Kinematics and dynamics of a particle on a non-simple harmonic vibrating screen

The motion of a particle on a screen is directly affected by the motion of the screen if airflow and intergranular friction are ignored. To study this effect, a mathematical model was established to analyze the motion of a planar reciprocating vibrating screen, and a matrix method was employed to derive its equation of motion. The motion of the screen was simulated numerically and analyzed using MATLAB. The results show that the screen undergoes non-simple harmonic motion and the law of motion of each point in the screen is different. The tilt angle of the screen during screening is not constant but varies according to a specific periodic function. The results of numerical simulations were verified through experiments. A high-speed camera was used to track the motion of three points in the longitudinal direction of the screen. The balance equation for forces acting on a single particle on the screen was derived based on the non-simple harmonic motion of the screen. These forces were simulated using MATLAB. Different types of particle motion like slipping forward, moving backward, and being tossed to different parts of the screen were analyzed. A vibro-impact motion model for a particle on the non-simple harmonic vibrating screen was established based on the nonlinear law of motion of the particle. The stability of fixed points of the map is discussed. Regimes of different particle behaviors such as stable periodic motion, period-doubling bifurcation motion, Hopf bifurcation motion, and chaotic motion were obtained. With the actual law of motion of the screen and the behavior of a particle on the screen, a theoretical basis for design optimization of the screen is provided.     

捷联惯导系统中的圆锥和伪圆锥运动研究

分别对圆锥运动和伪圆锥运动的产生原因、表达形式,以及对捷联惯导系统的影响进行了分析.由于圆锥运动和伪圆锥运动并不相同,因此圆锥运动补偿算法将对两者产生不同的效果.数字仿真表明,圆锥补偿算法可以大大降低经典圆锥运动对捷联导航系统的不利影响,但同时却会增大伪圆锥运动对捷联导航系统的不利影响.因此在实际应用当中,应当结合圆锥运动和伪圆锥运动对系统的影响比重,选择合适的圆锥补偿算法.     

An Experimental Study of the Modulation of the Bubble Motion by Gas–Liquid-Phase Interaction in Oscillating-Grid Decaying Turbulence

The purpose of the present research is to understand dynamic bubble–liquid interaction in a bubbly flow based on the experimental results of the modulation of the bubble motion in oscillating-grid decaying turbulence. By comparing the experimental results obtained from stagnant water and those from oscillating-grid decaying turbulence, we discussed and described detailed process of the modulation of the bubble motion in a water vessel. We discussed the enhancement of the transition of the bubble motion from 2D to 3D by combining the liquid-phase motion obtained through particle imaging velocimetry/laser-induced fluorescence (PIV/LIF) measurement and the bubble wake motion captured through the LIF/HPTS (8-hydroxypyrene-1, 3, 6-trisulfonic acid) method, under both conditions (in the stagnant water and in the oscillating-grid decaying turbulence) in which the initial bubble formation and the bubble motion (gravity-center motion and surface oscillation) were considered to be the same. In addition, by using PIV/LIF measurement along with an infrared shadow technique, we simultaneously obtained the bubble motion (2D zigzagging motion in stagnant water, and 3D motion in the decaying turbulence) and the standard deviation of the liquid-phase motion (the bubble Reynolds number: 775; the turbulent Reynolds number: 62.2). Taking all of the results together, the modulation of the bubble motion in the decaying turbulence, and the dynamic interaction between the bubble and the liquid-phase motion were experimentally and carefully investigated. Consequently, the enhancement and the modulation of the bubble wake motion were considered to be triggered by the collapse of the symmetric property of the bubble–liquid (i.e. ambient liquid-phase turbulence) interaction.     

杆状弯曲行波型超声电机运动机理研究

为了深入研究杆状弯曲行波型超声电机的运动机理，本文分析了定子表面质点椭圆运动轨迹的形成，并将椭圆运动分解为产生驱动力的有效椭圆运动与使定、转子产生径向滑动的径向直线运动；然后基于有效椭圆运动变化情况，分析了在两相振幅不平衡和任意相位差情况下对转子运动平稳性的影响，为这类电机的设计和性能控制提供理论依据。     

Finite amplitude waves superimposed on pseudoplanar motions for Mooney-Rivlin viscoelastic solids

This paper deals exclusively with finite amplitude motions in viscoelastic materials for which the stress is the sum of a part corresponding to the classical Mooney-Rivlin incompressible isotropic elastic solid and of a dissipative part corresponding to the classical viscous incompressible fluid. Of particular interest is a finite pseudoplanar elliptical motion which is an exact solution of the equations of motion. Superposed on this motion is a finite shearing motion. An explicit exact solution is presented. It is seen that the basic pseudoplanar motion is stable with respect to the finite superposed shearing motion. Particular exact solutions are obtained for the classical neo-Hookean solid and also for the classical Navier-Stokes equations. Finally, it is noted that parallel results may be obtained for a basic pseudoplanar hyperbolic motion.     

