普氏摆运动规律研究

通过建立数学模型,利用相似三角形找到普氏摆运动各个量之间的关系,推导出其运动方程,画出其运动轨迹,并在运动方程的基础上讨论了影响普氏摆演示效果的重要因素.     

滚摆运动的研究

从实验和理论上研究了滚摆的运动,得到了滚摆滚动最大高度和滚动时间随滚动次数的变化关系。揭示了空气阻力及摆线间摩擦力等因素对滚摆运动的影响及其引起的系统机械能损失。     

漏摆运动的研究

研究了物理摆的周期、质量和有效长度随时间变化的规律。     

弹簧摆运动的研究

由初值用差分递推方法模拟弹簧摆的运动,把小球的运动分为横向和径向两个方向,经过研究得出:初始摆角的增大会影响径向的周期运动规律,而劲度系数的变化会影响横向的周期运动规律,大的劲度系数也会对径向周期振动的幅度造成起伏,选择小的摆角和合适的劲度系数可以近似地使小球在横向和径向两个方向上都作周期性运动,且两个方向上运动的耦合影响都很小.     

圆弧摆的运动

给出"圆弧摆"的摆动方程和周期,并分别就悬点的相对位置和圆弧长度对摆的周期的影响作了分析讨论.     

三维弹簧摆的内共振特性分析

通过理论推导和MATLAB数值计算分析了三维弹簧摆的内共振特性,发现在一定条件下,三维弹簧摆在水平面内投影的运动可以近似为不断偏转的线段.通过分析三维弹簧摆在水平面内投影运动的极角,发现其在一段时间内在某一定值附近变化不大;在微振动情形下,极角的变化值与初始条件的变化满足线性关系.     

威尔伯福斯摆运动模式的研究

本文建立了威尔伯福斯摆上下振动与扭转摆动耦合共振的数学模型,并分析了其相关影响因素;通过搭建实验系统,用PASCO传感器观测其运动模式,基于控制变量法进行了探究.研究结果表明,摆上下振动和扭转摆动之间存在共振性的能量转化,摆锤的转动惯量会对其运动状态产生影响,且两种运动的耦合导致了“拍”现象的出现.     

利用Tracker软件研究牛顿摆的运动

通过Tracker软件的自动追踪功能描绘牛顿摆的运动轨迹,得到牛顿摆运动过程中的位移与动量变化图像,由此分析牛顿摆运动过程中的周期变化特点、轨迹特点以及动量衰减过程.本实验能够定量分析牛顿摆的运动特点,实验过程直观、高效,实验结果具有科学性,对物理教学有一定的参考价值.     

Directly forced oscillations of an inverted pendulum

Directly forced, symmetric oscillations of an inverted, lightly damped pendulum are predicted analytically on the hypothesis of sinusoidal motion in a frequency interval terminated by turning-point and symmetry-breaking bifurcations. The predictions are confirmed by numerical simulation.     

From the inverted pendulum to the periodic interface modes

The physics of the spatial propagation of monochromatic waves in periodic media is related to the temporal evolution of the parametric oscillators. We transpose the possibility that a parametric pendulum oscillates in the vicinity of its unstable equilibrium position to the case of monochromatic waves in a lossless unidimensional periodic medium. We develop this concept, that can formally applies to any kind of waves, to the case of longitudinal elastic wave. Our analysis yields us to study the propagation of monochromatic waves in a periodic structure involving two main periods. We evidence a class of phonons we refer to as periodic interface modes that propagate in these structures. These modes are similar to the optical Tamm states exhibited in photonic crystals. Our analysis is based on both a formal and an analytical approach. The application of the concept to the case of phonons in an experimentally realizable structure is given. We finally show how to control the frequencies of these phonons from the engineering of the periodic structure.     

