On the dynamics of vibro-impact systems with ideal and non-ideal excitation

This study is concerned with modelling and analyses of a vibro-impact system consisting of a crank-slider mechanism and one oscillator attached to it, where the system is exposed to a non-ideal excitation. The impact occurs during the motion of the oscillator when it fits a base, and the excitation of the driving source is affected by this behaviour. The aim is to determine the interaction between a driving torque and the motion of the oscillator. To achieve this aim in a methodologically sound manner, both vibrating and vibro-impact systems with an ideal and non-ideal excitation are analysed. Analytical and numerical solutions are obtained for the vibrating system with the ideal excitation. Numerical analyses of the vibrating system with the non-ideal excitation is then conducted, where the characteristic curves for this system are found analytically. Numerical simulations are also carried out for other two systems and the results obtained are shown in terms of frequency–response diagrams, time-displacement diagrams and basins of attraction. The results found for different systems are compared mutually, and the differences between them are pointed out. Impact solutions for different regions of the excitation frequency are shown. For the vibro-impact system with the non-ideal excitation, the average value of its frequency is used.

     

圆柱体双自由度涡激振动轨迹的模型试验

对水平放置的直径 5cm,长120cm的圆柱体开展了双自由度涡激振动模型试验研究. 试验中发现,圆柱体在顺流向上的振动频率表现为"多频"的现象,即不光有2倍横向振动的频率,在某些振动固有频率和约化速度的条件下,还出现了单倍横向振动的频率,从而使圆柱体的轨迹呈现出"卵"形以及"雨滴"形等明显异于传统"8"字形与"新月"形的运动轨迹. 此外,通过研究初步得到了各种其他形式的振动轨迹向"8"字形变化的趋势,并认为不同的横向、顺流向振动固有频率以及流速是导致圆柱体涡激振动轨迹产生多种形式的主要原因.      

Suppression of self-excited vibrations by a random parametric excitation

Previous theoretical and experimental studies have shown that some vibrating systems can be stabilized by zero-averaged periodic parametric excitations. It is shown in this paper that some zero-mean random parametric excitations can also be useful for this stabilization. Under some conditions, they can be even more efficient compared to the periodic ones. Two-mass mechanical system with self-excited vibrations is considered for this comparison. The so-called bounded noise is used as a model of the random parametric excitation. The mean-square stability diagrams are obtained numerically by considering an eigenvalue problem for large matrices.     

高层钢结构TMD风振舒适度控制优化设计方法

研究高层钢结构系统的ＴＭＤ风振舒适度控制设计方法,导出了受控结构的内振加速度设计计算公式,给出了受控结构脉动增大系数设计表格和控制设计步骤。算例表明,ＴＭＤ对结构风振加速度的控制是十分有效的。     

Nonlocal vibration of carbon nanotubes with attached buckyballs at tip

Nonlocal longitudinal vibration of single-walled-carbon-nanotubes (SWCNTs) with attached buckyballs is considered. Attached buckyball at the tip of a SWCNT can significantly influence the resonance frequency of the vibrating system. Closed-form nonlocal transcendental equation for vibrating system with arbitrary mass ratio i.e. mass of buckyball to mass of SWCNT is derived. Nonlocal elasticity concept is employed to develop the frequency equations. Explicit analytical expressions of axial frequencies are proposed when mass of the attached buckyball is larger than the mass of SWCNT. Nonlocal longitudinal frequencies are validated with existing molecular dynamic simulation result. For arbitrary mass ratios, the frequency shifts in SWCNT due to (i) added buckyballs and (ii) nonlocal-effects are investigated. The present communication may be useful when designing tuneable resonator in NEMS applications.     

浮筏隔振系统功率流特性分析

针对工程实际中浮筏隔振装置，建立了柔性基础上机组多支承弹性浮筏耦合隔振系统动力学普遍模型，提出了子系统动态特性综合分析法，给出了耦合系统动态传递方程及功率流表达式。根据工程中两机组浮筏隔振系统功率流理论计算结果，着重探讨安装频率与支承结构柔性耦合作用及其对隔振效果影响。研究结果表明：合理设计安装频率，可有效控制振动能量传输。     

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.     

