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RESEARCH OF THE periodic motion AND STABILITY OF TWO-DEGREE-OF-FREEDOM NONLINEAR OSCILLATING SYSTEMS

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Applied Mathematics and Mechanics(English Edition) 2002年第10期23卷 1229-1236页

作者： LIU Jun(刘俊) Department of Mathematics Qujing Normal CollegeQujing Yunnan 655000P R China

The periodic motion and stability for a class of two-degree-of-freedom nonlinear oscillating systems are studied by using the method of Liapunov function. The sufficient conditions which guarantee the existence, uniqu... 详细信息

关键词： nonlinear oscillation periodic motion Liapunov function periodic solution

Bifurcation of periodic motion of Rigid Rotor System Supported by Angular Contact Ball Bearings

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Transactions of Tianjin University 2011年第6期17卷 404-410页

作者：崔立刘长利郑建荣 Key Laboratory of Safety Science of Pressurized System of Ministry of Education School of Mechanical and Power EngineeringEast China University of Science and Technology

Rotor systems supported by angular contact ball bearings are complicated due to nonlinear Hertzian contact force. In this paper, nonlinear bearing forces of ball bearing under five-dimensional loads are given, and 5-DOF dynamic equations of a rigid rotor ball bearing system are established. Continuation-shooting algorithm for periodic solutions of the nonlinear non-autonomous dynamic system and Floquet multipliers of the system are used. Furthermore, the bifurcation and stability of the periodic motion of the system in different parametric domains are also studied. Results show that the bifurcation and stability of period-1 motion vary with structural parameters and operating parameters of the rigid rotor ball bearing system. Avoidance of unbalanced force and bending moment, appropriate initial contact angle, axial load and damping factor help enhance the unstable rotating speed of period-1 motion.

关键词： angular contact ball bearing rigid rotor system bifurcation periodic motion continuation-shooting algorithm

A LARGE-SCALE ESTIMATE OF THE NUMBEROF periodic SMALL OSCILLATIONS OFNONLINEAR SYSTEMS

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Acta Mathematica Scientia 1997年第3期17卷 301-308页

作者：古志鸣 NANJING UNIV AERONAUT & ASTRONAUT NANJING 210016PEOPLES R CHINA

A conservative system performing a small oscillation near every equilibrium position is analysed in classical way. The paper tries to answer the following question: How many types of the periodic small oscillation in the whole configuration space of the system are there? Making some hypotheses, it expresses the lower bounds of the number of the types for two cases where critical points of the potential function are nondegenerate and degenerate respectively by the Betti numbers and dimension of the constraint manifold only.

关键词： large-scale estimate periodic motion Morse theory

Symmetry,cusp bifurcation and chaos of an impact oscillator between two rigid sides

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Applied Mathematics and Mechanics(English Edition) 2007年第8期28卷 1109-1117页

作者：乐源谢建华 Department of Applied Mechanics and Engineering Southwest Jiaotong University Chengdu 610031P.R.China

Both the symmetric period n-2 motion and asymmetric one of a one-degree- of-freedom impact oscillator are considered. The theory of bifurcations of the fixed point is applied to such model, and it is proved that the symmetric periodic motion has only pitchfork bifurcation by the analysis of the symmetry of the Poincar6 map. The numerical simulation shows that one symmetric periodic orbit could bifurcate into two antisymmet- ric ones via pitchfork bifurcation. While the control parameter changes continuously, the two antisymmetric periodic orbits will give birth to two synchronous antisymmetric period-doubling sequences, and bring about two antisymmetric chaotic attractors subse- quently. If the symmetric system is transformed into asymmetric one, bifurcations of the asymmetric period n-2 motion can be described by a two-parameter unfolding of cusp, and the pitchfork changes into one unbifurcated branch and one fold branch.

关键词： periodic motion Poincaémap symmetry pitchfork bifurcation chaotic attractor cusp

Bifurcations of Single-impact periodic motions of a Three-degree-of-freedom Vibratory System with a Gap

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Bifurcations of Single-impact Periodic Motions of a Three-de...

Complex Transition of Double-Diffusive Convection in a Rectangular Enclosure with Height-to-Length Ratio Equal to 4: Part I

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作者： Yanlong ZHANG Li WANG Li MA School of Mechatronic Engineering Lanzhou Jiaotong University Department of Mathematics Lanzhou City University School of Mathematics Physics and Software Engineering Lanzhou Jiaotong University

A Three-degree-of-freedom vibratory system with a gap is considered in this paper. The system is uncoupled by using modal matrix approach. Based on the impacting conditions and the matching conditions according to the impact law, the single-impact periodic motion and the Poincaré mapping of the system are derived analytically. Stability and local bifurcations of single-impact periodic motion are analyzed theoretically by using Jacobian matrix of the Poincaré mapping. It is certain that Neimark-Sacker bifurcation and period doubling bifurcation exist in this kind of vibratory system under the suitable system parameters. The Neimark-Sacker bifurcation and period doubling bifurcation are shown in the projected Poincaré sections by numerical simulations. Here two typical routes from Neimark-Sacker bifurcation of single-impact periodic motion via phase locking and torus doubling to chaos are discussed.

