Dynamic analysis of beam-cable coupled systems using Chebyshev spectral element method

The dynamic characteristics of a beam–cable coupled system are investigated using an improved Chebyshev spectral element method in order to observe the effects of adding cables on the beam. The system is modeled as a double Timoshenko beam system interconnected by discrete springs. Utilizing Chebyshev series expansion and meshing the system according to the locations of its connections,numerical results of the natural frequencies and mode shapes are obtained using only a few elements, and the results are validated by comparing them with the results of a finiteelement method. Then the effects of the cable parameters and layout of connections on the natural frequencies and mode shapes of a fixed-pinned beam are studied. The results show that the modes of a beam–cable coupled system can be classified into two types, beam mode and cable mode, according to the dominant deformation. To avoid undesirable vibrations of the cable, its parameters should be controlled in a reasonable range, or the layout of the connections should be optimized.     

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.     

Constitutive parameters for liquid-fluidized beds

The constitutive parameters (particulate phase effective elasticity, particulate effective viscosity, added mass coefficient and drag gradient) in an unstable liquid-fluidized bed are determined as functions of voidage and slip velocity. To identify these system parameters, first, forced instability wave properties are measured in water-fluidized beds, then an optimum parameter identification method is developed to reliably determine these system parameters based on a generic instability model. The results give some insight into the internal mechanics of liquid-fluidized beds and are compared with other models when they are available.     

The method of variation on parameters for integration of a generalized Birkhoffian system

This paper focuses on studying the integration method of a generalized Birkhoffian system.The method of variation on parameters for the dynamical equations of a generalized Birkhoffian system is presented.The procedure for solving the problem can be divided into two steps:the first step,a system of auxiliary equations is constructed and its general solution is given;the second step,the parameters are varied,and the solution of the problem is obtained by using the properties of generalized canonical transformation.The method of variation on parameters for the generalized Birkhoffian system is of universal significance,and we take a nonholonomic system and a nonconservative system as examples to illustrate the application of the results of this paper.     

非线性转子-轴承系统的周期解及近似解析表达式

通过对普通打靶方法进行改造提出一种确定非线性系统周期轨道及周期的新型打靶算法。首先通过改变系统的时间尺度，将非线性系统周期轨道的周期显式地出现在非线性系统的系统方程中，然后对传统打靶法进行改造，将周期也作为一个参数一起参与打靶法的迭代过程，迭代过程包含对周期轨道和周期的求解，迭代过程中的增量通过优化方法选择，从而能迅速确定出系统的周期轨道及其周期。应用所求的结果结合谐波平衡方法求得了非线性系统的周期轨道的近似解析表达式，理论上通过增加谐波的阶数任何精度的周期解都可以得到。最后将该方法应用于非线性转子轴承系统，求出了在某些参数下转子的周期解及其近似解析表达式，通过与四阶Runge-Kutta数值积分结果比较，验证了方法的有效性，计算结果对于转子系统运动的定量控制有重要理论指导意义。     

A fractional model for robust fractional order Smith predictor

In this paper, we propose to use a fractional order model to predict the process output in Smith predictor. The parameters of the model are determined by minimizing the error between its output and one of the processes using a genetic algorithm. After determining the model’s parameters, a fractional PID controller is proposed to improve the controlled system performances. The parameters of the controller are also determined in an optimal way by minimizing the position error taking into account the sensitivity and the complementary sensitivity conditions. Applications on a dead time and multiple lags processes have been performed, where the simulation results show that the proposed Smith predictor enhance the closed loop control system.     

