振动运输机系统的动力学特性研究

通过完全塑性碰撞的理想条件假设,建立了振动运输机的力学模型.推导了系统运动的解析解并建立了Poincaré映射.利用半解析法,对其塑性碰撞的全过程进行了分析.借助分岔图、相轨迹图、时间历程曲线、Poincaré映射图对振动运输机系统进行了研究,发现了在不同参数下其分岔形式以及通往混沌的道路具有多样性,同时擦边分岔的产生会使系统具有一定的运动趋势但不会改变系统的最小运动周期,为振动运输机系统的动力学优化设计提供了理论依据.     

含间隙振动系统的周期运动和分岔

研究了一类多自由度含间隙振动系统的动态响应,根据碰撞条件和由碰撞规律所确定的衔接条件求得系统的对称型周期碰撞运动及相关Poincare映射,讨论了该映射不动点的稳定性与局部分岔。用一个2自由度含间隙振动系统阐述了方法的有效性,分析了对称型周期碰撞运动稳定性、分岔、擦边奇异性和混沌形成过程。通过数值仿真研究了铁道车辆轮对的横向周期碰撞振动,分析了轮对对称型周期碰撞运动的叉式分岔和擦边映射奇异性。     

三自由度含间隙塑性碰撞振动系统的分岔与混沌

研究了一类三自由度含间隙双边塑性碰撞振动的模型的分岔和混沌运动。建立其Poincaré映射,通过数值仿真和解析解结合的方法揭示了系统通过倍化分岔、Hopf分岔和概周期通向混沌的道路,分析了系统在分岔点附近的复杂的动力学行为。     

塑性冲击振动系统的非光滑分岔

考虑塑性碰撞工况下的单自由度冲击振动系统,推导了擦边分岔和余维一滑动分岔的条件。结合二维参数和单参数分岔分析,研究了单冲击周期运动的分岔特征,揭示了冲击振动系统的穿越滑动分岔、切换滑动分岔和余维二滑动分岔等非光滑分岔以及擦边分岔和混沌激变等不连续分岔行为。非黏滞型周期运动与黏滞型周期运动经穿越滑动分岔相互转迁。在二维参数平面的低频小间隙区域,(1,1,1)周期运动与(1,2,1)周期运动交替出现。两类周期运动的临界线为切换滑动分岔线。混沌边界激变导致混沌吸引子及其吸引域突然消失。     

一类三自由度碰撞振动系统的Hopf-pitchfork余维二分岔与混沌

建立了一类三自由度振动碰撞系统的力学模型,推导了系统周期运动的解析解及Poincaré映射。基于六维Poincaré映射方法研究了系统的Hopf-pitchfork余维二分岔。在Hopf-pitchfork余维二分岔中先发生Pitchfork分岔,后发生Hopf分岔。系统通过概周期通向混沌的非常规道路揭示了在余维二分岔点附近的复杂动力学行为。     

高维复杂碰撞振动系统的概周期环面分岔与混沌

建立了一类三自由度含间隙碰撞振动系统的力学模型,推导了系统周期运动的解析解及Poincaré映射。基于六维Poincaré映射方法研究了系统的Hopf-flip余维二分岔和倍化分岔。在Hopf-flip余维二分岔中先发生Flip分岔后发生Hopf分岔,并展现了由环面倍化和"贝壳形"概周期吸引子向混沌演化的两种非常规路线。其后分析了系统周期运动经倍化分岔向混沌的演化的过程中,存在着十分复杂的非常规转迁过程和精彩的动力学行为。     

两自由度单侧碰撞振动系统的分岔与混沌

建立了一类两自由度单侧碰撞振动系统的力学模型和Poincaré映射。通过计算机编程仿真,得到了以Poincaré截面上的不变圈表示的拟周期运动,证明了系统在一定条件下存在Neimark-Sacker分岔和周期倍化分岔,并分析了其向混沌演化的不同道路,可为工程实际中该类系统的优化设计提供依据。     

一类三自由度碰撞振动系统的分岔与混沌演化

利用解析法对建立的三自由度碰撞振动系统进行求解,通过分析系统周期运动的边界条件,推导出系统周期运动的解析解;再利用受扰运动的边界条件推导出了系统的Poincaré映射,并通过编程进行数值仿真,分析了系统发生分岔与混沌的非线性行为。     

两自由度赫兹接触碰撞振动系统的动力学研究

以含间隙非线性赫兹接触力碰撞振动系统动力学模型为研究对象,建立了该模型的Poincaré映射,通过数值模拟,揭示了该系统在低频率、小间隙下存在非完全颤振现象,总结了系统响应从1-1-1周期运动经过Grazing分岔和Saddle-node分岔转迁到非完全颤振1-■-■运动的变化规律,数值结果表明由于初值的影响周期1-p-p运动与1-(p+1)-(p+1)运动间出现了迟滞区域共存现象。在一定的频率下基本周期1-p-p运动与1-(p+1)-(p+1)运动之间存在擦边、逆倍化分岔、混沌等运动形式,文章得出高频下对称周期运动转迁到非对称的周期运动的变化规律。     

