The reduction method,I

As a further development of the well-known algorithms for deriving theorems of the method of Lyapunov vector functions, this paper suggests the reduction method as a logical technique for formulating hypotheses.     

结构动力学逆特征值问题的同伦解法

将结构动力学反问题视为拟乘法逆特征值问题,利用求解非线性方程组的同伦方法来解决结构动力学逆特征值问题,这种方法由于沿同伦路径求解,对初值的选取没有本质的要求,算例说明了这种方法是可行的．     

旋量法在机器人动力学分析中的应用

本文用旋量方法研究机器人的动力学模型，将速度和角速度，力和力矩的内在联系有机地融合为一体，使Ｎｅｗｔｏｎ－Ｅｕｌｅｒ方法更加简明有效率．文中相对于机器人各臂质心建立参考系，使惯性张量和质心加速度计算简化，进一步减少计算量，达到快速实时计算．     

A NEW APPROACH TO SOLVE SYSTEMS OF LINEAR EQUATIONS

1. IntroductionThe new aPProaCh is based on the analysis of the motion of a damped harmonic oscillatorin the gravitational field 11]. The associated equation of motion ismXtt + oXt + aX = b (1)where X = X(t), is the one dimensions di8PlaCement of Of a mass m under a dissipation(o > 0), a ~nic potential (a > 0) and a constant acceleration (b, gravitational field). Thetotal energy variation is given by the equationwhereThe solution of the motion equation (1) is given by the sum of two contr…     

Numerical approximations for population growth models

This paper aims to introduce a comparison of Adomian decomposition method and Sinc–Galerkin method for the solution of some mathematical population growth models. From the computational viewpoint, the comparison shows that the Adomian decomposition method is efficient and easy to use.     

受外冲击的多刚体拉氏动力学方程

本文讨论了多刚体系统受外冲击的动力学响应问题,给出了其拉氏动力学方程,所得的方程便于计算机程式化计算。     

结构刚度函数识别的一个途径

为了计算结构的刚度函数,将结构振动微分方程分解为关于已知的原始刚度函数的微分方程和关于未知待求的刚度函数的第一类Fredholm积分方程,利用p个光滑因子进行外插值的求解方法,数值计算当光滑因子为零时的积分方程的稳定解．从而可得到结构的刚度函数．通过数值模拟说明方法是可行的．     

台风异常路径的模拟(Ⅱ)--CD方法

我们提出采用等值线动力学（ＣＤ）方法研究台风的运动·讨论了在不同的环境引导气流下,台风的非对称内部结构对台风异常路径的影响·为了证明该方法的可行性,我们以Ｙａｎｃｙ（９０１２）台风为例,模拟了台风从８月２０日到２２日的运动·数值计算结果表明,这一方法能定性地描述台风打转趋势     

ANALYSIS OF A MECHANICAL SOLVER FOR LINEAR SYSTEMS OF EQUATIONS S

1. Introduction/ A new approaCh to solve systems of linear eqttations, equlvaleat to solve the ~ion of adamped harmonic oscillator, has been PrOPosed in a previous paper[11. Due to this parallelism,we call such methods Mechanical Solvers for systems of linear equations. The present study isdevoted to the analysis of these methods.Let be the linear systemwhere we assume that A is an m x m nonsingular matriX (i.e. the system has a ~ solution).We may associate to it the Newton's equation for …     

Analysis of a Mechanical Solver for Linear Systems of Equations

In this contribution we analyse some fundamental features of an iterative method to solve systems of linear equations, following the approach introduced in a previous work [1]. Such questions range from optimal parameters and initial conditions to comparison with other methods. An interesting result is that a priori we can give an estimation of the number of iterations to get a given accuracy.     

崎岖地形环境中月球车的动力学建模与仿真

以六轮摇臂-转向架关节式月球车为研究对象,根据其机械原理和结构特点,并参考车辆动力学理论,分析其在崎岖地形中的受力情况,利用Kane方法建立了理想状态下的非线性动力学模型,并基于此模型对月球车进行速度跟踪控制仿真,证实了模型和控制方案的可行性,为设计轨迹跟踪和避障控制器提供依据.     

Rotor dynamics behavior of turbo-expander involving droplet impact

ABSTRACT

This paper dedicates on the rotor dynamics behaviour research on the turbo-expander rotor system involving droplet impact. A stochastic model based on Beta distribution and Bernoulli distribution of droplet generation is established and the formulations of droplet impact forces are deduced, which is applied on the rotor dynamics equations of the tilting pad bearing supported turbo-expander considering the temperature gradient for a further analysis. A time domain research is carried out and a conclusion that continuously droplet impact will perturb the steady vibration of the turbo-expander rotor system is obtained. Monte Carlo method is implemented for a statistics dynamics research and the results suggests that in the design of expander impellers, in order to decrease the uncertainty brought by droplet impact, the number of channels should be as few as possible, the droplet impact should be controlled to occur uniformly, and the collision, entrainment of the primary droplets and the stripping of the liquid film on the blade should be strictly restrained.     