DYNAMICS ANALYSIS OF STOCHASTIC SPATIAL FLEXIBLE MULTIBODY SYSTEM 1)

轻质、高精度的柔性多体系统被广泛应用于实际工程领域中.由于实际设计公差、制造误差及环境温度等多种不确定因素的存在,使得柔性多体系统的结构参数(物理参数和几何参数)表现出随机性.具有随机结构参数的动力学模型能够客观地反映出真实系统的动力学行为,且结构参数的不确定性对空间柔性多体系统动力学响应的影响是不容忽视的.针对具有多个随机参数的空间柔性多体系统,提出了一种基于广义alpha算法的非侵入式随机柔性多体系统动力学计算方法.采用绝对节点坐标公式(absolute node coordinate formulation, ANCF)来描述柔性体, 推导建立多体系统动力学模型.利用混沌多项式展开(polynomial chaos expansion, PCE)法构建系统随机动力学方程的代理模型,然后将随机响应面法(stochastic response surface method, SRSM)嵌入广义-alpha方法中,分别采用改进抽样的回归方法(regression method of improved sampling, RMIS)和单项求容积法则(Monte Carlo simulation, MCR)来确定样本点.将数值计算结果与蒙特卡洛模拟(Monte Carlo simulation, MCS)结果进行对比, 验证了所提算法的有效性.在相同的定积分精度的条件下,根据单项求容积法则确定的样本点的计算结果稳定性更强, 且其计算效率更高.     

Nonlinear control in an electromechanical transducer with chaotic behaviour

The electromechanical transducer considered in this work is composed of a mechanical oscillator linked to an electronic circuit. Simulations results have determined that for some combination of parameters the electromechanical system is subject to chaotic motion with resonant transient behavior, and after the resonant transient the mechanical system (MS) synchronizes with the electrical system (ES). In order to improve the transient response, avoiding both the chaotic and resonant behaviors, a nonlinear control system is designed, a feedback control strategy is used to drive the system into the desired periodic orbit, and a nonlinear feedforward strategy is used to keep the system into the periodic orbit, obtained by the Fourier series. Two control techniques are used and compared, namely: the state dependent Ricatti equation and the optimal linear feedback control. Numerical simulations results are shown in order to compare the results, considering parametric uncertainties. Additionally, the energy transfer “pumping” between the ES and the MS is also analysed.     

随机空间柔性多体系统动力学分析

轻质、高精度的柔性多体系统被广泛应用于实际工程领域中.由于实际设计公差、制造误差及环境温度等多种不确定因素的存在,使得柔性多体系统的结构参数(物理参数和几何参数)表现出随机性.具有随机结构参数的动力学模型能够客观地反映出真实系统的动力学行为,且结构参数的不确定性对空间柔性多体系统动力学响应的影响是不容忽视的.针对具有多个随机参数的空间柔性多体系统,提出了一种基于广义alpha算法的非侵入式随机柔性多体系统动力学计算方法.采用绝对节点坐标公式(absolute node coordinate formulation, ANCF)来描述柔性体, 推导建立多体系统动力学模型.利用混沌多项式展开(polynomial chaos expansion, PCE)法构建系统随机动力学方程的代理模型,然后将随机响应面法(stochastic response surface method, SRSM)嵌入广义-alpha方法中,分别采用改进抽样的回归方法(regression method of improved sampling, RMIS)和单项求容积法则(Monte Carlo simulation, MCR)来确定样本点.将数值计算结果与蒙特卡洛模拟(Monte Carlo simulation, MCS)结果进行对比, 验证了所提算法的有效性.在相同的定积分精度的条件下,根据单项求容积法则确定的样本点的计算结果稳定性更强, 且其计算效率更高.      

A Study of the Nonlinear Response of a Resonant Microbeam to an Electric Actuation

An investigation into the response of a resonant microbeam to anelectric actuation is presented. A nonlinear model is used to accountfor the mid-plane stretching, a DC electrostatic force, and an ACharmonic force. Design parameters are included in the model by lumpingthem into nondimensional parameters. A perturbation method, the methodof multiple scales, is used to obtain two first-order nonlinearordinary-differential equations that describe the modulation of theamplitude and phase of the response and its stability. The model and theresults obtained by the perturbation analysis are validated by comparingthem with published experimental results. The case of three-to-oneinternal resonance is treated.The effect of the design parameters on the dynamic responses isdiscussed. The results show that increasing the axial force improves thelinear characteristics of the resonance frequency and decreases theundesirable frequency shift produced by the nonlinearities. In contrast,increasing the mid-plane stretching has the reverse effect. Moreover,the DC electrostatic load is found to affect the qualitative andquantitative nature of the frequency-response curves, resulting ineither a softening or a hardening behavior. The results also show thatan inaccurate representation of the system nonlinearities may lead to anerroneous prediction of the frequency response.     

