Fly-wheel model exhibits the hither and thither motion of a bouncing ball

The to and fro motion of a bouncing ball on a flat surface is represented by a low-dimensional model. To describe the repeated reversals of the horizontal velocity of the ball, the elasticity of the ball has to be taken into account. We show that a simple fly-wheel model exhibits the observed hither and thither motion of elastic balls. The suggested model is capable of describing oblique impacts of spherical bodies, which can be important in many applications, including dynamical simulation of granular materials. We find that the behaviour of the bouncing fly-wheel is sensitive to the initial conditions, and the escape time plots are used to illustrate this observation.     

Computational study of bouncing and non-bouncing droplets impacting on superhydrophobic surfaces

We numerically investigate bouncing and non-bouncing of droplets during isothermal impact on superhydrophobic surfaces. An in-house, experimentally validated, finite element method-based computational model is employed to simulate the droplet impact dynamics and transient fluid flow within the droplet. The liquid–gas interface is tracked accurately in Lagrangian framework with dynamic wetting boundary condition at three-phase contact line. The interplay of kinetic, surface and gravitational energies is investigated via systematic variation of impact velocity and equilibrium contact angle. The numerical simulations demonstrate that the droplet bounces off the surface if the total droplet energy at the instance of maximum recoiling exceeds the initial surface and gravitational energy, otherwise not. The non-bouncing droplet is characterized by the oscillations on the free surface due to competition between the kinetic and surface energy. The droplet dimensions and shapes obtained at different times by the simulations are compared with the respective measurements available in the literature. Comparisons show good agreement of numerical data with measurements, and the computational model is able to reconstruct the bouncing and non-bouncing of the droplet as seen in the measurements. The simulated internal flow helps to understand the impact dynamics as well as the interplay of the associated energies during the bouncing and non-bouncing. A regime map is proposed to predict the bouncing and non-bouncing on a superhydrophobic surface with an equilibrium contact angle of 155°, using data of 86 simulations and the measurements available in the literature. We discuss the validity of the computational model for the wetting transition from Cassie to Wenzel state on micro- and nanostructured superhydrophobic surfaces. We demonstrate that the numerical simulation can serve as an important tool to quantify the internal flow, if the simulated droplet shapes match the respective measurements utilizing high-speed photography.     

The dynamics of a bouncing ball with a sinusoidally vibrating table revisited

The dynamical behavior of a bouncing ball with a sinusoidally vibrating table is revisited in this paper. Based on the equation of motion of the ball, the mapping for period-1 motion is constructured and thereby allowing the stability and bifurcation conditions to be determined. Comparison with Holmes's solution [1] shows that our range of stable motion is wider, and through numerical simulations, our stability result is observed to be more accurate. The Poincaré mapping sections of the unstable period-1 motion indicate the existence of identical Smale horseshoe structures and fractals. For a better understanding of the stable and chaotic motions, plots of the physical motion of the bouncing ball superimposed on the vibration of the table are presented.     

The bouncing motion appearing in a robotic system with unilateral constraint

The hopping or bouncing motion can be observed when robotic manipulators are sliding on a rough surface. Making clear the reason of generating such phenomenon is important for the control and dynamical analysis for mechanical systems. In particular, such phenomenon may be related to the problem of Painlevé paradox. By using LCP theory, a general criterion for identifying the bouncing motion appearing in a planar multibody system subject to single unilateral constraint is established, and found its application to a two-link robotic manipulator that comes in contact with a rough constantly moving belt. The admissible set in state space that can assure the manipulator keeping contact with the rough surface is investigated, and found which is influenced by the value of the friction coefficient and the configuration of the system. Painlevé paradox can cause either multiple solutions or non-existence of solutions in calculating contact force. Developing some methods to fill in the flaw is also important for perfecting the theory of rigid-body dynamics. The properties of the tangential impact relating to the inconsistent case of Painlevé paradox have been discovered in this paper, and a jump rule for determining the post-states after the tangential impact finishes is developed. Finally, the comprehensively numerical simulation for the two-link robotic manipulator is carried out, and its dynamical behaviors such as stick-slip, the bouncing motion due to the tangential impact at contact point or the external forces, are exhibited.     

Pitting formation under rolling contact

The mechanism of pitting caused by rolling contact is analyzed using the fracture mechanics approach. The governing factors are the initial crack length, crack angle, contact force, friction, strain hardened layer, and the hydraulic pressure of trapped fluid acting on the crack surface. Mode I and II stress intensity and the strain energy density factors are calculated by application of the two-dimensional finite element method. The strain energy density criterion is applied to show that shallow angle crack under small rolling contact force and friction enhances the probability of pitting under the roller’s running surface. The presence of a strain hardened surface layer also tends to affect the fracture behavior. The analytical results agree well with the experimental observations.     

