摩擦力对非弹性蹦球倍周期运动的影响

分析了摩擦力对竖直振动台面上完全非弹性蹦球动力学行为的影响.当控制参数Γ由1逐渐增大时,作用在蹦球上的恒定摩擦力不会改变倍周期分岔的序列,但会使倍周期分岔点的数值变大.与无摩擦力时的情况相比,在飞行时间的分岔图中也存在倍周期分岔密集区,只是被横向拉伸纵向压缩,且具有不同的分形特性.与受振颗粒体系中的倍周期分岔过程做了比较,发现当摩擦力取值为颗粒总重量的20%—30%时两者符合很好.     

完全非弹性蹦球的动力学行为

对振动台面上的完全非弹性球的蹦跳行为进行了初步分析.受约化振动加速度的控制，球的运动可以表现出一系列倍周期分岔过程.对几种典型的倍周期运动及分岔情况进行了讨论. 关键词： 蹦球 倍周期分岔 混沌 颗粒物质     

竖直振动颗粒床中的倍周期运动

实验研究了竖直振动颗粒床中颗粒对容器底部的压力随振动强度的变化情况.发现压力随振动加速度的增加经历倍周期分岔，典型的分岔序列为：2P，4P，混沌，3P，6P，混沌，4P，8P，混沌.观察表明，伴随倍周期分岔现象，在颗粒床底部出现颗粒的聚集态.聚集态内颗粒密堆积在一起并作整体的上下运动.采用完全非弹性蹦球模型分析了颗粒对容器底的冲击力，并给出了倍周期分岔现象的一种解释. 关键词： 颗粒物质 混沌 倍周期分岔 非弹性碰撞     

竖直振动颗粒物厚层中冲击力分岔现象

实验研究了竖直振动颗粒物厚层中颗粒对容器底部的压力. 发现这种压力是脉冲式的，并表现出受振动加速度控制的倍周期分岔现象. 在颗粒层底部观察到颗粒密堆积在一起的聚集态. 聚集态内颗粒的自由程较小，并像一个整体一样运动. 关键词： 颗粒物质 混沌 倍周期分岔 非弹性碰撞     

完全非弹性蹦球倍周期运动的分形特征

一个落在振动台面上的完全非弹性球的运动是倍周期的.倍周期分岔过程受约化振动加速度的控制,倍周期分岔图由疏密相间的区域构成.在密集区内,倍周期分岔过程敏感地依赖于控制参数,呈现出复杂的几何结构.分析了密集区的分形特性,并计算了各密集区的分维数.结果表明密集区的分维数是依次增大的,逐渐趋于一个约为1.8的常数. 关键词： 蹦球 倍周期分岔 分形 颗粒物质     

窄振动颗粒床中的运动模式

实验研究了竖直振动情况下,窄容器中颗粒的运动模式.发现运动模式与颗粒床厚度及振动加速度有很强的依赖关系.实验表明横向尺寸较小的容器可以抑制对流卷及拱起现象.对于足够厚的颗粒床,即使振动加速度很大,颗粒床下部仍然存在着颗粒聚集态.出现聚集态时,颗粒床对容器底的冲击力是倍周期分岔的.实验表明倍周期分岔点与颗粒床厚度无关.对于较薄的颗粒床,颗粒可以是聚集态或对流卷,视颗粒尺寸而定.如果使用尺寸分布非常窄的球形颗粒,可以观察到颗粒的有序排列.出现同心的圆筒形“壳”结构,每个“壳”上的颗粒是二维六角密排列的. 关键词： 颗粒物质 倍周期分岔 颗粒聚集态 球堆积     

颗粒物质内部滑动摩擦力的非线性振动现象

实验研究了探测棒竖直穿过圆筒中颗粒物质运动时所受的滑动摩擦阻力.研究发现，厚度为容器直径的0.5到2倍之间，粒径为2 mm的颗粒堆，对探测棒的滑动摩擦力在一个平均水平上随时间作非线性振动.当探测棒以小于2×10^-3 m/s的匀速率上升时，滑动摩擦力平均水平超过初始最大静摩擦力F₀的0.2到0.5倍，变化范围可从F₀到2F₀.频率低于1.35 Hz时，各种频率成分的强度随频率增加按幂函数方式衰减，其主要部分的平均周期T与探测棒运动速率v成反比关系. 关键词： 颗粒物质 滑动摩擦力 非线性振动     

振动颗粒物质中倍周期运动对尺寸分离的影响

实验研究了竖直振动颗粒床中,倍周期运动对尺寸分离的影响.实验中,当振动加速度足够大时,系统中出现稳定的对称对流,进一步增大振动加速度到某个临界值时,还会出现倍周期运动.观察表明,背景颗粒的对流运动对分离过程起主导作用,对流速度决定着分离过程的快慢,而在2倍周期和4倍周期分岔之后,分离时间有所减慢.对引起对流运动的起因进行了分析,以此为基础分析了倍周期运动产生影响的物理机理,并对分离时间进行了定量计算,结果与实验值符合很好. 关键词： 颗粒物质 “巴西果”效应 倍周期分岔 对流     

空气阻力对完全非弹性蹦球动力学行为的影响

一个在振动台面上蹦跳的小球具有复杂的运动形式，如倍周期分岔和混沌．如果球与台面间的碰撞是完全非弹性的，则球的运动是倍周期的，不存在混沌．在分岔相图中，鞍一结不稳定性引入“平台”结构，同时存在倍周期轨道的密集区．这里将研究空气的黏滞阻力对完全非弹性蹦球动力学行为的影响．分析表明，空气阻力很弱时，分岔序列不受影响，但分岔点的数值变大，“平台”和密集区加宽．空气阻力较大时，“平台”与密集区重叠．重叠区内原有产生倍周期运动的机理被破坏，球的运动是混沌的．     