泊松类型方程边界元解法

本文采用高阶拉普拉斯算子基本解将泊松类型方程的区域积分全部变换成边界积分，使计算问题的维数减少一维．通过斯托克斯方程的算例，表明本文所用的方法是有效的方法。     

Preservation of local dynamics when applying central difference methods: application to SIR model

We apply the central difference method (u _t+1 ? u _t ? 1)/(2Δt) = f(u _t ) to an epidemic SIR model and show how the local stability of the equilibria is changed after applying the numerical method. The above central difference scheme can be used as a numerical method to produce a discrete-time model that possesses interesting local dynamics which appears inconsistent with the continuous model. Any fixed point of a differential equation will become an unstable saddle node after applying this method. Two other implicitly defined central difference methods are also discussed here. These two methods are more efficient for preserving the local stability of the fixed points for the continuous models. We apply conformal mapping theory in complex analysis to verify the local stability results.     

C-L方法及其在工程非线性动力学问题中的应用

C-L方法可以揭示非线性振动系统的分岔特性,它结合对称性和奇异性理论并将Liapunov-Schmidt(简称LS)约化方法推广到非自治系统.作为应用实例,分析了非线性转子动力学低频振动分岔失稳问题的机理及其控制.     

Modified iteration method for solving fractional gas dynamics equation

This paper is devoted to the time‐fractional gas dynamics equation with Caputo derivative. Fractional operators are very natural tools to model memory‐dependent phenomena. Modified iteration method is proposed to obtain the approximate and analytical solution of the fractional gas dynamics equation. This method is a combined form of the new iteration method and Laplace transform. Modified iteration method really is powerful and simple method compared with other methods. Existence and uniqueness of solution are proven. Numerical results for different cases of the equation are obtained. Copyright © 2016 John Wiley & Sons, Ltd.     

Dynamic adaptation method in gasdynamic simulations with nonlinear heat conduction

A dynamic adaptation method is applied to gas dynamics problems with nonlinear heat conduction. The adaptation function is determined by the condition that the energy equation is quasi-stationary and the grid point distribution is quasi-uniform. The dynamic adaptation method with the adaptation function thus determined and a front-tracking technique are used to solve the model problem of a piston moving in a heat-conducting gas. It is shown that the results significantly depend on the thermal conductivity chosen. The numerical results obtained on a 40-node grid are compared with self-similar solutions to this problem.     

A new load-dependent Ritz vector method for structural dynamics analyses: quasi-static Ritz vectors

Existing load-dependent Ritz vector (LDRV) methods employ static recurrence procedures to generate the Ritz vectors. As such, these vector methods are best suited for low-frequency problems. For higher-frequency problems, the existing methods may engender large sets of Ritz vectors, which significantly reduces the methods’ efficiency. A new algorithm is presented for LDRV generation using a quasi-static recurrence procedure, denoted as the quasi-static Ritz vector (QSRV) method. A tuning parameter, designated as the centering frequency, controls the behavior of the QSRV approach, enabling the new method to improve upon existing LDRV methods for particular frequency ranges of interest. Compared with existing LDRV methods, the QSRV method is more efficient (in terms of the number of Ritz vectors), more accurate (in terms of response errors), and more stable (in terms of orthogonality). Numerical examples are provided to illustrate the accuracy, efficiency and generality of the proposed method.     

逐步删除法确定复杂系统主导结构及其应用

在流率基本入树建模法、反馈环行列式计算法和系统基模X-0-1行列式计算法的基础上,结合系统行为模拟分析的变化曲线,提出了确定系统关键变量主导结构的逐步删除法,为复杂系统的动态结构和行为模式的分析提供有效的方法.运用此方法,对"公司+农户"规模经营模式的系统关键变量主导结构进行了分析,并提出相应的管理方针,实现了用系统科学方法分析"三农"问题的目的.     

径向质量偏心的自由转子陀螺的漂移运动

讨论均匀重力场中具有微小径向质量偏心的刚体定点运动,建立用状态变量描述的刚体动力学方程．对于刚体高速自旋情形应用平均法求出其近似解析积分,用以分析径向质量偏心对自由转子陀螺进动特性的影响．对径向质量偏心引起陀螺漂移现象给出物理解释,并导出陀螺常值漂移的简明的解析公式,与数值计算结果符合．