80°/65°双三角翼摇滚特性风洞实验研究

介绍了在FL-23高速风洞中研究自由摇滚的装置、试验方法、数据采集等试验技术.在马赫数从0.3到0.6范围内,对应的雷诺数从0.56×107/m至1.126×107/m范围内,开展了双三角翼大迎角下的摇滚特性的研究,包括迎角、马赫数、初始释放等参数的影响,给出了典型的结果.结果表明,随着模型迎角的增加,双三角翼呈现不同的滚转运动形态,包括静态稳定、准极限环摇滚、双周期震荡等;试验中马赫数提高对翼摇滚起抑制作用;摇滚运动的最终平衡状态和摇滚幅值与初始状态无关.     

Simple model of bouncing ball dynamics: displacement of the table assumed as quadratic function of time

Nonlinear dynamics of a bouncing ball moving in gravitational field and colliding with a moving limiter is considered. Displacement of the limiter is a quadratic function of time. Several dynamical modes, such as fixed points, 2-cycles, grazing and chaotic bands are studied analytically and numerically. It is shown that chaotic bands appear due to homoclinic structures created from unstable 2-cycles in a corner-type bifurcation.     

基于碰撞模型的斜坡滚石颗粒速度预测

滑坡滚石灾害是西部山区常见的地质灾害类型,具有突发性和随机性强的特点,是山区地质灾害预测和防治工作的重点和难点. 本文基于颗粒接触理论,考虑影响斜坡滚石碰撞过程中的随机因素,建立了用于预测斜坡滚石颗粒碰撞后速度的理论模型. 根据冲量及冲量矩定理建立滚石颗粒碰撞基本方程,得到斜坡滚石颗粒碰撞后反弹速度的解析解. 结果表明:斜坡滚石碰撞后反弹速度的解析解包含了坡角、坡体上被碰颗粒速度以及角度、入射速度和角度以及撞击角度等随机因素;当考虑入射滚石颗粒与坡体上被碰颗粒的撞击角度变化时,模型预测结果与试验结果吻合较好;本文进一步预测了滚石颗粒碰撞后颗粒反弹线速度和角度以及反弹旋转角速度的概率分布情况. 结果显示,反弹颗粒速度和角度以及反弹旋转角速度的概率分布均服从高斯分布;当坡体上被碰颗粒速度和坡角发生变化时,其对反弹颗粒速度和角度以及反弹旋转角速度概率分布定性上没有影响,但是对概率分布的中心参数有显著影响.      

Shift in Optimal Joint Angle of the Ankle Dorsiflexors Following Eccentric Exercise

Exposure to unaccustomed eccentric exercise causes muscle damage. Popping sarcomere theory [1] has been proposed and assumed that eccentric contraction-induced muscle damage predominantly occurs at muscle length on the descending limb of the force-length relationship. This study investigated changes in the mechanical properties following maximum effort eccentric exercise at systematically different muscle lengths for the human ankle dorsiflexors. The results of this study showed that the eccentric exercise of the ankle dorsiflexors decreased the peak torque, shifted the optimal joint angle towards longer muscle length without changes in the level of muscle activation. However, no difference in the shift of the optimal ankle joint angle was observed between the groups that performed eccentric exercise at long muscle length (ECC_L) and at short muscle length (ECC_S). In conclusion, the muscle length at which the eccentric exercise was performed did not produce differential effects on the neuro-mechanical properties of in-vivo human ankle dorsiflexors, and thus the popping sarcomere theory might not be the sole mechanism to account for the eccentric contraction-induced optimal muscle length change.     

方形截面弹俯仰振荡对滚转特性的影响

飞行器在大气环境中飞行时,经常受阵风等的干扰,引发非指令的自激振荡,威胁飞行安全.通过建立刚体六自由度运动方程和N-S方程的松耦合求解技术,研究强迫俯仰振荡过程对滚转特性的影响.针对背风区涡流形态及横侧向气动特性复杂的方形截面飞行器,数值模拟研究了其不同攻角下的静态滚转气动特性、自由滚转运动特性,以及俯仰振荡时不同振荡速率对滚转气动和运动特性的影响.结果表明,此飞行器在静态时临界攻角约为13°,当攻角小于临界攻角时,滚转方向是静不稳定的,诱发快速滚转运动;当攻角大于临界攻角时,滚转方向是静稳定,其滚转运动是收敛的.研究发现,俯仰振荡一般会降低飞行器滚转方向静稳定或静不稳定的量值,增强滚转方向的动态稳定性.在俯仰振荡的影响下,即使滚转方向是静不稳定的,如果俯仰振荡的频率足够大,飞行器的滚转运动也可能是收敛的.     

