramer-Rao lower bound centroid measurement uncertainty is derived for Gaussian particle images with Poisson noise recorded on a CCD array. The optimal particle image diameter is determined to be approximately 11/2 pixels. The centroid error increases for particle image diameters larger or smaller than the optimal value. The particle centroid results are carried over to the case of a cross-correlation peak centroid estimate. Particle tracking techniques are shown to have higher accuracy than auto or cross-correlation techniques when the individual velocity measurements are averaged over a comparable correlation subregion.A version of this paper was presented at the 13th Symposium on Turbulence, University of Missouri-Rolla, Sept. 21–23, 1992.