Dynamic analysis of the earth pole oscillation process

In the framework of classical mechanics, we perform an amplitude-frequency analysis of a small-parameter model of the Earth pole diurnal oscillations under the action of luni-solar gravitational-tidal torques. The Euler–Liouville dynamic equations with irregular perturbations taken into account are used to obtain the structural properties of diurnal oscillations of the Earth pole coordinates. The results of the Earth pole motion simulation are compared with the high-precision data of VLBI observations on a short time interval.     

Oscillatory-rotational processes in the Earth motion about the center of mass: Interpolation and forecast

The celestial-mechanics approach (the spatial version of the problem for the Earth-Moon system in the field of gravity of the Sun) is used to construct a mathematical model of the Earth’s rotational-oscillatory motions. The fundamental aspects of the processes of tidal inhomogeneity in the Earth rotation and the Earth’s pole oscillations are studied. It is shown that the presence of the perturbing component of gravitational-tidal forces, which is orthogonal to the Moon’s orbit plane, also allows one to distinguish short-period perturbations in the Moon’s motion. The obtained model of rotational-oscillatory motions of the nonrigid Earth takes into account both the basic perturbations of large amplitudes and the more complicated small-scale properties of the motion due to the Moon short-period perturbations with combination frequencies. The astrometric data of the International Earth Rotation and Reference Systems Service (IERS) are used to perform numerical simulation (interpolation and forecast) of the Earth rotation parameters (ERP) on various time intervals.     

结构控制中输出反馈鲁棒极点配置优化方法

给出了输出反馈鲁棒性极点配置的数学描述和数值解法,基于任何结构控制都要求极点对系统矩阵元素的改变不敏感,通过选择鲁棒度量,并以其尽可能小为判据,用优化方法寻求近似解,最后将该方法应用于一个大跨度桥在确定的运动载荷作用下的控制,计算结果表明方法合理、有效。     

端部切向载荷作用下的压杆失稳分析及其应用

细直杆件在压应力作用下会产生横向屈曲即失稳．直杆撞击刚性平面或拉断卸载后将形成压缩波，因承载压缩载荷的长度增加可以引起失稳．冲击速度转换的压应力沿着杆件切线方向，该处弯矩和剪力为零；而众多文献设定的失稳段固支边界条件并不准确．基于精确的杆件变形曲率方程得到端部载荷指向杆件中固定点时的受压失稳条件，得到其极限状态即载荷沿杆端切向作用时失稳长度相当于两端简支的1.5 倍．对于钢丝绳拉断形成的冲击失稳，载荷恒定而长度增加，可以产生高阶屈曲即在侧向出现多次曲折，并基于尼龙-橡胶带的模拟试验给出了定性说明．     

摩擦作用下直杆在对称斜面间的稳定平衡分析

摩擦提供的约束反力在由正应力所确定的范围之内．对称平板支承下的直杆在水平状态时平衡,但重心最高,因而没有摩擦时不能稳定平衡;摩擦作用下直杆平衡的倾角范围与平板坡度相关,可依据摩擦力达到极限值确定;若直杆与平板夹角小于90o,则平衡是稳定的,否则将跳跃到一侧平板,且摩擦角小于板面倾角时下滑到底部．支承板倾角变化时,处于稳定平衡状态的直杆将在一端发生滑移：倾角增大则高端向上、减小则低端向下,以使直杆重心位置较低．若支承板倾角作周期性变化,则直杆将逐渐倾斜而失稳：下滑到底部或跳跃到一侧平板．摩擦使力学系统具有非线性特征,其平衡位置可以在状态参数连续变化时发生跳跃．     

Formulation and solution of the problem of the stability of a cohesionless channel bottom

The problem of the stability of the sandy bottom of a rectangular channel with respect to spatially onedimensional perturbations is formulated. The channel stability problem is solved using the sediment discharge formula modified by taking into account the effect of free-surface perturbations on sediment transport. Analytic dependences of the propagation velocity of bottom perturbations on time are obtained for small Froude numbers. Wavelengths for the most rapidly growing bottom perturbations are obtained analytically, and the problem of the evolution of a single bottom perturbation is solved.     