Moving eccentric crack in a piezoelectric strip bonded to elastic materials

Summary  The steady-state of a propagation eccentric crack in a piezoelectric ceramic strip bonded between two elastic materials under combined anti-plane mechanical shear and in-plane electrical loadings is considered in this paper. The analysis based on the integral transform approach is conducted on the permeable crack condition. Field intensity factors and energy release rate are obtained in terms of a Fredholm integral equation of the second kind. It is shown for this geometry that the crack propagation speed has influence on the dynamic energy release rate. The initial crack branching angle for a PZT-5H piezoceramic structure is predicted by the maximum energy release rate criterion. Received 23 January 2001; accepted for publication 18 October 2001     

Capillary effects on a particle rolling on a plane surface in the presence of a thin liquid film

An experimental study has been performed of the effects of a liquid film on a particle rolling on a planar surface using a combination of laser-induced fluorescence and particle-image velocimetry. Contact angle hysteresis leads to asymmetry of the liquid meniscus, resulting in a difference in contact angle between the front and rear sections of the meniscus relative to the rolling particle. This asymmetry results in a capillary torque that resists the rolling motion of the particle. The particle rolling motion also induces a viscous transport of fluid from the front to the rear of the particle, which acts to shift the location of the contact point. The laser-induced fluorescence method is used to characterize the meniscus asymmetry and the resulting change in contact angle on the two sides of the particle. Particle-image velocimetry in various horizontal and vertical cross-sectional planes is used to examine the flow trajectories and velocity magnitude within the meniscus in the presence of rolling. All experiments are conducted at small capillary number, so that the meniscus is approximately circular in shape.     

ELECTROMECHANICAL COUPLING MODEL AND ANALYSIS OF TRANSIENT BEHAVIOR FOR INERTIAL RECIPROCATION MACHINES

Introduction Inertialvibratingmachinesexcitedbytworotatingeccentricweightsarewidelyusedto siftmaterialsinindustriessuchasmine,metallurgy,chemicalindustry,foodstuff,etc.The eccentricweightisgenerallydrivenbyanasynchronouselectromotor,anditssteady state ope…     

Periodic motion and bifurcations induced by the Painlevé paradox

In this paper we study the periodic motion and bifurcations of the Frictional Impact Oscillator, which consists of an object with normal and tangential degrees of freedom that comes in contact with a rigid surface. The Frictional Impact Oscillator contains the basic mechanism for a hopping phenomenon observed in many practical applications. We will show that the hopping or bouncing motion in this type of systems is closely related to the Painlevé paradox. A dynamical system exhibiting the Painlevé paradox has nonuniqueness and nonexistence of solutions in certain sliding modes. Furthermore, we will show that this type of systems can exhibit the Painlevé paradox for physically realistic values of the friction coefficient.     

On dual-grid level-set method for contact line modeling during impact of a droplet on hydrophobic and superhydrophobic surfaces

In this paper, a numerical methodology for modeling contact line motion in a dual-grid level-set method (DGLSM) – solved on a uniform grid for interface which is twice that for the flow equations – is presented. A quasi-dynamic contact angle model – based on experimental inputs – is implemented to model the dynamic wetting of a droplet, impacting on a hydrophobic or a superhydrophobic surface. High-speed visualization experiments are also presented for the impact of a water droplet on hydrophobic surfaces, with non-bouncing at smaller and bouncing at larger impact velocity. The experimental results for temporal variation of the droplet shapes, wetted-diameter and maximum height of the droplet match very well with the DGLSM based numerical results. The validation of the numerical results is also presented with already published experimental results, for the non-bouncing on a hydrophobic and bouncing on a superhydrophobic surface, at a constant impact velocity. Finally, a qualitative as well as quantitative performance of the DGLSM as compared to the traditional level set method (LSM) is presented by considering our experimental results. The accuracy of the partially refined DGLSM is close to that of the fine-grid based LSM, at a computation cost which is close to that of the coarse-grid based LSM. The DGLSM is demonstrated as an improved LSM for the computational multi-fluid dynamics (CMFD) simulations involving contact line motion.     