一类碰撞振动系统的概周期运动及混沌形成过程

基于Poincar啨映射方法和数值仿真,对一类双自由度碰撞振动系统单碰撞周期运动的稳定性与分岔进行分析。着重研究单碰撞周期运动在非共振和弱共振条件下的内依马克沙克分岔、强共振情况下的亚谐分岔、Hopfflip分岔和多碰撞周期运动的内依马克沙克分岔。通过数值仿真分析概周期碰撞运动向混沌运动的演化过程。     

Dynamics of vibro-impact mechanical systems with large dissipation

An n-degree-of-freedom system having placed single stop and subjected to periodic excitation is considered. Based on the analysis of dynamics of the vibratory system with plastic impacts, we introduce a (2n−1)-dimensional map with dynamical variables defined at the impact instants. The nonlinear dynamics of the vibro-impact system is analyzed by using the Poincaré map, in which piecewise property and singularity are found to exist. The piecewise property is caused by the transitions of free flight and sticking motions of the impact mass immediately after the impact, and the singularity of the map is generated via the grazing contact of both the impact mass and the rigid stop and corresponding instability of periodic-impact motions. These properties of the map have been shown to exhibit particular types of sliding and grazing bifurcations of periodic-impact motions under parameter variation. The single-impact periodic motions and disturbed map, associated with free flight motion of the system, are derived analytically. Stability, sliding and period-doubling bifurcations of the single-impact periodic motions are analyzed by the presentation of results for a three-degree-of-freedom plastic impact oscillator. Finally two actual examples, the impact-forming machine and inertial shaker, are considered to further analyze periodic-impact motions and bifurcations of plastic impact oscillators. The free flight and sticking solutions of two impact machines are analyzed numerically, and regions of existence and stability of different periodic-impact motions are therefore presented. The influence of non-standard bifurcations and system parameters on dynamics of the vibro-impact machines is elucidated accordingly.     

碰撞-渐进振动系统的亚谐振动与分岔分析

建立了碰撞-渐进振动系统的力学模型。分析了激振器和缓冲垫发生碰撞的类型,以及滑块渐进运动的条件。给出了系统可能呈现的4种运动状态的判断条件和运动微分方程。通过二维参数分岔分析,得到系统的各类周期振动在激振频率和预压量参数平面内的存在域及其分布规律。详细分析了1/n亚谐振动的分岔过程。当激振频率增大时,由于发生周期振动的实擦边分岔、虚擦边分岔或鞍结分岔等非光滑分岔,使得1/n亚谐振动的分岔过程变得更加复杂,而且受预压量的影响比较大。     

Dynamics of an impact-forming machine

An impact-forming machine is considered. Dynamics of the impact-forming system are studied with special attention to stability of period n single-impact motion, Hopf bifurcations in non-resonance and weak resonance cases, subharmonic and Hopf bifurcations in 1:4 strong resonance case, codimension two bifurcations and chaotic motions, etc. Period n single-impact motion is derived analytically. The Poincaré section associated with the state of the impact-forming system, just immediately after the impact, is chosen, and then the disturbed map of period n single-impact motion is established. Stability and local bifurcations of period one single-impact motion are analyzed by using the Poincaré map. Local bifurcation analyses and numerical simulation show that period one single-impact motion, in most cases, undergoes period doubling bifurcation or Hopf bifurcation with change of control parameters. Period one single-impact motion undergoes either subharmonic or Hopf bifurcation in 1:4 strong resonance case. The grazing instability occurs in the strong resonance case. Generally on the grazing boundary of periodic-impact motion a new impact in the motion period appears or an impact in the motion period vanishes. Near the points of codimension two bifurcations there exists not only Hopf bifurcation of period one single-impact motion, but also Hopf bifurcation of period two double-impact motion. Finally, the influences of system parameters on periodic motions and global bifurcations of the impact-forming system are discussed. In designing impact tools it is of great interest to achieve the desired periodic impact velocities. In order to facilitate such design, the global bifurcation diagrams for the relative impact velocities of the impact-forming system versus the forcing frequency are plotted, which enable the practicing engineer to select excitation frequency ranges in which stable period one single-impact response can be expected to occur, and to predict the larger impact velocities and shorter impact period of such response. In designing and remaking the impact-forming machine, if some system parameters have been given or limited, the other parameters and forcing frequency can be optimized by analyses of stability and bifurcation of periodic impact motion so that the impact-forming system exhibits stable period one single-impact motion with larger impact velocity and shorter impact period.     

