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  • 1  Linear feedback control for synchronization of Liu chaotic system
    Chen Baoying
    2006, 4(1):1-4.
    [Abstract](587) [HTML](0) [PDF 0.00 Byte](1278) [Cited by](27)
    This paper studied the chaotic synchronization of a new chaotic system Liu chaotic system. Based on the Lyapunov stable theory, linear single variable and multivariable feedback control methods were given. The two methods can both achieve chaotic synchronization of Liu chaotic system efficiently. Compared with nonlinear controls, the two linear controls have simpler structures and can be obtained more easily. Finally, the numerical simulation results verified the effectiveness of the two methods.
    2  Analytical structural mechanics and finite element
    Zhong Wanxie
    2004, 2(4):1-8.
    [Abstract](558) [HTML](0) [PDF 0.00 Byte](1167) [Cited by](24)
    Traditionally,analytical mechanics is described by means of dynamics,and the common foundation for structural mechanics and optimal control is analytical mechanics.So,under the framework of structural mechanics or optimal control theory,there should also be a whole set of analytical mechanics theory,which we define as analytical structural mechanics.A conservative system can be described with the Hamilton system methodology,and its characteristic is the symplectic conservation,which is the most important feature of conservative system.The finite element method was initiated from structural mechanics,and its element stiffness matrices should be symmetric,which is,in fact,the symplectic conservation.Based on the fact that the interval deformation energy depends only on the two end displacements vector,we derive the Lagrange and Poisson brackets analytically,the symplectic duality system,the canonical equations,and the canonical transformations,etc.
    3  Advances in dynamics of rigid-flexible coupling system
    Hong Jiazhen You Chaolan
    2004, 2(2):1-6.
    [Abstract](1059) [HTML](0) [PDF 0.00 Byte](1167) [Cited by](19)
    This paper first gives a brief review about the three phases of the research of flexible multi-body system dynamics.Then in order to solve the deficiency in the traditional zero-order approach coupling model,a new modeling theory is proposed,and the discretizing method and experiment about "dynamics stiffening" problem and rigid-flexible coupling dynamics problem are investigated based on the new one-order approach coupling model.A set of experiment platform used for the theoretical study and the discovery of dynamic phenomenon is designed and built.Some research results are introduced.Some research targets are given at the end of this paper.
    4  A simplified trial function method for seeking the exact solutions to a class of nonlinear pdes
    Xie Yuanxi Tang Jiashi
    2005, 3(1):15-18.
    [Abstract](548) [HTML](0) [PDF 0.00 Byte](1090) [Cited by](11)
    By utilizing the trial function method, a class of nonlinear partial differential equations (PDEs for short) that are hard to be solved by the usual ways can be reduced to a set of algebraic equations, which can be easily solved, and their related coefficients can be easily determined by the undetermined coefficients method. Then, the exact analytical solutions to the class of nonlinear PDEs were successfully derived. Moreover, the method was applied to the Burgers equation, the KdV equation and the KdV-Burgers equation and the results were in very good agreement with those given in the reference. The method may be generalized to construct the solutions of other nonlinear PDEs.
    5  Chaos and its forming mechanism of a new Lorenzlike system
    Wang Lin Ni Qiao Liu Pan Huang Yuying
    2005, 3(4):1-6.
    [Abstract](721) [HTML](0) [PDF 0.00 Byte](1012) [Cited by](11)
    This article introduced a new Lorenzlike system of threedimensional quadratic autonomous ordinary differential equations. For theoretical analysis, the Lyapunov criterion was applied to study the stability of the equalibria of the system. Based on this, numerical simulations indicated that the considered system may display abundant dynamical behaviour, such as chaotic and various periodic motions. Moreover,the effect of two key parameters on the stability of the system was investigated,and the forming mechanism of the chaotic attractor was studied via constructing a controller of the system.
    6  The on-off control of asemi-active suspension of the full-model based on mr dampers
    Wang Hao Hu Haiyan
    2004, 2(4):71-76.
    [Abstract](413) [HTML](0) [PDF 0.00 Byte](902) [Cited by](10)
    The control of a semi-active suspension of the full-vehicle model has been investigated. According to the Lagrange equation of the second type, a special Lagrange equation of the second type for the semi-active suspension of the full-vehicle model is obtained. Then the equation of motion and its state space form for the system are established, considering the comprehensive coupling of the vertical motion, the pitch motion and the roll motion of the sprung mass. The semi-active suspension of the full-vehicle model is controlled with some on-off control laws, using four MR dampers as actuators for the system. The simulation results demonstrate that the on-off control is just of little use for the control of the vertical acceleration and the roll angular acceleration of sprung mass, the pitch angular acceleration is even deteriorated. However, it can effectively control the dynamic deflection of the suspension, the dynamic deflection of the tire and the vertical acceleration of unsprung mass. Furthermore, the rear suspension is much better controlled than the front one. Here, the No.4 control law is the best on-off control law and easy to be realized. The results can be the reference of the more advanced control law for the semi-active suspension of the full-vehicle model.
