转子系统随机支撑刚度参数的识别

基于Riccati摄动随机传递矩阵方法建立的转子系统特征值与随机参数变量间的函数关系,给出了转子系统随机参数的识别方法和详细步骤,可用于识别随机参数的均值和方差。以改装的Bently实验转子为研究对象,通过大量测试,识别出了转子系统的随机支撑刚度参数,建立了该转子系统的随机参数动力学模型。该模型可用于研究转子系统的随机参数动力学问题。     

Analysis of hydrodynamic behaviors of multiple net cages in combined wave–current flow

Numerical simulation is performed to analyze the hydrodynamic response of a net cage and submerged mooring grid system exposed to waves and current. A series of experiments are conducted to validate the numerical model of net cage and grid mooring system. The numerical results of this model correspond with those obtained from experimental observations. Then, the numerical simulation of a multi-cage and mooring system under the action of waves combined with current is conducted. The influence of waves and current directions and the length of grid lines on the cage responses are discussed. The twin mooring system and the orthogonal mooring system are compared. Results show that for the orthogonal mooring system, the maximum tension force on the anchor line of the four-cage system is less than four times of that of the single-cage system, when both waves and current travel along the x-axis. The minimum net cage volume holding coefficient of the single-cage system is smaller than that of the four-cage system. The amplitude of the mooring line tension force for the twin mooring system is larger than the orthogonal mooring system.     

Stability for manifolds of equilibrium states of fractional generalized Hamiltonian systems

For a fractional generalized Hamiltonian system, in terms of Riesz derivatives, stability theory for the manifolds of equilibrium states is presented. The gradient representation and second order gradient representation of a fractional generalized Hamiltonian system are studied, and the conditions under which the system can be considered as a gradient system and a second order gradient system are given, respectively. Then, equilibrium equations, disturbance equations, and first approximate equations of a fractional generalized Hamiltonian system are obtained. A theorem for the stability of the manifolds of equilibrium states of the general autonomous system is used to a fractional generalized Hamiltonian system, and three propositions on the stability of the manifolds of equilibrium states of the system are investigated. As the special cases of this article, the conditions which a fractional generalized Hamiltonian system can be reduced to a generalized Hamiltonian system, a fractional Hamiltonian system and a Hamiltonian system are given, respectively, and the stability theory for the manifolds of equilibrium states of these systems are obtained. Further, a fractional dynamical system and a fractional Volterra model of the three species groups are given to illustrate the method and results of the application. Finally, by using the method in this paper, we construct a new kind of fractional dynamical model, i.e. the fractional Hénon–Heiles model, and we study its stability of the manifolds of equilibrium states.     

The effect of the random parameter on the basins and attractors of the elastic impact system

The global dynamic behavior of the elastic impact system with one random parameter is researched in this paper. First, based on the orthogonal polynomial approximation, the stochastic system is transformed into an equivalent deterministic system. Then the composite cell coordinate system method is used to derive the basins and attractors of the equivalent system. It is found that the random parameter affects the global dynamics of the system tremendously. Under the same conditions, the basins and attractors of the stochastic system are entirely different from that of the deterministic system.     

惯容器对隔振系统动态性能影响研究

本文设计了一种滚珠丝杠惯容器及ISD隔振系统,通过实验研究了惯性轮的转动惯量对惯容值的影响;同时,分析了滚珠丝杠惯容器的机械动力学特性,推导了ISD隔振系统的振动传递率计算公式,探讨了惯容器对ISD隔振系统动态特性的影响。在电机被动、主动和混合隔振工况下,开展了弹簧阻尼系统和ISD隔振系统的振动性能对比实验,验证了惯容器对振动系统固有频率和减振效果的影响规律。研究结果表明,惯容器可降低振动系统的固有频率,使共振频率向低频移动,共振振幅降低;在共振频率附近,惯容器可抑制共振振幅,惯容值越高,抑制效果越明显;ISD隔振系统在低频的减振效果优于传统的弹簧阻尼系统;随着频率比的增加,ISD隔振系统的传递率趋于稳定值,惯容器会引起高频隔振性能降低。     

Influence of dilatancy on the type of the system of equation in the plane problem of plasticity

In the classical model of an ideal rigid-plastic material without hardening, the governing system of equations is a system of hyperbolic type, and, if hardening is taken into account, the type of the system of equations changes from hyperbolic to elliptical. In this case, the correlation between the experimentally observed strain localization lines and the characteristics of the quasilinear system is violated. It is shown that if dilatancy is taken into account, the system of equations remains hyperbolic.     