关键词： Vibratory periodic motion Bifurcation Chaos

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Communications in Computational Physics 2009年第7期6卷 247-268页

作者： Xian Liang Xinliang Li Dexun Fu Yanwen Ma Shanghai Institute of Applied Mathematics and Mechanics Shanghai UniversityNo.149 Yanchang RoadShanghai 200072China LNM Institute of MechanicsChinese Academy of SciencesNo.15 Beisihuanxi RoadBeijing 100190China

This is the first part of direct numerical simulation(DNS)of double-diffusive convection in a slim rectangular enclosure with horizontal temperature and concentration *** consider the case with the thermal Rayleigh number of 105,the Pradtle number of 1,the Lewis number of 2,the buoyancy ratio of composition to temperature being in the range of[0,1],and height-to-width aspect ration of 4.A new 7thorder upwind compact scheme was developed for approximation of convective terms,and a three-stage third-order Runge-Kutta method was employed for time *** DNS suggests that with the buoyancy ratio increasing form 0 to 1,the flow of transition is a complex series changing from the steady to periodic,chaotic,periodic,quasi-periodic,and finally back to *** are two types of periodic flow,one is simple periodic flow with single fundamental frequency(FF),and another is complex periodic flow with multiple *** process is illustrated by using time-velocity histories,Fourier frequency spectrum analysis and the phase-space trajectories.

关键词： Double diffusive convection transition periodic motion chaotic motion high order compact

Dynamic Behavior of Two Part Towing Cable System During Turning

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Journal of Shanghai Jiaotong university(Science) 2018年第3期23卷 444-455页

作者： GAO Hui WANG Zhibo Jiangsu University of Science and Technology Zhangjiagang 215600 Jiangsu China Shanghai Ship and Shipping Research Institute Shanghai 200135 China

An improved numerical method is used to simulate the dynamic behavior of a two part towing cable systems during turnings. In U turns and full turns, periodical heave motions are found both for the towed vehicle and for the depressor. periodic motions of the subsea units and of the cable surface tension are closely related to the turning parameters, such as turning velocity and turning radius. System parameters, such as length of the second cable and the vehicle bydrodynamics, also damp turning instability.

关键词： towing cable systems dynamic behavior periodic motion turning operation

Nonlinear dynamics of controlled mechanical systems with time delays

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Progress in Natural Science:Materials International 2000年第11期 3-13页

作者：胡海岩王在华 China Institute of Vibration Engineering Research Nanjing 210016 Nanjing University of Aeronautics and Astronautics

Unavoidable time delays in the feedback path of a controlled mechanical system may render the system unstable, and block the development and the application of dynamic control. This paper summarizes the recent work of the authors on the dynamics of controlled mechanical system with time delays. It starts with the dimensional reduction of delayed nonlinear systems composed of stiff and soft substructures and then presents the experimental modeling of linear and nonlinear mechanical systems with the time delays in state feedback taken into account. In the frame of linear controlled systems, this paper outlines the analysis of delay-independent stability and stability switches with the increase of time delay, the stability analysis in the case of short time delay, and the robust stability analysis of the system possessing uncertain parameters. Afterwards, the paper briefly discusses the primary resonance and subharmonic resonance, as well as the corresponding stability analysis, of a kind of harmonically f

关键词： time delay mechanical system system reduction stability analysis periodic motion active vehicle chassis.

Leading Chaos to Period by Two Unfeedback Methods in a Two-degree-of-freedom Vibrating System with Two Rigid Constraints

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International Journal of Plant Engineering and Management 2011年第1期16卷 21-27页

作者： GOU Xiang-feng LUO Guan-wei LV Xiao-hong School of Mechatronics Engineering Lanzhou Jiaotong University Lanzhou 730070P. R. China

The equations of the asymmetrical periodic motion in a two- -of-freedom vibrating system with two rigid constraints are constructed analytically. Its Poincard mapping equation is established too. periodic motions of the system and their routes to chaos are also illustrated by numerical simulation. The ranges of the system excited frequency from periodic motions to chaotic motions are obtained. The chaotic motions of the system are shown by di- agrams of Poincarg mapping, phase portraits and diagrams of bifurcation. The chaos controlling methods by the addition of constant load and the addition of phase are dissertated and analyzed numerically by the numerical solu- tion. The chaos of the system is controlled by the two methods. The allowable range controlling variables and the steady orbits of the controlled system are obtained.

关键词： vibro-impact mapping periodic motion chaos chaos controlling