整立电杆三点吊最优吊点的研究分析

根据输电线路中杆塔施工的实际工程需要,主要研究分析了整立电杆三点吊最优吊点的确定方法,建立了整体电杆三点吊的数学模型,编制了微机软件,解决了整体电杆三点吊方案设计中的难题。     

Effect of turbulent viscosity on the formation and motion of bottom waves

The problem of linear perturbations of the sandy bottom in a rectangular channel with a heavy incompressible fluid is formulated. The turbulent viscosity of the flow is defined as a drag coefficient function, and the hydrodynamic equations are written in the long-wave Boussinesq approximation. In the expression for the hydrostatic pressure, a correction is applied to the Boussinesq approximation that changes the sediment discharge. The problem of the development of bottom perturbations is solved taking into account the modified formula of sediment discharge, resulting in analytical expressions for the velocity of bottom perturbations and the wavelength of the fastest-growing bottom perturbations at small Froude numbers.     

Dissipativity-based stable controller redesign for nonlinear MIMO switched systems in the presence of perturbations

This paper offers a control redesign method for a class of nonlinear MIMO perturbed dissipative switched systems. The controller for the nominal switched system without perturbation is considered to have been designed based on dissipativity. The nominal model is considered affine with perturbations in both nonlinear terms. The controller is then redesigned such that the dissipativity of the switched system with perturbations is maintained by including a robustifying term in the control law. The design is developed for the two cases of 2-norm and infinity-norm bounded perturbations. The proposed method is applied to a nonlinear MIMO switched system to verify the convergence of the state vector to the origin in the presence of perturbations.     

Long-wave instability of an advective flow in an inclined fluid layer with perfectly heat-conducting boundaries

Stability of a steady convective flow in a plane inclined layer with perfectly heat-conducting solid boundaries in the presence of a uniform longitudinal temperature gradient to long-wave perturbations is studied. The boundaries of the domain of stability to long-wave perturbations are found, and the critical Grashof numbers for the most dangerous even helical perturbations are determined.     

Linear Dynamics of Perturbations in Flows with Constant Horizontal Shear

The dynamics of perturbations in shallow water and incompressible stratified fluid flows with constant horizontal shear are described using the nonmodal analysis. It is shown that the shear flow perturbations can be divided into two classes on the basis of the potential vorticity: rapidly oscillating wave perturbations with zero potential vorticity and slow vortex perturbations with nonzero potential vorticity. In the cases of weak and strong shear the main features of the dynamics of wave and vortex perturbations are studied analytically (using the WKBG method) and numerically. It is shown that for large times the wave perturbation energy increases linearly, i.e., the shear flow is algebraically unstable due to the growth of rapid wave perturbations. This instability can be of importance in processes of turbulence development and surface and internal wave generation.     

Stability of plane-parallel convective fluid flow in a horizontal layer relative to spatial perturbations

The stability of stationary plane-parallel convective flow between horizontal planes along which a constant temperature gradient is given, is investigated relative to spatial perturbations. It is shown that the flow crisis is caused by spiral perturbations in a broad range of Prandtl number values (P > 0.24). Spiral perturbations are developed in unstably stratified fluid layers adjoining the upper and lower layer boundaries, and are of Rayleigh nature.     

Investigation of Mechanisms of Excitation and Growth of Unstable Perturbations in Pulsating Flows

General laws of the processes of generation and amplification of secondary perturbations in oscillating viscous fluid flows are studied theoretically. The stability and receptivity are analyzed with reference to perturbations generated by fluctuations of the flow rate of Poiseuille flow induced by small two-dimensional roughnesses of the channel walls. It is shown that the presence of roughness leads to excitation in the flow of perturbations at all multiples of the main flow oscillation frequency. Using the Fourier transform along the streamwise coordinate, the problem of calculating the frequency harmonics is reduced to a system of equations of the Orr-Sommerfeld type interrelated via the oscillatory component of the main flow. On the basis of an investigation of the analytic properties of the Fourier-image it is shown that upstream and downstream of the roughness the perturbation can be represented in the form of a superposition of modes of the time-dependent Poiseuille flow. The modes are classified and their spectrum is calculated. The structure of the mean-square fluctuations generated by free perturbations is investigated. Examples of calculating the evolution of forced perturbations are given for cases in which the scattering of the oscillations of the main flow on the roughness leads to the generation of one or two modes growing downstream.     

