A simple and efficient fourth-order approximation solution for nonlinear dynamic system

In the present paper, based on the classical Magnus expansion, a simple and efficient fourth-order integrator is given for an arbitrary nonlinear dynamic system, which can preserve the qualitative properties of the exact solution. The proposed method can be considered an averaging technique, and only requires evaluations of exponentials of simple unidimensional integrals. Finally, the numerical examples are given to demonstrate the validity and effectiveness of the method of this paper.     

Adaptive explicit Magnus numerical method for nonlinear dynamical systems

Based on the new explicit Magnus expansion developed for nonlinear equations defined on a matrix Lie group, an efficient numerical method is proposed for nonlinear dynamical systems. To improve computational efficiency, the integration step size can be adaptively controlled. Validity and effectiveness of the method are shown by application to several nonlinear dynamical systems including the Duffing system, the van der Pol system with strong stiffness, and the nonlinear Hamiltonian pendulum system.     

Forecasting supercritical and subcritical Hopf bifurcations in aeroelastic systems

A novel method of forecasting bifurcations based on only the observation of the pre-bifurcation regime is proposed. The method is an extension of previous approaches with a focus on oscillatory systems. The method also enables the use of much less measurement data. Numerical results are presented to demonstrate that this new approach predicts the post-bifurcation regime accurately and to explore the robustness of this method to process noise.     

A modified incremental harmonic balance method for rotary periodic motions

The determination of periodic solutions is an essential step in the study of dynamic systems. If some of the generalized coordinates describing the configuration of a system are angular positions relative to certain reference axes, the associated periodic motions divide into two types: oscillatory and rotary periodic motions. For an oscillatory periodic motion, all the generalized coordinates are periodic in time. On the other hand, for a rotary periodic motion, some angular coordinates may have unbounded magnitude due to the persistent circulation about their pivots. In this case, although the behaviour of the system is periodic physically, those angular coordinates are not periodic in time. Although various effective methods have been developed for the determination of oscillatory periodic motion, the rotary periodic motion can only be determined by brute force integration. In this paper, the incremental harmonic balance (IHB) method is modified so that rotary periodic motions can be determined as well as oscillatory periodic motions in a unified formulation. This modified IHB method is applied to a practical device, a rotating disk equipped with a ball-type balancer, to show its effectiveness.     

Nonlinear integral resonant controller for vibration reduction in nonlinear systems

A new nonlinear integral resonant controller (NIRC) is introduced in this paper to suppress vibration in nonlinear oscillatory smart structures. The NIRC consists of a first-order resonant integrator that provides additional damping in a closed-loop system response to reduce high-amplitude nonlinear vibration around the fundamental reso-nance frequency. The method of multiple scales is used to obtain an approximate solution for the closed-loop system. Then closed-loop system stability is investigated using the resulting modulation equation. Finally, the effects of different control system parameters are illustrated and an approximate solution response is verified via numerical simulation results. The advantages and disadvantages of the proposed controller are presented and extensively discussed in the results. The controlled system via the NIRC shows no high-amplitude peaks in the neighboring frequencies of the resonant mode, unlike conventional second-order compensation methods. This makes the NIRC controlled system robust to excitation frequency variations.     

刚柔耦合约束多体系统的动力分析

本文提出了描述柔性多体系统的牵连坐标系统。该系统由惯性参考系,牵连坐标系,物体坐标系及单元坐标系组成,实现了对刚体平动,刚体转动及弹性运动的连续分解,最大限度地消除了由于刚体大角度转动导致的非线性特性。以有限元法为基础,应用拉格朗日方程建立了在该坐标下的刚柔耦合约束多体系统的动力学控制方程。该方程具有耦合程度小、易于推导、编程及求解等优点,为大规模约束多体系统的动力分析提供了新的途径。本文还讨论了平面铰链约束的约束形式及约束方程,最后给出了一个典型多体系统的数值算例。     

ADAPTIVE REGULATION OF HIGH ORDER NONHOLONOMIC SYSTEMS

The problem of adaptive regulation of a class of high-order parametric non holonomic systems in chained-form was discussed. Using adding a power integrator technique and state scaling with discontinuous projection technique, a discontinuous adaptive dynamic controller was constructed. The controller guarantees the estimated value of unknown parameter is in the prescribed extent.     