    7  Dynamics analysis and simulation of spacecraft docking mechanism
    Yu Wei Yang Lei Qu Guangji
    2004, 2(2):38-42.
    [Abstract](719) [HTML](0) [PDF 0.00 Byte](1149) [Cited by](9)
    This paper studied the internal-petal androgynous peripheral attachment system (APAS),its differential electro-mechanical attenuation mechanism,and the dynamics properties of the docking mechanism.The docking mechanism virtual prototyping model was establlished by using Automatic Dynamic Analysis of Mechanical Systems (ADAMS).According to the simulation,the characteristics of the mechanism's equivalent stiffness and damping were obtained.These findings have been essential in ensuring a successful mission.
    8  Analysis of impact process model based on restitution coefficient
    Qin Zhiying Lu Qishao
    2006, 4(4):294-298.
    [Abstract](921) [HTML](0) [PDF 0.00 Byte](724) [Cited by](9)
    The meaning and function of restitution coefficient were introduced, and some kinds of impact process models were analyzed. By deriving the relationship between the restitution coefficient and the model parameters, the energy dissipation was described as restitution coefficient, and the contact deformation was described as contact stiffness for different models. This also demonstrated the difference and connection between the impact process models and the rigid impact model. Through the numerical simulations of an impact system of falling ball, the derived relationship were verified and these models were compared in view of computation precision, efficiency and micro-contact process.
    9  Non-linear dynamic charactersistics of single-layer shallow conical lattice shells
    Wang Xinzhi Liang Congxing Li Lei Han Mingjun Ding Xuexing
    2004, 2(3):14-17.
    [Abstract](389) [HTML](0) [PDF 0.00 Byte](698) [Cited by](8)
    By using the method simulated shells, the axisymmetrical non-linear dynamic equations of three-dimensional single-layer shallow conical lattice shells with equilateral triangle mesh are founded. Though the separating variables function method, a quadric and cubic non-linear differential equation is gotten by using Galerkin method. In order to study chaos movement, Accurate solution of non-linear free vibration differential equation is by solving a kind of free vibration equation of non-linear dynamics system. Critical Condition is gotten by using Melnikov function. Besides, numerical-graphic method also confirm the existence of chaos.
    10  Study on the laterally nonlinear vibration of axially moving beams
    Chen Shuhui Huang Jianliang She Jinyan
    2004, 2(1):40-45.
    [Abstract](560) [HTML](0) [PDF 0.00 Byte](1196) [Cited by](8)
    The laterally nonlinear vibration of axially moving beams weve analyzed by the incremental harmonic balance(IHB) method.Firstly the motion equations of an axially moving beam weve derived by Hamilton's principle,Then the Galerkin method was used to discretize the governing equations.Finally, the IHB method was employed to solve the nonlinear vibration equations.Particular attention was paid to the fundamental,subharmonic resonance with internal resonance under the condition ω20/ω10≈3 as ω is near ω20,ω10,where ω is the forcing frequency,and ω10 and ω20 are the first and the second natural frequencies.The number results show that the IHB method is a very effective semi-analytical and seminumerical method for nonlinear vibration of axially moving system.
    11  A study on optimal sensor placement for structural modal parameters testing
    Wang Shanshan Ren Qingwen
    2005, 3(1):67-71.
    [Abstract](431) [HTML](0) [PDF 0.00 Byte](916) [Cited by](8)
    The testing of structural modal parameters is an important basis of dynamic response analysis and structural damage detection. Modal parameters of real structure are usually tested by ambient excitation. The sensor placement affects testing accuracy during this detection. The affection of sensor placement on structural parameters testing are studied by finite bandwidth white noise vibration experiment. The experimental result shows that optimal sensor placement can improve testing accuracy of structural modal parameters.
    12  PID control based on BP neural network adjusting
    Zhu Haifeng Li Wei Zhang Lin
    2005, 3(4):93-96.
    [Abstract](878) [HTML](0) [PDF 0.00 Byte](814) [Cited by](8)
    Traditional PID control has been widely used in real applications. But for traditional PID control, mathematical model must exist when adjusting PID parameters, and the parameters are constant after adjusted. However, in real systems, when the system state and parameters change and become uncertain, system performance cannot keep in the best state. For the purpose of improving system performance of PID control and making use of the existing study fruit of PID control, BP neural network was used for adjusting PID parameters. After simulating, the results show that the algorithm based on BP neural network adjusting has better control characteristics than those of traditional PID and BP neural network.
    13  The chaotic characters of a 3dimensional nonlinear dynamics
    Zhang Lili Lei Youfa
    2006, 4(1):5-7.