轴向加速运动黏弹性梁受迫振动中的混沌动力学

研究了黏弹性轴向运动梁在外部激励和参数激励共同作用下横向振动的混沌非线性动力学行为. 引入有限支撑刚度, 并考虑黏弹性本构关系取物质导数, 同时计入由梁轴向加速度引起的沿径向变化的轴力, 建立轴向运动黏弹性梁横向非线性振动的偏微分-积分模型. 通过Galerkin截断方法研究了外部激励的频率和因速度简谐脉动引起的参数激励的频率在不可通约关系时轴向运动连续体的非线性动力学行为, 并对不同截断阶数的数值预测进行了对比. 基于对控制方程的Galerkin截断, 得到离散化的常微分方程组, 使用四阶Runge-Kutta方法求解. 基于此数值解, 运用非线性动力学时间序列分析方法, 通过Poincaré 映射, 观察到轴向运动梁随扰动速度幅值的倍周期分岔现象, 并比较了有无外部激励对倍周期分岔的影响. 分别在低速以及近临界高速运动状态下, 从相平面图、Poincaré 映射以及频谱分析的角度识别了系统中存在的准周期运动形态. 关键词： 轴向运动梁 非线性 混沌 分岔     

Parametric study of horizontally vibrated grain packings: comparison between Discrete Element Method and experimental results

Numerical and experimental studies have been undertaken to analyze three parameters controlling the compaction of granular media submitted to sinusoidal horizontal vibrations. We have characterized the influence of the dimensionless acceleration Γ, the geometry of the container and the friction coefficients on the grain velocities and on the packing densities. Above a critical acceleration Γ, the velocities increases with Γ. For low values of Γ, the surface layers are compacted, whereas the bottom layers remain at their initial density. For high values of Γ, the bottom layers get compacted, the surface layers are fluidized so that the bulk dynamic and relaxed densities decreased. In the same way, the effect of the dimensions of the container and of the friction coefficients on the packing properties has been studied for given heights of sand, acceleration and frequency. It has been shown that the influence of the two last parameters is similar to that of acceleration. The numerical results given by the Discrete Element Method appear to be in good agreement with experimental results.     

Stochastic solutions of Navier-Stokes equations: an experimental evidence

An electrodynamic loudspeaker has been operated in anharmonic regime indicated by the nonlinear ordinary differential equation when spring constant γ in restoring term, as well as, viscoelasticity of the membrane material, increases with displacement. For driving currents in the range of 2.8-3.3 A, doubling of the vibration period appears, while for currents in the range of 3.3-3.6 A, multiple sequences of subharmonic vibrations begin with f/4 and 3f/4. An application of currents higher than 3.6 A results in a spectrum, characteristic for the chaotic state. The loudspeaker was then operated in a closed chamber, and subharmonic vibrations disappeared by an evacuation. Subsequent injection of air revoked them again at ～ 120 mbar (Re(')=476) when air viscous forces dominate the Morse convection. At 430 mbar (Re=538) single vibration state was restored, and the phenomenon is in an agreement with prediction of the five mode truncation procedure applied to the Navier-Stokes equations describing a two-dimensional incompressible fluid.     

Parametric study of horizontally vibrated grain packings Comparison between Discrete Element Method and experimental results

Numerical and experimental studies have been undertaken to analyze three parameters controlling the compaction of granular media submitted to sinusoidal horizontal vibrations. We have characterized the influence of the dimensionless acceleration G \Gamma , the geometry of the container and the friction coefficients on the grain velocities and on the packing densities. Above a critical acceleration G_crit \Gamma_{{\rm crit}}^{} , the velocities increases with G \Gamma . For low values of G \Gamma , the surface layers are compacted, whereas the bottom layers remain at their initial density. For high values of G \Gamma , the bottom layers get compacted, the surface layers are fluidized so that the bulk dynamic and relaxed densities decreased. In the same way, the effect of the dimensions of the container and of the friction coefficients on the packing properties has been studied for given heights of sand, acceleration and frequency. It has been shown that the influence of the two last parameters is similar to that of acceleration. The numerical results given by the Discrete Element Method appear to be in good agreement with experimental results.     

受振颗粒“毛细”系统中的对流与有序化

将球形颗粒倒入内径较窄的管状容器时,管壁的曲率会对颗粒的堆积结构产生影响,存在壁效应. 实验表明通过连续的竖直方向的振动,壁效应可以被强化,颗粒可以经由对流由无序排列转变为稳定的同轴筒形“壳层”结构. 每一壳层内,颗粒是二维的六角密堆积, 在这一转变过程中,颗粒堆积率的径向分布由初始的衰减振荡转变为等幅振荡. 分析了堆积率的不均匀性及空气在对流中的作用,以及形成“壳层”结构的动力学过程,对“壳层”结构的稳定性亦进行了讨论. 关键词： 颗粒物质 对流 有序化 毛细     

Impact and vibration testing of shipping containers

Equations are developed for experimental evaluation of restoring and dissipative parameters, as used in a non-linear mathematical unit load model. A specially developed transportation damage simulation test jig is described. This jig is suitable for impact and vibration load reproduction on bottom tier containers in unit loads, but only a single container sample is needed. A detailed case study is described, exemplifying how these parameters may be evaluated by impact (shock) or vibration testing of corrugated produce shipping containers. The initial spring rate K₀ was found to be approximately equal in impact and vibration loading. The parameter r, expressing the non-linearity, was significantly larger in vibration loading than in impact loading. On the other hand, both viscous and Coulomb damping are significantly greater in impact loading than in vibration loading. The same modus operandi may be used for determination of dynamic restoring and dissipative parameters of other products, such as cushioning foams and elastomers.