Adaptive robust fuzzy control for a class of uncertain chaotic systems

In this paper, the output feedback control of uncertain chaotic systems is addressed via an adaptive robust fuzzy approach. Fuzzy logic systems are employed to approximate uncertain nonlinear functions in the chaotic systems. Because only partial information of the system’s states is needed to be known, an observer is given to estimate the unmeasured states. Compared with the existing results in the observer design, the prior knowledge on dynamic uncertainties is relaxed and a class of more general chaotic systems is considered as well as robustness to the approximation error is improved. It can be proven that the closed-loop system is stable in the sense that all the variables are bounded. Simulation example for the unified chaotic systems is given to verify the effectiveness of the proposed method. This work was supported in part by the National Natural Science Foundation of China (60874056) and the Foundation of Educational Department of Liaoning Province (2008312).     

Non-intrusive hybrid interval method for uncertain nonlinear systems using derivative information

This paper proposes a new non-intrusive hybrid interval method using derivative information for the dynamic response analysis of nonlinear systems with uncertain-butbounded parameters and/or initial conditions. This method provides tighter solution ranges compared to the existing polynomial approximation interval methods. Interval arithmetic using the Chebyshev basis and interval arithmetic using the general form modified affine basis for polynomials are developed to obtain tighter bounds for interval computation.To further reduce the overestimation caused by the "wrapping effect" of interval arithmetic, the derivative information of dynamic responses is used to achieve exact solutions when the dynamic responses are monotonic with respect to all the uncertain variables. Finally, two typical numerical examples with nonlinearity are applied to demonstrate the effectiveness of the proposed hybrid interval method, in particular, its ability to effectively control the overestimation for specific timepoints.     

Determination of mode shapes using wavelet transform of free vibration data

In this article, a new method is proposed to determine the mode shapes of linear dynamic systems with proportional viscous damping excited by an impact force. The time signals of responses and a priori knowledge of the natural frequencies are required in this method. The method is particularly suitable for the wavelet techniques which can precisely estimate the natural frequencies. A previously proposed method based on a modified Morlet wavelet function with an adjusting parameter is used to identify the natural frequencies and damping ratios of system, and the mode shapes are estimated using the proposed method in this work. It is shown that the extracted mode shapes are not scaled. Therefore, mass change method is used for scaling the mode shapes. Moreover, the effect of noise on the extracted modal parameters is investigated. The validity of method is demonstrated using numerical and experimental case studies.     

Identification of Fractional Systems Using an Output-Error Technique

An original method for modeling, simulation and identification of fractional systems in the time domain is presented in this article. The basic idea is to model the fractional system by a state-space representation, where conventional integration is replaced by a fractional one with the help of a non-integer integrator. This operator is itself approximated by a N-dimensional system composed of an integrator and of a phase-lead filter. An output-error technique is used in order to estimate the parameters of the model, including the fractional order N. Simulations exhibit the properties of the identification algorithm. Finally, this methodology is applied to the modeling of the dynamics of a real heat transfer system.     

不确定车轨耦合系统辛随机振动分析

建立了轨道不平顺作用下具有不确定参数车轨耦合系统随机振动评估方法. 车辆系统采用物理坐标下多刚体系统模型,并应用高斯随机变量模拟车体、转向架和轮对一系、二系连接系统中动力学参数具有的不确定性. 采用无穷周期结构进行弹性轨道模拟,在哈密顿状态空间下建立了典型轨道子结构的状态运动方程,通过轮轨耦合关系建立了混合 物理坐标及辛模态坐标车轨耦合系统运动方程. 应用Hermite正交多项式展开得到了耦合系统动力响应相对于不确定性参数的控制方程. 由于利用轨道周期特性建模,所获得的控制方程有效地降低了方程维度. 轮轨接触处轨道不平顺载荷模拟为完全相干多分量平稳随机过程,推广和发展虚拟激励法建立了耦合系统随机振动受不确定动力学 参数影响的量化评估方法. 通过Monte Carlo数值模拟,验证了该方法在不确定参数变异很大时也能够保持较好的精度,具有一定的工程实用性.     