Modeling,nonlinear dynamic analysis and control of fractional PMSG of wind turbine

This study aims to reveal the laws of the relationship between fractional-order system and integer-order system. Meanwhile, delayed feedback control is introduced to control the fractional-order PMSG (permanent magnet synchronous generator) model of a wind turbine. First, the fractional-order mathematical model of PMSG is established. Next, numerical simulations under different system orders are given and the system dynamic behaviors are analyzed in detail. Then, the delayed feedback control method is introduced to control the fractional-order PMSG and the control results when different parameters vary are analyzed. Complex dynamics are presented and some interesting phenomena are discovered. It is found that the system order influences the dynamics of the system in many aspects such as chaos pattern, bifurcation behavior, period window, shape and size of strange attractor. The delayed time, feedback gain, feedback limitation, system order can obviously influence the control result except the initial state of the system. Moreover, the feedback limitation has a minimum to successfully control the system to stable states and the system order also has a maximum to do so.     

Stability for manifolds of equilibrium states of generalized Hamiltonian systems

For a generalized Hamiltonian system, stability for the manifolds of equilibrium states is presented based on Lyapunov’s stability theories. Equilibrium equations, perturbation equations and first approximate equations of the system are given. A theorem for the stability of manifolds of equilibrium states of general autonomous system is used to the generalized Hamiltonian system, and three propositions on the stability of manifolds of equilibrium states of the system are obtained. Two examples are given to illustrate application of the method and results.     

The application of controlled variable magnetic eddy current damping to the study of vortex-induced vibrations

A powerful variable magnetic eddy current damping system has been constructed and utilized in an experimental study of vortex-induced vibrations (VIV). This damping system allows us to impose precise values of nearly ideal viscous damping over a wide range of damping values of interest. This new damping system offers improvements over previously utilized damping methods. Unlike most studies of VIV, where the damping cannot be independently controlled, we are able to impose our system damping independent of the other system parameters. Also, because the system only requires that a thin conductive plate be attached to the oscillating system, the overall mass of the system does not increase dramatically and still allows the investigation of very low mass systems. Finally, the system can operate in a steady-state fashion, supplying a constant damping value for an extended period of time, or in a transient fashion, where the damping value is intentionally varied over time. With this damping system, we have systematically explored both steady and transient damping effects on VIV behavior and provide a brief overview of some sample results.     

Extensions of hyperbolic systems of balance laws

An algorithm is presented for the extension of a hyperbolic system of balance laws to a system of higher dimension, in such a manner that weak solutions of the original system form a subset of the weak solutions of the extended system. Hyperbolicity and the symmetry group of the original system survive the extension, and some information on the characteristic speeds of the extended system is obtained. Applying the method to isentropic fluid flow, a new form of model for two-fluid flow is obtained. PACS 52.30.Ex, 52.35.Tc AMS Subject clssification Primary 35L65, Secondary 76T99     

On Local Analysis of Oscillations of a Non-ideal and Non-linear Mechanical Model

It is of major importance to consider non-ideal energy sources in engineering problems. They act on an oscillating system and at the same time experience a reciprocal action from the system. Here, a non-ideal system is studied. In this system, the interaction between source energy and motion is accomplished through a special kind of friction. Results about the stability and instability of the equilibrium point of this system are obtained. Moreover, its bifurcation curves are determined. Hopf bifurcations are found in the set of parameters of the oscillating system.     

基于进气射流的压气机失速主动控制系统仿真

针对一轴流压气机，构造了利用进气射流对旋转失速进行主动控制的控制系统，发展了以Ｍｏｏｒｅ－Ｇｒｅｉｔｚｅｒ模型为基础的系统数学模型并进行了数值仿真研究。结果表明，该控制系统可有效地抑制压气机中旋转失速的发生。     

广义Hamilton系统的保结构算法

基于广义Hamilton系统微分方程解析解理论。给出了构造保持系统真解典则性的高阶显式积分格式的方法,并说明其可推广到广义Hamilton控制系统。该方法保持了原系统的几何定性特征,因而是稳定的。数值例子说明了算法的有效性。     

Development of a vehicle to study the tractive performance of integrated steering-drive systems

This paper describes a test-bed vehicle for studying the integration of the steering system of a wheeled vehicle with the drive system. The vehicle was produced in order to determine whether such an integrated system is practical; to investigate tractive performance compared to other steering-drive systems; and to determine under which conditions such a system has better performance. The integrated steering-drive system of the test-bed vehicle uses a computer to co-ordinate the independently driven wheel speeds of the drive system (which is also the primary steering system) with the steer angles of the non-driven steerable wheels to produce a beneficial secondary steering effect. The secondary steering system assists the primary steering system when side forces act on the vehicle, while producing minimal conflict. This concept can be applied to agricultural vehicles such as tractors, harvesters, mowers, sprayers and self-propelled windrowers. The test-bed vehicle is able to be configured for the following steering-drive systems types: open differential drive with steerable wheels, independent drive wheels with castors, locked differential drive with steerable wheels and a computer integrated steering-drive system. The capacity of the test-bed vehicle to be configured as described is a significant advantage when measuring tractive performance, as the results obtained will be more valid due to the vehicle parameters being the same.     