Nonlinear systems synchronization for modeling two-phase microfluidics flows

The aim of this work is to identify a class of models that can represent the two-phase microfluidic flow in different experimental conditions. The identification procedure adopted is based on the nonlinear systems synchronization theory. The experimental time series were assumed as the asymptotic behavior of a generic state variable of an unknown Master system, and this information was used to drive a second Slave system, with a known model and undefined parameters. To reach the convergence between the time evolutions of the two systems, so the flow identification, an error was evaluated and optimized by tuning the parameters of the Slave system, through genetic algorithm. The Chua’s oscillator has been chosen as a Slave model, and an optimal parameters set of Chua’s system was identified for each of the 18 experiments. As proof of concept on approach validity, the changes in the parameters set in the different experimental conditions were discussed taking into account the results of the nonlinear time series analysis. The results confirm the possibility with a single model to identify a variety of flow regimes generated in two-phase microfluidic processes, independently of how the processes have been generated, no directed relations with the input flow rate used are in the model.     

Fractional order spring/spring-pot/actuator element in a multibody system: Application of an expansion formula

Fractional order models of a spring/spring-pot and spring/spring-pot/actuator element connected into a multibody system are proposed in order to represent smart materials and components in adaptronic systems by introducing new tuning parameter. The models are introduced into dynamic equations via generalized forces and using the Lagrange's equations of the second kind in covariant form. Generalized forces are derived by taking into account fractional order derivatives in force–displacement relations and by using the principle of virtual work. The numerical scheme for solving fractional order differential equations proposed in Atanacković and Stanković (2008) is used in order to approximate fractional order derivative of a composite function appearing in the presented fractional order model. Numerical example for the multibody system with three degrees of freedom is presented. The results obtained for generalized forces are compared for different values of parameters in the fractional order derivative model.     

多自由度参激系统稳定性的数值分析

提出多自由度周期参激系统稳定性的数值直接法。通过将扰动方程表示成状态方程形式,再根据Flo-quet理论将扰动解表示成指数特征分量与周期分量之积,并将其周期分量与系统周期系数展成Fourier级数,导出一系列代数方程,建立矩阵特征值问题,从而由数值求解特征值可直接确定参激系统的稳定性。该方法可用于一般周期参激阻尼系统,特征值矩阵不含逆子阵。应用于斜拉索在支座周期运动激励下的参激振动不稳定性分析,数值结果表明该方法的有效性。     

An adaptive quenching algorithm for a nonlinear single-degree-of-freedom system

An indirect adaptive quenching algorithm for a nonlinear single-degree-of-freedom system with unknown constant system parameters is presented. The system is subject to external or parametric sinusoidal disturbances and the resulting control signal is also sinusoidal. The quenching algorithm provides a reduction in the control effort required compared to direct disturbance cancellation. The disturbance sinusoid and the unknown parameters are incorporated into the system model and an extended Kalman filter (EKF) with modified update equations is used to estimate the system state and parameters. The estimates are then used to form the quenching signal. The adaptive quenching algorithm is found to work well inside a quenching region defined by the separatrices and suggests the use of a hybrid control law. The algorithm was verified by implementing it on an analog computer.     

A partially saturated adaptive learning controller for overhead cranes with payload hoisting/lowering and unknown parameters

For underactuated overhead cranes with payload hoisting/lowering, a partially saturated adaptive controller subject to unknown or uncertain system parameters is presented in this paper. To decrease the convergence time in the case of the overhead crane parameters already experienced by the system, the learning component is added to the proposed partially saturated adaptive controller. By introducing hyperbolic tangent functions into the control methods, the proposed controllers can guarantee soft trolley start even in the case of high initial velocities of trolley and cable. The convergence and stability performance of the closed-loop system is proven by Lyapunov techniques and LaSalle’s invariance theorem. Simulation results are listed to verify the adaptive performance with reduced actuating forces and strong robustness with respect to different external disturbances of the proposed controllers.     