倒摆运动的混沌行为

设计一个受周期外力驱动的倒摆实验装置,并建立该系统的动力学方程,用线性稳定性分析方法讨论了平衡点附近邻域的稳定性,利用数值计算并结合多种分析方法求解非线性方程并判断解的性质．通过改变系统参数,画出时域图、相图及分岔图,计算分析和实验发现,这个简单的力学系统存在十分丰富的动力学行为（分岔、混沌）．理论分析、数值模拟和实验结果一致．     

Stability of the parametrically excited damped inverted pendulum: theory and experiment

The parametrically driven, damped, inverted pendulum can be dynamically stabilized in particular regions of the parameter space. The impact of damping on dynamic stabilization can be stabilizing or destabilizing depending on the location in parameter space (i.e., drive frequency and amplitude). Floquet analysis and numerical simulations were used to determine the stable regions. An experiment was conducted that verifies the model. Physical explanations and simple bounding approximations are provided to summarize findings. The utility of the highly damped pendulum results are illustrated by drawing the analogy to dynamic stabilization of the Rayleigh-Taylor instability: it permits ready demonstration that dynamic stabilization is impossible in that system absent surface tension.     

外周期力驱动的倒摆混沌运动演示仪

设计并制作了受周期外力驱动的倒摆演示实验装置．利用自主开发的软件可自动演示和记录摆球运动状态的时间序列并存储实验数据．通过改变摆长、驱动电压，观察到该系统存在通过倍周期分岔通向混沌的过程．     

韦氏耦合摆共振机理探索

分析了韦氏摆的共振机理. 韦氏摆可以看作是扭摆和弹簧振子的组合,两者在垂直方向上可以达到共振,有相互间力的作用. 通过实验证实了传递力的存在,并测量了传递比率,通过计算机实时测量,完全符合理论推断.     

Harvesting base vibration energy by a piezoelectric inverted beam with pendulum

We proposed a two-degrees-of-freedom inverted piezoelectric beam with pendulum to promote the performance of vibration energy harvesting. This configuration is composed of an inverted elastic beam and a pendulum attached to its free end. The electromechanical equations governing the nonlinear system were derived. The harmonic balance method(HBM)is applied to solve the equation and the results prove that there exists a 1:3 super-harmonic resonance. The simulation results show that owing to the particular nonlinearity, there appears a special bending effect in the amplitude-frequency response, i.e., bending right for the first natural frequency and left for the second natural frequency, which is beneficial for harvesting vibration energy. The HBM results are verified by the entity simulations. Furthermore, over a relatively wide range of power spectral density, it could reach a dense jumping and give a dense high pulse voltage.     

一种双惯性轮空间倒立摆及其动力学建模和分析

针对现有的惯性轮倒立摆在模拟多自由度不稳定系统的局限性,提出了一种双惯性轮空间倒立摆系统,其具有四个自由度和两个控制量,可同时模拟不稳定系统俯仰和滚转姿态控制。运用拉格朗日方法建立了双惯性轮空间倒立摆的动力学模型,分别采用模型退化、数值仿真验证了所建立的模型的正确性,并分析了双惯性轮空间倒立摆的动力学特性。建立的双惯性轮空间倒立摆可应用于多自由度非平稳系统的模拟实验,提出的物理结构、模型和相关分析结论为双惯性轮空间倒立摆系统的进一步研究奠定了理论基础。     

Bifurcation in an inverted pendulum with tilted high-frequency excitation: analytical and experimental investigations on the symmetry-breaking of the bifurcation

In this study, we investigate the dynamics of an inverted pendulum subjected to high-frequency excitation. In particular, we focus on bifurcation phenomena in the dynamics and analyze the effect of the tilt of the excitation direction with respect to gravity direction on the bifurcation. It is analytically clarified that the tilt produces stable equilibrium states different from the directions of the gravity and the excitation. The stability of the stable equilibrium states under the effect of the tilt is discussed non-locally. Also, an analogy of the bifurcation of the inverted pendulum to that of the buckling phenomenon is presented. The theoretically predicted effects of the tilt are qualitatively confirmed by performing some experiments.