主动移频式动力吸振器及其动力特性的研究

动力吸振器是振动控制中比较有效的减振装置,只要吸振器(子系统)的振动固有频率与振动物体(主系统)的振动频率相同,即可有效地消除主系统的振动。但传统动力吸振器的控制频率带宽较窄,限制了其稳定性和减振效果的提高。本文通过独特的机械设计,研制了一种可以通过调节自身的几何参数,使得其固有频率随几何参数线性变化的主动移频的新型动力吸振器,并初步设定了相应的控制方法。文中还对其动力学特性进行了理论分析和实验测试,分析了它的机理,评估了它的实际减振效果。研究结果表明该吸振器可以大范围调节自身固有频率,有效拓宽吸振频带,具有良好的减振性能和稳定性。     

Vibration suppression of a time-varying stiffness AMB bearing to multi-parametric excitations via time delay controller

The applications of active magnetic bearings are growing in industry due to its amazing advantages in reducing friction losses. In this research, the vibration of a two-degree-of-freedom rotor, active magnetic bearings system is suppressed via a nonlinear time delay controller at the confirmed worst resonance case. The selected resonance case is the simultaneous primary and sub-harmonic resonance case. The main aim of this paper was to study the effects of the nonlinear, time delay controller on the behavior of the vibrating system. The multiple time scale perturbation technique is applied to obtain an approximate solution to the second-order approximation. The steady-state solution is obtained around the worst resonance case. The stability of the system is studied applying both frequency response equations and phase-plane method. The worst resonance case is confirmed applying numerical technique. The effects of the different parameters on the steady-state response of the vibrating system are investigated. The obtained approximate solution is validated numerically. Some recommendations are given regarding the design of such system. At the end of the work, a comparison is made with the available published work.     

Towards non-linear modeling of molecular interactions arising from adsorbed biological species on the microcantilever surface

Microcantilever-based biosensors are rapidly becoming an enabling sensing technology for a variety of label-free biological applications due to their extreme applicability, versatility and low cost. These sensors operate through the adsorption of species on the functionalized surface of microcantilevers. This paper presents a general framework towards modeling resonance frequency changes induced due to the surface stress arising from the adsorption of biological species on the surface of the microcantilever. Very few works have dealt with the effect of surface stress on the resonance frequency shifts of microcantilevers and have mainly assumed a simple model for the vibrating microcantilever beam. In the proposed modeling framework, the non-linear terms due to the beam's flexural rigidity from macro- to microscale as well as varying nature of the adsorption induced surface stress are considered. It is first shown that the non-linearity of the system originates from two different sources, namely, microcantilever flexural rigidity and adsorption induced surface stress. Through simulation results, it is demonstrated that the non-linearity due to the surface stress does not have a considerable effect on the resonance frequency change of the microcantilever. However, non-linearity due to flexural rigidity (which is directly attributed to beam's dimensions) plays an important role in the resonance frequency shift, and hence, in the resultant molecular recognition capability. It is then shown that the adsorption induced resonance frequency shift highly depends on the size of the microcantilever. It is also demonstrated that the effect of surface stress and molecular arrangement modeling presented in this paper is more sensitive to the change of the microcantilever length.     

振荡燃烧的动态测试及信息处理

作者用随机信息处理方法研究了某型火箭发动机的燃烧状况,不仅发现该型发动机存在有振荡燃烧,而且获得了振荡燃烧信息的功率谱及功率谱阵。针对振荡燃烧信息在时间域和频率域上的随机性特点,作者精心地设计了测试系统,并对系统的性能参数进行了全面标定。经多次实测证明该系统工作可靠,信噪比较高。测试与分析结果表明:该型发动机振荡燃烧的主振测率为800Hz,最大振幅为43dB;并存在有1600Hz和2500Hz两个次级振荡频率;而且该发动机的振荡燃烧是以纵向振荡为主。为研究该型火箭发动机振荡燃烧的产生原因和消除方法提供了科学依据。     

电磁作用激发的水电机组转子轴系振动研究

水轮发电机组的振动问题是长期困扰广大科研工作者的一个难题,也一直是学术界研究的热点.本文针对某大型水轮发电机转子轴系,首先建立了轴系扭振的微分方程组,给出了轴系整体扭振零频的计算公式,并计算了零频数值.接着在考虑了转子静偏心、振动偏心和转动偏心的综合影响后,求得了气隙磁场能量和单边电磁拉力的表达式,并应用机电耦联系统的能量法,求得了系统由电磁力激发的组合强迫共振响应的一次近似解.最后并应用奇异性理论对分岔方程进行了分析,求得了分岔集、滞后集、双极限集和转迁集的参数区间,给出了普适开折平面和物理参数平面上的分岔图,求得了机组稳定运行区域的电磁参数.本文所得结论对水电机组的工程设计人员具有重要的指导意义.     