    [Abstract](559) [HTML](0) [PDF 0.00 Byte](1147) [Cited by](8)
    Based on the linear coefficient character of Lorenz attractor and Chen's attractor, we coined a 3dimension nonlinear dynamics, and studied its chaotic characters, including the space trajectory, the largest Lyapunov exponent, the Lyapunov exponent spectra and the Poincare map. All these characters show that the nonlinear dynamics exists chaotic attractor.
    14  Optimal synchronization of hyperchaotic Lü system with uncertain parameters
    Gao Jie Lu Junan
    2006, 4(4):320-325.
    [Abstract](393) [HTML](0) [PDF 0.00 Byte](878) [Cited by](8)
    This paper investigated the optimal synchronization of the hyperchaotic Lü system. Based on the Hamilton-Jocobi-Bellman equation, a scheme for the optimal synchronization of the hyperchaotic Lü system with uncertain parameters was designed. The optimal controllers and the control laws of parameters were respectively derived on the infinite and finite time intervals. And the numerical simulations were given to verify the correctness of the theoretical analysis.
    15  Development and problems of nonlinear dynamics of the mechanisms with clearances for spacecrafts
    Yan Shaoze
    2004, 2(2):48-52.
    [Abstract](445) [HTML](0) [PDF 0.00 Byte](969) [Cited by](7)
    This paper introduces the development of dynamics of space mechanisms for aerospace,and discusses the important senses to study nonlinear clearance models for both designing the structures of new spacecrafts and analyzing the performances of spacecrafts on orbit.Some key problems to be solved are proposed,which include the dynamic modeling and analyzing of space mechanisms with clearances,the movement stability analysis of the mechanisms,the simulation software for realizing the global simulations of performances of the mechanisms.
    16  Three kinds of symmetries and three kinds of conserved quantities for holonomic systems
    Mei Fengxiang
    2004, 2(1):28-31.
    [Abstract](321) [HTML](0) [PDF 0.00 Byte](911) [Cited by](7)
    The Noether symmetry,the Lie symmetry and the form invariance for holonomic systems were presented.The Noether conserved quantity,the Hojman conserved quantity and a new conserved quantity deduced by the above three kinds of symmetries were studied.
    17  Chaos synchronization control of comtinuous chaotic systems
    Chen Baoying Bao Fangxun
    2004, 2(4):14-18.
    [Abstract](634) [HTML](0) [PDF 0.00 Byte](903) [Cited by](7)
    This letter gives a method that can achieve chaos synchronization of chaotic systems. This method makes synchronization problems changed into the asymptotic stability questions of the 0 solution of the linear systems, then gives the control variable according to the control theory of linear system. This method is simple and it can achieve chaos synchronization of two chaotic systems efficiently. The synchronization is overall asymptotic stable. The basic theory and the numerical experiments of two identical and nonidentical chaotic systems are performed. The numerical example is a new system.
    18  Small parameter perturbation method and symplectic conservation
    Zhong Wanxie Sun Yan
    2005, 3(1):1-6.
    [Abstract](415) [HTML](0) [PDF 0.00 Byte](936) [Cited by](7)
    The small parameter perturbation approximation is applied quite often in applied mathematics and mechanics. There are tremendous conservative system analyses in physics and applied mechanics, and one of the most important characteristics of a conservative system is its symplectic conservation. The present paper emphasizes that the symplectic conservative behavior should be considered in small parameter perturbation approximations. The strip domain structural analysis is considered, and we gave both the perturbation solutions with the displacement method, which is symplectic conservative, and the perturbation solutions with the corresponding transfer symplectic matrix method, which is symplectic nonconservative.
    19  A general solution of free vibration for rectangular thin plates in hamilton systems
    Bao Siyuan Deng Zichen
    2005, 3(2):10-16.
    [Abstract](652) [HTML](0) [PDF 0.00 Byte](1015) [Cited by](7)
    Based on the basic equations of free vibration of thin plate, the Hamilton canonical equations were obtained. By variable selection of moment, equivalent shear force, rotation angel and deflection forming dual variables, the analytical solutions for free vibration of thin plate were obtained under different boundary conditions, which were divided into symmetrical and asymmetrical about xaxial. The computational example of a quadrilateral rectangular plate bending was given, which demonstrated the effectiveness of the proposed method, thus extending the application of Hamilton system.
    20  Hopf bifurcation and chaos of a two-degree-of-freedom vibro-impact systems
    Le Yuan Xie Jianhua Ding Wangcai
    2004, 2(3):36-41.
    [Abstract](389) [HTML](0) [PDF 0.00 Byte](612) [Cited by](6)
    The periodic motion and Poincaré maps of a two-degree-of-freedom vibro-impact system are studied in this paper.The stability of the periodic motion is determined by the eigenvalues of the Jacobian matrix.It is shown that there exist Hopf bifurcations and period-doubling bifurcations in the vibro-impact system under suitable system parameters.The quasi-periodic responses of the system represented by invariant circles in the projected Poincaré section are obtained by numerical simulations, and routes to chaos are described briefly.

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