TAILIEUCHUNG - On the transition from regular to chaotic behaviors in the two degrees of freedom dynamical system

The main objective of the present paper is to study the transition from periodic regular mot ion to chaos in a two degrees of freedom dynamical system by changing control parameters. The nonlinear differential equations governing motion of the system a rc derived from the Lagrange equations. | Vietnam Journa l of l\llecha ni cs, VAST, Vol. 29, No . 3 (2007), pp . 353 - 3711 Special Iss ue Dedicated to the Memory of Prof. Nguyen Van Dao ON THE TRANSITION FROM REGULAR TO CHAOTIC BEHAVIORS IN THE TWO DEGREES OF FREEDOM DYNAMICAL SYSTEM NGUYEN VAN KHANG AND NGUYEN HOANG DUONG Hanoi University of T echnology Abstract. The main object ive of the present pape r is to study the transition from period ic reg ular mo t ion to chaos in a two degrees of fr eedo m dynamical system by changing control parameters. The nonlinear differential equations governin g motion of the system a rc derived from the Lagrange equations. I3y use of the Poincare map , the dynami cal behavior is identified based on nume rical solutions of the ordinary differential equations. The Lyapunov ex ponent and the frequ ency spectrum a re calc ul ated to ide nti fy chaos. From numerical simulations, it is indica ted that the periodic, quasi-periodic and chaotic motions occur in the conside red system. 1. INTRODUCTION Fig. 1. l'viechani cal model In recent , the study of chaot ic behaviors a nd strange attractors in deterministic nonlinear systems has undoubtedly developed into one of the main topics i11 the study of nonlinear phenomena in dynamical systems performed by engineers and applied scicutists [1-10]. Many important and interest ing applicat ions are found in nonlinear oscillatio11s. which docs not come as a surprise since nowadays the classical met hods of solution for such nonlinear problems are well known, and also since the new and rather a bstract mathematical tools arise in a rather nat ural way in nonlinear oscillations . .r-v1uch interest has been devoted to the study of chaos in nonlinear osci llators of the Duffing type [l, 7, 8], Mathieu type [l, 12, 13] and Van der Pol type [7, 10, 15, 16]. Let us consider here the two-degree-of-freedom dynamical system (Fig. 1). It is a system with connects t he Duffing and the linear oscillators. 354 Nguyen Van Khang and .

• Cơ khí - Chế tạo máy
• Vietnam Journal of Mechanics
• On the transition from regular to chaotic behaviors
• The two degrees of freedom dynamical system
• The Lagrange equations
• Freedom dynamical system
• Dang Dinh Ang
• Nonlinear analysis and mechanics
• Dynamic problems involving stationary cracks
• The Wiener Hopt technique
• Dual integral equations
• Dual integrals in non linear fracture mechanics
• Non linear fracture mechanics
• Energy release rate
• Discuss the obtained
• The alpha finite element method (αFEM)
• Solid mechanics using triangular and tetrahedral elements
• Suitable computational cost
• NS FEM makes
• The upper bound property
• Non linear constitutive problems in solid mechanics
• Non linear constitutive problems
• Languages Gibian and special operators
• The application FEM
• Betts miller janjic convective parameterization scheme
• H14 31 model to forecast heavy rainfall in Vietnam
• Betts Miller Janjic
• Three rain seasons
• Manufacturing dry mixed cement mortar
• High compressive strength
• High flexural strength
• Low shrinkage and high watertightness for restoration
• Damaged hydraulic structures in Vietnam
• Standard gradient models and crack simulation
• Standard gradient models
• The propagation of cracks
• Damage mechanics and crack simulation
• The interaction between two parametric excitations
• The second and third degrees
• The asymptotic method of nonlinear mechanics
• Dynamic system governed
• Comparison of two hydrological model simulations
• Nam and Xinanjiang for Nong Son catchment
• The Central Vietnam
• The runoff components
• 3 D numerical simulation
• The tidal circulation
• The gulf of Tonkin
• The kinetic energy distribution
• Duality in the analysis of responses to nonlinear systems
• The analysis of responses
• The original nonlinear systems
• The study of nonlinear mechanics
• Aerodynamics of a wing in surface effect ship
• Theory and experiment
• Wing in surface effect ship
• The aerodynamic characteristics
• The Institute of Mechanics
• The error estimate
• The convergence rate for h
• p refinement
• The finite element analysis
• Three dimensional elastostatic mechanics problems
• Some initial experimental results
• Free water layer formation in horizontal pipes
• Water layer formation
• Hanoi Institute of Mechanics
• Bending vibration of beam elements under moving loads
• Considering vehicle braking forces
• Fluctuations of structures
• Beam elements according
• Continuous element for vibration analysis
• Thick shells of revolution
• Continous Element Method
• Finite element solutions
• Natural frequencies and harmonic responses
• Cast3m implementation of the extended finite element method
• The extended finite element method for cohesive crack
• Quasi brittle materia
• The proposed implementation
• The displacement discontinuities
• Buckling analysis of simply supported composite laminates subjected
• In plane compression load
• A novel mesh ffree method
• Alternative numerical technique
• Mesh free method
• A three story building
• Hedge algebras based fuzzy controller
• The structural system
• The El Centro earthquake
• Three story building against earthquake
• Laminar separation phenomenon combining with numerical calculations
• The turbulent separation
• The laminar separation
• Experimental study on mechanical properties
• Three phase polymer composite reinforced
• Glass fibers and titanium oxide particles
• Polymer composite reinforced
• Three phase composite
• Dynamic characteristics of elastically supported beam subjected
• A compressive axial force and a moving load
• The implicit Newmark method
• The Galerkin finite element method
• The axial force
• Eccentrically stiffened functionally graded plates and shallow shells
• Von Karman Donnell sense
• The formulation of governing equations
• The classical shell theory
• Mathematical modelling and control of the evolution
• Dynamic systems interacting with medium
• Mathematical modeling evolutional systems interacting
• Two conjugate mechanical subsystems
• Evaluating structural safety based on fuzzy set theory
• Evaluating structural safety
• The fuzzy reliability
• Simple beam structure