Effects of axial preload of ball bearing on the nonlinear dynamic characteristics of a rotor-bearing system

This research studies the effects of axial preload on nonlinear dynamic characteristics of a flexible rotor supported by angular contact ball bearings. A dynamic model of ball bearings is improved for modeling a five-degree-of-freedom rotor bearing system. The predicted results are in good agreement with prior experimental data, thus validating the proposed model. With or without considering unbalanced forces, the Floquet theory is employed to investigate the bifurcation and stability of system periodic solution. With the aid of Poincarè maps and frequency response, the unstable motion of system is analyzed in detail. Results show that the effects of axial preload applied to ball bearings on system dynamic characteristics are significant. The unstable periodic solution of a balanced rotor bearing system can be avoided when the applied axial preload is sufficient. The bifurcation margins of an unbalanced rotor bearing system enhance markedly as the axial preload increases and relates to system resonance speed.     

Non-Linear Dynamics of a Rotor-Bearing-Seal System

The non-linear dynamic behaviors of a rotor-bearing-seal coupled system are investigated by using Muszynska’s non-linear seal fluid dynamic force model and non-linear oil film force, and the result from the numerical analysis is in agreement with the one from the experiment. The bifurcation of the coupled system is analyzed under different operating conditions. It is indicated that the dynamic behavior of the rotor-bearing-seal system depends on the rotation speed, seal clearance and seal pressure of the rotor-bearing-seal system. The system state trajectory, Poincaré maps, frequency spectra and bifurcation diagrams are constructed to analyze the dynamic behavior of the rotor center. Various non-linear phenomena in the coupled system, such as periodic motion and quasi-periodic motion are investigated. The results show that the system has the potential for chaotic motion. The study may contribute to a further understanding of the non-linear dynamics of such a rotor-bearing-seal coupled system.     

框架结构振动控制系统可靠性研究

振动控制系统的可靠性可以反映出主动控制的效果,本文提出了一种适合于确定框架结构控制系统可靠性的计算方法。该方法利用模态变换,把系统变为模态独立的振动方程,根据Field提出的假设,先定义阈值,假设控制后系统响应对阈值的穿阈率服从泊松分布,然后根据各模态的控制结果确定相应的可靠性,最后根据Veneziano提出的方法给出系统的可靠性。文中提出针对框架最大位移的控制输出来确定系统可靠性概念;此外,在系统降阶和控制方法方面,选择了基于系统可控性的平衡降阶法和针对系统不确定性具有较好控制效果的广义预测控制,最后给出了计算实例,算例表明这一方法是有效的。     

Method of large-scale system and analysis of three-axis stability of system partially filled with liquid

In the paper the method of large-scale system is investigated. The criteria of three-axis stability of a partially liquid-filled system are obtained by means of the method of large-scale system. Numerical results are given for a liquid-filled system with three-flywheels.     

Nonlinear Dynamic Behaviour of Coupled Suspension Systems

A two degrees of freedom model of two coupled suspension systems characterised by piecewise linear stiffness has been studied. The system, representing a pantograph current collector head, is shown to be sensitive to changes in excitation and system parameters, possessing chaotic, periodic and quasiperiodic behaviour. The coupled system has a more irregular behaviour with larger motions than the uncoupled suspension system, indicating that the response from the uncoupled suspension system cannot be used as a worst case measure. Since small changes in system parameters and excitation affect the results drastically then wear and mounting as well as actual operating conditions are crucial factors for the system behaviour.     

一类生物流体力学连续系统的分岔研究

连续动力系统的非线性动力学研究,由于其应用的广泛性与问题的复杂性,近年来越来越受到重视。本文对一类生物流体力学中的连续系统-动脉局部狭窄时血液流动的分岔特性进行了研究,采用有限差分方法,将由偏微分方程组描述的边境动力系统约化为由常微分方程组描述的高维离散动力系统。求得了离散动力系统的平衡解并分析其稳定性,同时讨论了流场中变量空间分布的变化情况。求得了离散动力系统的前三个Lyapunov指数,以此作为系统是否发生混沌的判别条件。