Variable knot-based spline approximation recursive Bayesian algorithm for the identification of Wiener systems with process noise

Wiener systems consist of a linear dynamic block in cascade with static nonlinearity. One of the challenging issues in the identification of a process noise disturbed Wiener system is that the influence of noise is difficult to eliminate. For Wiener systems with process noise, traditional algorithms will result in biased estimates. To solve this problem, a novel recursive Bayesian algorithm based on variable knot spline approximation is proposed in this paper. First, a spline function is taken to approximate the inverse function of the nonlinear part, which can achieve excellent extrapolation and eliminate oscillatory behaviors. A knot selection method is then presented to achieve accurate estimates. Furthermore, a knot variation strategy to improve the accuracy of the spline approximation is described. Finally, the proposed algorithm is validated through a numerical simulation.     

Dynamics and optimal control of multibody systems using fractional generalized divide-and-conquer algorithm

In this paper, a new framework is presented for the dynamic modeling and control of fully actuated multibody systems with open and/or closed chains as well as disturbance in the position, velocity, acceleration, and control input of each joint. This approach benefits from the computed torque control method and embedded fractional algorithms to control the nonlinear behavior of a multibody system. The fractional Brunovsky canonical form of the tracking error is proposed for a generalized divide-and-conquer algorithm (GDCA) customized for having a shortened memory buffer and faster computational time. The suite of a GDCA is highly efficient. It lends itself easily to the parallel computing framework, that is used for the inverse and forward dynamic formulations. This technique can effectively address the issues corresponding to the inverse dynamics of fully actuated closed-chain systems. Eventually, a new stability criterion is proposed to obtain the optimal torque control using the new fractional Brunovsky canonical form. It is shown that fractional controllers can robustly stabilize the system dynamics with a smaller control effort and a better control performance compared to the traditional integer-order control laws.

     

航天器与运载火箭耦合分析相关技术研究进展

本文以载荷分析为主要内容, 概述航天飞行器结构动力学研究的一些进展. 首先介绍航箭(航天器/运载火箭简称为航箭) 耦合系统载荷分析基本思想. 然后介绍以下3 个方面的载荷分析方法: (1) 采用基础激励理论初始载荷分析的近似方法; (2) 考虑航箭耦合影响的航天器/运载耦合系统分支模态综合法. 导出采用约束模态质量界面加速度的航天器载荷计算方法; 当仅考虑静定约束特殊情况时, 退化的方程与Chen 采用有限元法导出的方程相同. 给出新航天器载荷瞬态分析技术, 即一个以前的航天器/运载耦合系统载荷结果可以用来获得相同运载火箭发射一个新航天器结构的必要的载荷信息. (3) 考虑航箭耦合影响的航天器/运载耦合系统模态综合法. 包括: 固定界面模态综合法, 以及航天器/运载耦合的界面综合动态响应计算新方法. 最后, 介绍验证载荷分析技术. 简要讨论验证技术的重要性, 提出了采用试验与理论相结合的结构动态试验仿真技术,该方法包括了一套修正数学模型的新技术, 称之为子结构试验建模综合技术. 该方法已应用于复杂的结构建模. 在进行CZ-2E 运载火箭实尺模态试验之前, 用建议的模态试验仿真技术给出CZ-2E 模态参数的预示结果, 并与随后获得的实际模态试验结果相比, 两个结果彼此之间高度一致. 这个结果证明了模态试验仿真技术已成功地预示了CZ-2E 运载火箭的模态参数, 验证了建议的模态试验仿真技术的可靠性. 讨论了振动台振动试验仿真技术. 介绍了振动台振动试验仿真的几个关键技术. 包括: 有限元模型修正技术, 40 t 振动台系统台面控制仿真方法和D 卫星振动台振动试验仿真.      