滚装船-滑动车辆浮基多体系统的横摇研究

波浪和内部滑动车辆共同作用,使滚装船的横摇加剧。这是许多滚装船发生倾覆的重要原因之一。本文对由滚装船和滑动车辆组成的浮基多体系统中,取滚装船的横摇角和车辆在甲板上的横向位移为此系统的两个自由度。考虑非线性恢复力矩和非线性阻尼力矩的影响,运用浮基多体系统动力学方法,建立了系统的动力学方程。以某型海峡滚装渡轮为例,对在若干车辆同步滑动和波浪共同作用下的滚装船非线性横摇响应和车辆位移响应进行了数值计算,并与线性响应进行了比较,得出了考虑非线性时横摇角显著偏大的结论。     

MOTION OF THE ECCENTRIC ELLIPSOID: GYROSCOPIC BALANCE CONDITION AND STABILITY

本文研究了摩擦系数 和偏心距离对偏心椭球体回转平衡的影响,得到了椭球极轴与地面法向夹角 的运动方程,导出了两类稳定解.结果表明摩擦力是椭球能否旋转至直立的必要条件,当 偏心距一定, 摩擦系数 越大其运动至直立所需的时间越短.偏心距阻碍直立现象的出现,摩擦系数 一定,偏心距 越大,其运动至直立所需的时间越长.当偏心距值增大到一定程度,其将无法直立而是至一稳定的角度,并且稳定角度正比于偏心距,偏心距继续增大,将不会出现回转平衡.     

刚性杆-弹簧摆模型复杂动力学特性的数值仿真

建立一种刚性杆-弹簧摆刚柔耦合强非线性动力学系统模型,给出了无量纲的动力学微分方程．该模型同时存在小幅度快速振荡和大范围慢速摆动的快、慢双时间尺度变量．针对工程中此类系统数值求解容易产生的刚性问题,采用一种三次Hermite插值精细积分法进行数值计算．将频率比、摆长比和初始摆角作为控制参数,研究刚性杆-弹簧摆刚柔耦合系统快、慢变量的复杂动力学行为．通过数值仿真分析,发现系统在不同的控制参数组合下呈现出混沌运动状态,并给出了与系统运动状态相关的控制参数范围,为复杂的刚柔耦合多体系统的设计与数值分析提供了参考．     

Development and evaluation of an in-situ tire testing facility with variable side slip angles

An in-situ tire test rig was developed for field research on tire tractive and maneuverability performances. The Single Wheel Tester (SWT) was mounted on a tractor and a tested wheel was driven by a hydromotor, along a frame of 3 m length. In the SWT, four load cells were utilized to measure longitudinal and lateral forces, input and self-aligning torques, and two optical counters were applied to calculate forward and angular velocities. Response Surface Methodology was used to execute experimental design and to analyze the collected data. Afterwards, reduced form of a 2 Factor Interaction model was extracted to predict rolling resistance using seven factors. The test results show that increasing the normal load and side slip angle will cause an increment of rolling resistance. The incremental growth rate of the rolling resistance due to the normal load increment was observed. At higher cone index values, increasing the angular velocity reduces the rolling resistance, although at lower cone index values, the effect of angular velocity on rolling resistance is in reverse order. In addition, the increasing moisture content effect on rolling resistance at lower side slip angle values was observed.     

浮力气泡对水平壁面的回弹动力学特性

黏性液体中的气泡浮升运动有趣而又复杂,而气泡与固壁边界的相互作用更是广泛存在于实际工程中.基于轴对称数值计算,模拟了浮力驱动下气泡在黏性液体中上升并与顶部水平固壁面碰撞、回弹的过程.采用考虑表面张力的不可压、变密度Navier-Stokes方程来描述气液两相流流动,并通过基于分级八叉树的有限体积法进行数值求解.为准确捕捉气泡在回弹过程中局部而迅速的拓扑变化,采用了动态自适应网格技术耦合流体体积法(volume of fluid,VOF)来重构气泡的形状. 从气泡对壁面的碰撞和回弹的基本现象入手,研究了伽利略数 Ga和接触速度$U_{a}$对气泡回弹动力学特性的影响, 分析了气泡碰撞过程中涡结构的变化.用回弹高度$H$、回弹周期$T$、长宽比{$A_{r}$}、浮升速度$U$、轴向位置$z$和回复系数$C_{r}$等参数来表征不同条件时气泡的运动和形状特性. 研究结果表明,气泡的回弹运动特性对 Ga十分敏感. Ga的增大可加剧气泡形变, 促进气泡的回弹运动, 增多回弹次数,增大回弹参数($T$和$H)$, 提升回复系数. 然而,接触速度并非决定气泡回弹动力学的控制参数, $U_{a}$的改变并不会改变回复系数.