Hydromagnetic flow and heat transfer adjacent to a stretching vertical sheet with prescribed surface heat flux

The similarity solution for the problem of mixed convection boundary layer flow adjacent to a stretching vertical sheet in an incompressible electrically conducting fluid in the presence of a transverse magnetic field is presented. It is assumed that the sheet is stretched with a power-law velocity and is subjected to a variable surface heat flux. The governing partial differential equations are first transformed into a system of non-linear ordinary differential equations, before being solved numerically by the Keller-box method. The numerical results obtained are then compared with previously reported cases available in the literature as well as the series solution for certain values of parameters, to support their validity. The effects of the governing parameters on the flow field and heat transfer characteristics are obtained and discussed.     

空间三轴机抖激光陀螺交流稳频系统设计

针对空间三轴机抖激光陀螺设计了交流稳频控制系统,分析了系统原理,进行了Simulink仿真建模和试验研究。在系统原理中分析了控制过程,推导了系统函数,通过Simulink交流稳频系统仿真建模摸索了空间三轴机抖激光陀螺交流稳频系统中PID参数对系统响应的影响,并得到了优化参数(K_P=0.048,K_I=0.0021,K_D=0.0037),为硬件调试提供了参考。将交流稳频控制系统应用于国产某型空间三轴机抖激光陀螺进行试验,试验结果显示通过PID参数调节后的交流稳频陀螺PZT码值变化平稳,陀螺静态脉冲输出稳定,与原直流稳频控制方法相比将空间三轴机抖激光陀螺的精度提高了20%。     

Complexity of triopoly price game in Chinese cold rolled steel market

This paper considers a Bertrand model based on nonlinear demand functions which are closer to reality and different from previous studies. We apply the model into Chinese cold rolled steel market and study game process of triopoly. By using the theory of bifurcations of dynamical systems, local stable region of Nash equilibrium point is obtained. Simulations show complex dynamical behaviors of the system. The results illustrate that altering the relevant parameters of system can affect the stability of Nash equilibrium point and cause chaos to occur, and the complex dynamical behaviors will disappear by parameters control method. The results have an important theoretical and practical significance to Chinese cold rolled steel market.     

THEORY AND METHOD OF OPTIMAL CONTROL SOLUTION TO DYNAMIC SYSTEM PARAMETERS IDENTIFICATION (I)──FUNDAMENTAL CONCEPT AND DETERMINISTIC SYSTEM PARAMETERS IDENTIFICATION

Based on the concept of optimal control solution to dynamic system parameters identification and the optimal control theory of deterministic system, dynamics system parameters identification problem is brought into correspondence with optimal control problem. Then the theory and algorithm of optimal control are introduced into the study of dynamic system parameters identification. According to the theory of Hamilton-Jacobi-Bellman (HJB) equations' solution, the existence and uniqueness of optimal control solution to dynamic system parameters identification are resolved in this paper. At last the parameters identification algorithm of determi-nistic dynamic system is presented also based on above mentioned theory and concept. Project supported by the National, Defence Science and Technology Foundation (A966000-50) and the Across Century Scientist Foundation from the State Education Commission of China     

Dynamic analysis of an offshore pipe laying operation using the reel method

A system designed for a rigid and flexible pipe laying purposes is presented in the paper.Mathematical and numerical models are developed by using the rigid finite element method(RFEM).The RFEM is an efficient solution in the time domain.Static and dynamic problems related to pipe installation are solved by taking the advantage of simple interpretation and implementation of the method.Large deformations of the pipe during spooling and when it is reeled out at sea are considered.A material model implemented is used to take into consideration nonlinear material properties.In particular,the full elasto-plastic material characteristics with hardening and Bauschinger effect are included.Dynamic analyses are performed and the results attached in this work demonstrates how the sea conditions influence the machinery and pipeline,assuming a passive reel drive system. The influence of several other operational parameters on dynamic loads is verified.An active system,implemented as a part of the mathematical model,improves the system performance.Some results are presented as well.