基于多尺度方法的平动圆柱贮箱航天器刚——液耦合动力学研究

以充液航天器为工程背景,借助多尺度方法研究刚--液耦合动力学系统非线性动力学特性.利用多维模态方法,将描述横向外激励下圆柱贮箱中液体非线性晃动的自由边界问题转换为液体模态系数相互耦合的有限维非线性常微分方程组.推导液体晃动产生的作用于贮箱壁的晃动力和晃动力矩的解析表达式,进而建立航天器刚体部分平动和液体晃动耦合的非线性动力学方程组.应用多尺度方法对刚--液耦合系统的动力学特性进行解析分析,通过固有频率的特征方程求解耦合系统固有频率,推导外激励频率接近耦合系统第一阶固有频率时液体晃动稳态解的幅值频率响应方程.结合数值方法,研究了液体晃动稳态解的幅值频率响应曲线和激励--幅值响应曲线.结果表明, 随充液比变化,液体晃动稳态解的幅值频率响应曲线会发生软、硬弹簧特性转换现象和"跳跃"现象;幅值频率响应曲线的软、硬弹簧特性转换点受重力加速度和弹簧刚度系数影响;以上所得研究结果表明,考虑非线性效应时的刚--液耦合系统动力学特性与传统的线性系统模型所显示的动力学特性具有本质区别.本文的研究工作对进一步分析充液航天器刚--液耦合非线性动力学特性具有重要参考价值.      

基于变密度法的平模台振加强筋布局优化

针对混凝土预制构件水平成型振动台(简称平模台振)振动效果改进的问题,提出了通过优化振动台面加强筋布局来提高其振动效果的方法.基于变密度拓扑优化法,建立以加强筋单元相对密度为设计变量,振动台面柔度最小为目标的优化模型,并进行灵敏度分析,采用最优准则法求解优化模型;根据拓扑优化结果,对振动台面加强筋进行布局优化,获得了合理...     

Motion types and chaos of multi-body systems vibrating with impacts

In this paper, the limit sets theory for an autonomous dynamical system is generalized to a multi-body system vibrating with impacts. We discover that if every motion of the system is bounded, it has only four different types: periodic motion γ1, non·periodic recurrent motion γ2, and non-Poisson stable motions γ3 and γ4 approaching γ1 and γ2, respectively. γ2 is the source of chaos. It is very interesting that chaotic motions seem stochastic but possess the character of recurrence. By way of example, we discuss chaotic motions of a small ball bouncing vertically on a massive vibrating table. The result obtained by us is different from that obtained by Holmes. The project supported by National Natural Science Foundation of China     

Hybrid dynamics of two coupled oscillators that can impact a fixed stop

We consider two linearly coupled masses, where one mass can have inelastic impacts with a fixed, rigid stop. This leads to the study of a two degree of freedom, piecewise linear, frictionless, unforced, constrained mechanical system. The system is governed by three types of dynamics: coupled harmonic oscillation, simple harmonic motion and discrete rebounds. Energy is dissipated discontinuously in discrete amounts, through impacts with the stop. We prove the existence of a non-zero measure set of orbits that lead to infinite impacts with the stop in a finite time. We show how to modify the mathematical model so that forward existence and uniqueness of solutions for all time is guaranteed. Existence of hybrid periodic orbits is shown. A geometrical interpretation of the dynamics based on action coordinates is used to visualize numerical simulation results for the asymptotic dynamics.     

Active vibration control of a dynamical system via negative linear velocity feedback

In this paper, a negative velocity feedback is added to a dynamical system which is represented by second-order nonlinear differential equations having quadratic coupling, quadratic, and cubic nonlinearities. The system describes the vibration of the system subjected to multi-parametric excitation forces. The method of multiple scale perturbation technique is applied to obtain the response equation near the simultaneous internal and super-harmonic resonance case of this system. The stability to the system is investigated applying frequency response equations. The numerical solution and the effects of some parameters on the vibrating system are investigated and reported. The simulation results are achieved using MATLAB 7.0 program. A comparison is made with the available published work.     

Flow induced by a vibrating heated sphere

Mean flows induced by a heated or cold sphere vibrating in a liquid are studied. The cases of a sphere immersed in an unbounded liquid and a liquid layer of finite thickness, bounded by two rigid coaxial spheres, are considered. An analytical solution is obtained in the creeping flow approximation for small values of the governing parameters. The vibrating flow structure is shown to depend to a considerable extent on the clearance and to be fairly complex for small clearances. For a fixed clearance, the creeping flow structure is determined by a single parameter, the ratio of the vibrating Grashof number to the pulsating Reynolds number (Schlichting parameter). For large values of the parameters, the vibrating flow structure is determined by the vibrating Grashof number and the Schlichting parameter separately. The changes in the flow structure with increase in the values of the governing parameters are studied numerically by a finite difference method.Krasnoyarsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 31–39, January–February, 1996.     

用振动梁方法测量粘弹性材料的复模量和粘弹性参数

本文利用共振梁方法,通过对一点响应、相位滞后和共振频率的测量,可以获得粘弹性材料的复模量以及标准线性固体模型的三个参数,即松弛模量、松弛系数和蠕变系数.实验结果表明,实验原理正确,测试系统可靠而且简单实用.