Abstract:The aim of this paper is to study the nonlinear stability and dynamics behaviors of a simplified partially-filled satellite．The sufficient condition of stability of the satellite was obtained using Lyapunov direct method．Also we point out the critical parameter when Hopf bifurcation occurred and determine stability of Hopf bifurcation．At last，By the track in the phase space and the largest Lyapunov exponent，the nonlinear mechanisms in system are analyzed．

Abstract:The variational iteration method proposed by Ji-huan He was applied to a kind of strongly nonlinear oscillators.The obtained solutions are valid for the whole solution domain,and the first order approximation has high accuracy.

Abstract:This paper reveals the seeming ambiguity problem of the method of multiple scales in solving the third or higher order approximate solutions of nonlinear systems through an example of the famous van der Pol equation. By comparing the results obtained by the method of multiple scales with that of the KBM method, the paper indicates a proper way about how to apply the method of multiple scales to solving the third or higher order approximate solutions of nonlinear systems.

Abstract: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.

Abstract:This paper studies the flutter of a two-dimensional airfoil in the supersonic flow with cubic physical and aerodynamic non-linearity. First, the characteristic value of the system in the neighborhood of equilibrium point is analyzed. The parametric equations of flutter are obtained in the vicinity of Hopf bifurcation point. Then, the normal form of Hopf bifurcation is deduced by applying the normal form direct method. The dependence of response on initial values is certified by numerical analysis in the super- and sub-critical cases. Finally, study on the topological structure of bifurcation shows that the “hard” structural non-linearities render the airfoil safer, whereas the “soft” ones render the airfoil unsafe. In other respect, increasing the distance between the center of mass and the elastic axis appears to be beneficial from the point of view of the aeroelastic response.

Abstract:The Paper is devoted to the study of the oblique-impact vibrating system that is a double compound pendulum under the harmonic moment excitation with the end displacement limit. The specific relations between the pre-impact state and the post-impact state are presented in the case when the friction in the contact surface is not considered. Detailed numerical studies are presented for the transitional dynamics of the steady-state motions of the system with the variation of the excitation and the system parameters, with the illustrations given for rich nonlinear phenomena, such as the bifurcations of periodic vibro-impact motions and the chaotic vibro-impact motions. The dynamic complexity of the oblique-impact vibrating system is showed in these illustrations.

Abstract:An improved adjoint operator method is employed to compute the third order normal form of six dimensional nonlinear dynamical systems and the associated nonlinear transformation for the first time. First an improved adjoint operator method is briefly introduced. Then, a general six dimensional nonlinear system is analyzed to drive the formula of computing the third order normal form. Finally, the MAPLE symbolic program for calculating the third order normal form is given. The concrete normal form of six dimensional nonlinear systems is obtained. The results obtained here indicate that we may respectively obtain the normal forms, the coefficients of the normal forms and the associated near identity nonlinear transformations for six dimensional nonlinear systems in four different cases by using a same main Maple symbolic program.

Abstract: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.

Abstract:According to the delayed feedback control method and the phase space compression method, an improved method of delayed feedback scheme is proposed, which takes phase space compression as restriction for state variables in delayed feedback control. The method is testified in Bonhoeffer-van der Pol system, it is indicated that: the chaotic system with only one chaotic attractor can be controlled into a desired periodic orbit immediately. Comparing with Pyragas's method, the improved method reduces recovery time. For a system with double attractors, it can be stabilized simply into a desired periodic orbit embeded in different attractor by using appropriate the phase space limiter.

Abstract:A computation method was used for determination of time delay in phase space reconstruction based on first minimum of mutual information, which proved reliable by applying it to the example of the Mackey-Glass Equation and Lorenz ’s strange attractor data. The flow patterns of oil/water two phase flow were characterized by calculated correlation dimensions of chaotic attractor, it is shown that the dimensions calculated from fluctuating conductance signals of oil/water two phase flow had good correlation with water cut () ranging from 61% to 91% and total flow rate ranging from 10(m3/day) to 60(m3/day) for oil-in-water flow patterns. For water cut () of 51%, the dimensions showed irregular sudden changes to transitional flow pattern, it means that the dimensions of chaotic attractor is a sensitive “indicator” of oil water two phase flow pattern variations.