基于动力学响应的多组件系统布局优化方法

针对圆形安装板上多组件布局问题,以组件系统静平衡性为约束,以系统在随机振动下的动力学响应为优化目标,建立了多组件系统的动力学布局优化模型。针对所建立的优化模型,提出采用序列二次规划方法和改进遗传算法相结合的策略进行多约束条件下的组件布局优化。最后,对两个典型算例进行了动力学优化计算,结果表明,本文所建立的优化模型在多约束的情况下可提高组件系统的动力学性能,满足静力学和动力学性能要求。     

Dynamic response of a single-mesh gear system with periodic mesh stiffness and backlash nonlinearity under uncertainty

Parametric uncertainties play a critical role in the response predictions of a gear system. However, accurately determining the effects of the uncertainty propagation in nonlinear time-varying models of gear systems is awkward and difficult. This paper improves the interval harmonic balance method (IHBM) to solve the dynamic problems of gear systems with backlash nonlinearity and time-varying mesh stiffness under uncertainties. To deal with the nonlinear problem including the fold points and uncertainties, the IHBM is improved by introducing the pseudo-arc length method in combination with the Chebyshev inclusion function. The proposed approach is demonstrated using a single-mesh gear system model, including the parametrically varying mesh stiffness and the gear backlash nonlinearity, excited by the transmission error. The results of the improved IHBM are compared with those obtained from the scanning method. Effects of parameter uncertainties on its dynamic behavior are also discussed in detail. From various numerical examples, it is shown that the results are consistent meanwhile the computational cost is significantly reduced. Furthermore, the proposed approach could be effectively applied for sensitivity analysis of the system response to parameter variations.     

随机激励的耗散的Hamilton系统理论的研究进展

近几年中,利用Ｈａｍｉｌｔｏｎ系统的可积性与共振性概念及Ｐｏｉｓｓｏｎ括号性质等,提出了高斯白噪声激励下多自由度非线性随机系统的精确平稳解的泛函构造与求解方法,并在此基础上提出了等效非线性系统法,提出了拟Ｈａｍｉｌｔｏｎ系统的随机平均法,并在该法基础上研究了拟Ｈａｍｉｌｔｏｎ系统随机稳定性、随机分岔、可靠性及最优非线性随机控制,从而基本上形成了一个非线性随机动力学与控制的Ｈａｍｉｌｔｏｎ理论框架．本文简要介绍了这方面的进展．     

含随机参数的多体系统动力学分析

基于Lagrange方程建立了含随机参数的多体系统的动力学 模型,利用广义坐标分离法将随机微分代数方程转化为随机纯微分方程,利用Newmark法进行数值解算. 应用随机因子法求解系 统随机响应的数字特征,获得统计意义下的解. 以旋转杆滑块系统为例,考虑系统中载荷、物理和几何参数的随机性,通过与Monte Carlo法结果的对比验证了文中方法的正确性和有效性. 计算结果表明,部分随机参数的分散性对多体系统动力响应的影响不可忽略,利用随机参数的动力学模型将能客观地反映出系统的动力学行为.     

精细辛有限元方法及其相位误差研究

哈密顿系统是一类重要的动力系统,针对哈密顿系统,设计出多类辛方法:SRK、SPRK、辛多步法、生成函数法等.长久以来数值方法在求解哈密顿系统过程中辛特性和保能量特性不能得到同时满足,近年来提出的有限元方法,对于线性系统具有保辛和保能量的优良特性.但是,以上方法都存在相位漂移(轨道偏离)现象,长时间仿真,计算效果会大打折扣.提出精细辛有限元方法(HPD-FEM)求解哈密顿系统,该方法继承时间有限元方法求解哈密顿系统所具有的保哈密顿系统的辛结构和哈密顿函数守恒性的优良特性,同时,通过精细化时间步长极大地减小了时间有限元方法的相位误差.HPD-FEM相较与针对相位误差专门设计的计算格式FSJS、RKN以及SRPK方法具有更好的纠正效果,几乎达到机器精度,误差为O(10-13),同时,HPD-FEM克服了FSJS、RKN和SPRK方法不能保证哈密顿函数守恒的缺点.对于高低混频系统和刚性系统,常规算法很难在较大步长下,同时实现对高低频精确仿真,HPD-FEM通过精细计算时间步长,在大步长情况下,实现高低混频的精确仿真.HPD-FEM方法在计算过程中精细方法没有额外增加计算量,计算效率高.数值结果显示本文提出的方法切实有效.