舰船捷联惯导传递对准仿真验证系统设计

为解决船用捷联惯导系统传递对准仿真中载体机动方式与实际差别较大的问题,提出了基于舰船空间运动的传递对准精度考核的仿真验证系统,提高载体机动方式仿真逼真度。仿真验证系统通过舰船空间运动建模,提供接近真实运动环境的空间运动参数;通过设计空间变换算法,实现了空间运动参数与主惯导惯性器件模拟输入的转化;通过杆臂及挠曲变形计算,实现了子惯导惯性器件模拟输入的转化;文中给出了各模块的算法及解算流程。速度+姿态传递对准算法仿真验证结果为10 s内水平失准角精度优于0.02;方位失准角精度优于0.05。仿真验证试验结果表明了该方案的可行性和实用性,该方案为其他领域的传递对准方案分析及验证提供了有效的参考依据。     

An application of pattern mapping to plane motion

A new, highly automated method for measuring plane motion, pattern mapping, has been developed for rigidbody motion and strain analysis. Pattern mapping employs image processing and syntactic pattern recognition principles to recognize a known pattern before and after motion. In this paper, the Lagrangian definition of motion was used to map points in the two images, and the map was used to determine plane motion. Full-image analysis is thoroughly demonstrated.     

Marangoni效应下气泡上升过程的FTM模拟

采用界面跟踪法FTM(Front-Tracking Method),并结合CSF(continuum surface force)模型,研究了在垂直方向上温度分布不均匀的对称流场中由Marangoni效应引起的气泡上升运动问题。模拟了在不同的M a数和Pr数下单气泡及同轴双气泡的运动。研究结果表明,在不同的M a数下气泡的运动差异较大,M a数越大,气泡运动至稳态时的速度越大,且气泡运动的最大速度值与M a数呈正相关关系;增大Pr数所造成的粘度增大或热扩散率减小将削弱气泡的迁移运动;Marangoni对流中双气泡的局部运动证实了温度梯度和气泡运动速度紧密相关。     

亚音速气流作用下薄板结构混沌运动的时滞反馈控制

研究了亚音速气流下非线性二维薄板结构在横向周期载荷作用下的混沌运动及控制问题。基于von Karman大变形板理论和分离变量法,建立了亚音速下薄板结构的运动控制方程。对于未控系统,采用Melnikov方法判断其混沌运动阈值,并用Runge-Kutta法进行数值验证。对处于混沌运动状态的系统,采用时滞反馈控制方法对混沌运动进行控制。结果表明,Melnikov方法可以有效地预测系统的混沌运动行为,时滞反馈控制方法可以有效地将系统的混沌运动转化为周期运动。     

Synthesis of a controller for stabilizing the motion of a rigid body about a fixed point

A method for the approximate design of an optimal controller for stabilizing the motion of a rigid body about a fixed point is considered. It is assumed that rigid body motion is nearly the motion in the classical Lagrange case. The method is based on the common use of the Bellman dynamic programming principle and the averagingmethod. The latter is used to solve theHamilton–Jacobi–Bellman equation approximately, which permits synthesizing the controller. The proposed method for controller design can be used in many problems close to the problem of motion of the Lagrange top (the motion of a rigid body in the atmosphere, the motion of a rigid body fastened to a cable in deployment of the orbital cable system, etc.).     

Features of Movement of a Rotational Body

Vertical motion of a rotational body in an air environment as a mechanical model of a rotochute is considered. It is assumed that, in the process of motion, the symmetry axis of the rotational body remains vertical and the rotational body itself rotates relative to this axis. The aerodynamic impact model is based on a quasistatic approach. Steady regimes of motion are identified, their stability is analyzed, and certain features of transition regimes are explored, including those related to the exchange between the energy of rotational motion and the energy of translational motion.     

The geometry of the orbits of artificial satellites

A novel approach to the study of the orbits of artificial satellites is presented. Emphasis is placed upon the basic geometry and other aspects of satellite motion which are of first importance to satellite engineering. The motion of the orbital plane as a rigid body is introduced and a non-elliptical orbit motion in this plane is defined. The plane orbit so defined possesses the very desirable feature of representing a succession of satellite positions and hence reveals the true motion of the satellite. An analytical treatment yields a completely general second order theory of earth satellite motion which is suitable for engineering purposes. In the latter development, particular attention is paid to the apsidal motion of the orbit and the concomitant resonance effects at the critical orbit inclination. The basic nonlinear features of the apsidal motion, which have not been recognized in earlier theories, are incorporated in the analytical development so as to produce a theory valid at all angles of inclination of the orbit.     