各种极对数的高精度多级旋转变压器的轴角─—数字转换原理及软硬件实现

－国内国际常用的多级旋转变压器主要有１６对极，３０对极和３６对极几种。多级旋转变压器在导航设备中起着重要作用。本文叙述了其输出的高精度角度信号如何被计算机转换成数字信号，以便为主机显控提供数据，还从原理和软硬件实现方法上给出了一种实现方案。     

非自旋航天器混沌姿态运动及其参数开闭环控制

研究万有引力场中受大气阻力且存在结构内阻尼的非自旋航天器在椭圆轨道上平面天平动的混沌及其参数开闭环控制问题．在建立数学模型的基础上确定出现混沌的必要条件并数值验证混沌的存在性，提出非线性振动系统混沌运动的参数开闭环控制并应用于控制航天器的混沌姿态运动．     

Numerical Analysis of Laminar-Turbulent Transition in a Circular Pipe with Periodic Inflow Perturbations

The problem of the spatio-temporal evolution of perturbations introduced into the inlet cross-section of a circular pipe is solved numerically. The case of time-periodic inflow perturbations is considered for Re = 4000. It is shown that for relatively small inflow perturbations periodic flow regimes and for greater perturbations chaotic regimes are established.Periodic regimes the flow is a superposition of steady flow and a damped wave propagating downstream. The velocity profile of the steady component differs essentially from both the parabolic Poiseuille and developed turbulent flows and is strongly inhomogeneous in the angular direction. The angular distortion of the velocity profile is caused by longitudinal vortices developing as a result of the nonlinear interaction of inflow perturbations.Chaotic flow regimes develop when the amplitude of the inflow perturbations exceeds a certain threshold level. Stochastic high-frequency pulsations appear after the formation of longitudinal vortices in the regions of maximum angular gradient of the axial velocity. In the downstream part of the flow, remote from the transition region, the developed turbulent regime is formed. The distributions of all the statistical moments along the pipe level off and approach the values measured experimentally and calculated numerically for developed turbulent flows.     

Rotational-oscillational motions of the nonrigid Earth about the center of mass

We use the model of a nearly axisymmetric viscoelastic rigid body to study perturbed rotational-oscillational motions of the Earth’s pole. We point out that the Chandler component of oscillations is of celestial-mechanics nature and is caused by the gravitational-tidal actions of the Sun and the Moon. We analyze the pole oscillation excitation mechanism at a frequency close to the Chandler frequency and show that the undamped pole oscillations are caused by the resonance harmonic of the external perturbation at a frequency close to the free nutation frequency. We discuss whether it is possible to solve the problem of constructing a short-term forecast of the pole motion on the basis of a polynomial filter obtained by the least-squares method without taking into account small-scale oscillations caused by wide-band random factors of arbitrary physical nature. In the present paper, we perform numerical simulation of tidal inhomogeneities in the Earth’s axial rotation. Attention is mainly paid to the analysis of day length variations on short time intervals with periods less than or equal to one year (interannual oscillations) and to their forecast.     

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从静力平衡条件出发,研究撑杆跳高过程中撑杆的截面尺寸变化对应变能的影响, 给出了撑杆壁厚沿长度方向的变化规律. 利用有限单元法计算了极限变形状态下撑杆的变形 曲线,验证了极限状态变形曲线为圆弧的假定. 根据能量守恒,引入肌肉收缩做功对跳高高 度的贡献,修正了技能指标,得到了考虑运动员体重、身高及握杆高度等影响因素的跳高高 度计算公式.