Abstract:Symbolic time series analysis is a new tool for analysis of experimental data, it has been successfully applied in many fields. Results indicate that the symbolization can increase the efficiency of finding and quantifying information from dynamic systems, reduce sensitivity to measurement noise. Three statistical quantities were used to characterize symbolic time series, the method was validated by Henon equation. We also applied the methods to analyze the experimental data of oil/water two-phase flow in vertical upwards pipes and proved that the calculated statistical quantities from symbolic time series are sensitive to the transitional flow pattern variations of oil/water two phase flow.

Abstract:The model of high speed train pantograph-catenary system is established and analyzed using the perturbation method, the stable regions and periodic solution of the dynamics system are obtained, the Lyapunov exponents of the pantograph-catenary system are calculated, results show that the conclusions are same for analyzing the stable current-collecting of catenary-pantograph system with the two kind methods , which would be very useful for studying the high speed catenary-pantograph system and designing the new type pantograph .

Abstract:The collision and friction between rotor and stator result in a harmful and complex physics process. Most of the mechanical energy dissipated by collision，and friction converts to heat. Even though each collision does not affect the rotor significantly, the decreasing of temperature takes a longer time in comparing with the vibration period of rotor. Once collisions take place constantly, the accumulated thermal effects must be taken into account. When the rotor passes through the critical speed, rub-impacts are liable to happen because of the rather large vibration amplitude. Collisions cause the variation of vibration phase, and the corresponding thermal bending prolongs the process of collisions. At first, a simplified model is set up to describe the elastic collision contact and friction between rotor and stator, and then an example is numerically computed and analyzed in order to examine the influence of rub-impact thermal effects on the vibration characteristics of a rotor passing the critical speed.

Abstract:This paper analyzes the dynamics of a cantilever plate with piezoelectric actuators. A deadbeat state observer is achieved implicitly through processing of the general input-output data and the actual system Markov parameters are recovered from the observer Markov parameters. Finally, the Eigensystem Realization Algorithm (ERA) is then employed to develop an explicit state space model of the equivalent linear system. The mathematical model obtained by ERA is controllable and observable and is suitable for the purpose of controller design.

Abstract:In this paper, the problem of response’s prediction of nonlinear magnetic levitation control system to random vibration is discussed. Based on equivalent method of nonlinear differential equation, the paper gives a deep theoretical analysis to random response of nonlinear magnetic levitation control system; a nonlinear model of the multidimensional system is presented. Using flow form theorem, approximate analysis solution of the system’s response is achieved. The job provides valid theoretical basis to the system, on which can realize further improvement on stability control.

Abstract:The Chebyshev polynomial approximation is applied to the dynamical response problem of stochastic Duffing-van der Pol system, with random parameters. The stochastic Duffing-van der Pol system is first reduced into an equivalent deterministic one for substitution, then the response of the stochastic Duffing-van der Pol system can be obtained by numerical methods for this equivalent deterministic system. Moreover, the symmetry-breaking bifurcation and period-doubling bifurcation of stochastic Duffing-van der Pol system are presented while the excitation frequency vary. Numerical simulation implies that the proposed method is a new effective approach to dynamical responses of stochastic nonlinear systems.

Abstract:Coherence resonance in the Chay neuron model with noise in the slow dynamics is studied. Noise that is added to the slow dynamics amounts to calcium ionic fluctuation. So it is more biologically feasible. We find that the output signal-to-noise(SNR) of the Chay neuron system goes through a local maximum with increasing noise intensity at optimal noise level, which shows the occurrence of coherence resonance. Consequently the noise in the slow dynamics , namely, calcium ionic random fluctuation may enhance signal detection and transduction.

Abstract:According to the gray system theory, a control method to rotor system, the gray-related control scheme is proposed and studied in the first time. Based on the gray-related analysis, a gray-related control scheme for a rotor system with electromagnetic damper is designed. The result of the emulating shows that this gray-related control scheme for a rotor dynamic system has the property of rapid model building, timely control and high precision.

Abstract:The multiple scales method of Kuzmak-Luke is used to obtain the asymptotic solutions of pendulum with linear damping and slowly varying length, which are compared with the results of KBM and elliptic KB methods. Examples are given to show that the result of present method is more accurate than that of KBM and elliptic KB methods, although they are all effective to such problem.