ELASTIC WAVES IN 3-D DISCRETE GRIDS

Wave motion in finite element models presents some characteristics different from thoseof wave motion in continuum,which leads to the errors and other special phenomena in finite elementsimulation of wave motion.The wave propagation in a 3-D finite element model is studied by utilizingthe formal solution in the paper,and the corresponding dispersion relations are derived.Then the mainproperties of wave motion in 3-D grids such as dispersion,cut-off frequency and polarization drift arediscussed.Characteristics different from those of wave motion in 2—D grids are revealed.     

三维离散网格中的弹性波动

本文采用形式解法研究三维有限元离散模型中波动的传播规律。文中由波动方程得到它的特征方程，进而给出了三维离散网格中波的频散关系，分析了三维网格中平面波、非匀匀波、寄生振荡及其它可能存在的运动形式的基本特点；详细讨论了平面波的频散、截止频率及偏振漂移等重要的不同于连续介质中的波动传播性质的特点，提示了其中不同于低维网格中 波动的现象。     

捷联惯导姿态算法的测试输入研究

总结了经典圆锥运动、广义圆锥运动、规则进动运动、随机角运动、温和环境等捷联姿态算法的测试输入及各自评价姿态算法性能的标准。推导出了不同频率的圆锥运动的角速率，并考查了其不可交换性误差特性，证明在此输入下算法的性能可以由经典圆锥运动来反映。提出了沿参考坐标系方向的圆锥运动，推导出了机体的角速率，并对其不可交换性误差进行了仿真研究。最后给出了在此输入下姿态算法的评价方法。沿参考坐标系方向的圆锥运动是一种新的更为普遍的测试输入。     

A solar system model with dissipation

A problem of motion for an arbitrary number of planets is discussed with consideration of the forces of gravitational interaction according to the law of universal gravitation. The planets are assumed to be homogeneous viscoelastic spheres. In the process of motion, the planets are deformed and the dissipation of energy takes place due to internal viscous forces. On the basis of the motion separation method, an approximate system of equations is obtained to describe the motion of planet centers of mass and the variation of planet angular momenta with respect to the centers of mass. The equations of motion contain small conservative corrections to the law of universal gravitation and small dissipative forces whose influence causes a decrease of the total mechanical energy. The motion under consideration admits the following first integral: the law of angular momentum conservation for the system with respect to the centers of mass. When the system executes the steady motion corresponding to its rotation with a constant angular velocity as a rigid body, the dissipative forces do not perform work, since the deformed planets have no time-dependent deformations.     

碰摩裂纹转子轴承系统的周期运动稳定性及实验研究

根据碰摩裂纹耦合故障转子轴承系统的非线性动力学方程，利用求解非线性非自治系统周期解的延拓打靶法，研究了系统周期运动的稳定性。研究发现，小偏心量下系统周期运动发生Hopf分岔，大偏心量下系统周期运动发生倍周期分岔，偏心量的加大使周期解的稳定性明显降低；系统碰摩间隙变小，碰摩影响了油膜涡动的形成，使失稳转速有所提高；裂纹深度的加大降低了系统周期运动的稳定性。本文的研究为转子轴承系统的安全稳定运行提供了理论参考。     

活塞二阶运动及活塞裙部摩擦的瞬态分析

为分析不同工况下内燃机活塞-缸套系统的摩擦学和动力学行为,本文从内燃机系统动力学分析入手,结合流体润滑方程,建立了考虑系统变惯量影响的活塞二阶运动与摩擦学行为的瞬态分析模型.以某型号单缸机为例,计算和比较了整个启动过程中曲轴转速、二阶运动及摩擦功耗的变化;对比分析了启动时第一周期与稳定运行时某一周期内活塞二阶运动和活塞裙部摩擦学行为的差别.结果表明:该模型可应用于内燃机动力学和摩擦学行为的稳态及瞬态分析.     

流固偶合运动的边界元法

本文给出了流固偶合运动(包括物体散射辐射及偶合运动)的边界元法理论和应用.对于散射问题,求出了物体引起的散射势及入射波作用于物体的载荷.对于辐射问题,求出了辐射势及物体在流体中运动的附加质量和附加阻尼.偶合问题包括求其中包含的散射势和辐射势以及作用于物体之上的散射力、物体的附加质量、附加阻尼、物体在入射波作用下的运动.在偶合运动问题中,本文采取了边界积分方程与物体在流体中的运动方程联立求解的方法,并将其运用到边界元法的数值过程中.所编制的程序有较高的精度.最后给出了数值计算结果与理论解的比较.