Global Dynamic Characteristic of Nonlinear Torsional Vibration System under Harmonically Excitation

Torsional vibration generally causes serious instability and damage problems in many rotating machinery parts. The global dynamic characteristic of nonlinear torsional vibration system with nonlinear rigidity and nonlinear friction force is investigated. On the basis of the generalized dissipation Lagrange's equation, the dynamics equation of nonlinear torsional vibration system is deduced. The bifurcation and chaotic motion in the system subjected to an external harmonic excitation is studied by theoretical analysis and numerical simulation. The stability of unperturbed system is analyzed by using the stability theory of equilibrium positions of Hamiltonian systems. The criterion of existence of chaos phenomena under a periodic perturbation is given by means of Melnikov's method. It is shown that the existence of homoclinic and heteroclinic orbits in the unperturbed system implies chaos arising from breaking of homoclinic or heteroclinic orbits under perturbation. The validity of the result is checked numerically. Periodic doubling bifurcation route to chaos, quasi-periodic route to chaos, intermittency route to chaos are found to occur due to the amplitude varying in some range. The evolution of system dynamic responses is demonstrated in detail by Poincare maps and bifurcation diagrams when the system undergoes a sequence of periodic doubling or quasi-periodic bifurcations to chaos. The conclusion can provide reference for deeply researching the dynamic behavior of mechanical drive systems.     

基于钻头-岩石碰撞的激振冲击系统的非线性动力学研究

为了提升旋转冲击钻井过程中轴向冲击的辅助破岩效果,设计了一套用于测试钻头与岩石之间激振碰撞的试验装置,通过对钻头的激振频率、激振振幅和施加的静态压力3项可控参数的调节,研究了该激振冲击系统的动力学行为演化规律,且试验测试结果与数值模拟结果具有很好的一致性。通过进一步的分岔分析和相平面分析发现,由于激振冲击系统具有典型的接触非线性结构,其动态响应也呈现出复杂的非线性特征,钻头在与岩石发生激振碰撞后,主要保持单周期的振动状态,但随着控制参数的变化,钻头与岩石之间在一个激励周期内的碰撞次数会不断改变;此外,钻头的振动状态还会经由倍周期分岔转变为双周期振动,但最终又会经由逆倍周期分岔或者折叠分岔重新回到单周期振动状态。由于钻头的振动状态直接决定了其轴向冲击力的大小,因而会影响其破岩效率;因此,为了获得破岩效率最高的一周期一次碰撞的钻头振动状态,应该采用较高的激振频率和振幅,但应该避免较高的静态压力,因为它将触发钻头的颤振,反而降低其破岩效率。     

Stress singularities at angular corners in first-order shear deformation plate theory

The first-known Williams-type singularities caused by homogeneous boundary conditions in the first-order shear deformation plate theory (FSDPT) are thoroughly examined. An eigenfunction expansion method is used to solve the three equilibrium equations in terms of displacement components. Asymptotic solutions for both moment singularity and shear-force singularity are developed. The characteristic equations for moment singularity and shear-force singularity and the corresponding corner functions due to ten different combinations of boundary conditions are explicated in this study. The validity of the present solution is confirmed by comparing with the singularities in the exact solution for free vibrations of Mindlin sector plates with simply supported radial edges, and with the singularities in the three-dimensional elasticity solution for a completely free wedge. The singularity orders of moments and shear forces caused by various boundary conditions are also thoroughly discussed. The singularity orders of moments and shear forces are compared according to FSDPT and classic plate theory.     

航空发动机碰摩故障的非线性动力学分析

考虑系统的陀螺效应,建立含碰摩故障的滚动轴承支撑的系统动力学模型.利用打靶法分析系统在不同碰摩间隙下的分叉和混沌行为.分析表明系统随着碰摩间隙的增大,经历了混沌运动、周期运动、拟周期运动、再到混沌运动、最后进入正常周期运动的过程,且碰摩间隙对系统的动力学行为有较大的影响.     

一类自治离心式调速器系统的Hopf分岔与混沌

研究一类自治离心式调速器系统的Hopf分岔与混沌运动等复杂动力学行为。利用Taylor级数展开得到离心调速器系统在平衡点附近的运动方程,并利用Hopf分岔定理研究系统发生Hopf分岔的条件及相应分岔解的稳定性,数值模拟验证理论分析结果。用4阶Runge-Kutta方法对这类自治系统进行计算,利用相图、Poincaré截面、分岔图等研究该系统的混沌运动。通过对系统参数的不断变化,分析得出系统由Hopf分岔通向混沌又进入周期运动的演化过程。     

多因素条件下单级齿轮系统的非线性特性

考虑啮合刚度、齿侧间隙和轴承支撑间隙等因素,运用集中质量法建立了三自由度直齿圆柱齿轮副弯扭耦合非线性振动模型,并据此研究了各参数对齿轮系统非线性振动特性的影响。结果表明：齿侧间隙一定时,随着频率的升高,系统由周期运动通过激变直接进入混沌,然后又由混沌通过激变变为周期运动;在周期运动中,系统经过倍周期分岔,由双周期运动变为四周期运动,然后又通过逆倍周期分岔,由四周期运动变为双周期运动,之后又由双周期运动变为单周期运动;不同的输入转频条件下,间隙变化使系统表现出不同分岔特性,在某些特定频率下,间隙变化只增加系统响应能量变化,并不改变其动力学特性。