Abstract: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.

Abstract: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.

Abstract:This paper presents the origin, expression and principle of six traditional hysteretic nonlinear models, which are dry friction model, bilinear model, Davidenkov model, BoucWen model, trace method model and Bingham model, and analyzes their advantages, disadvantages and applications. In addition, some latest modified models are introduced and the corresponding investigations on these modified models are also presented. Finally, the status quo of hysteretic nonlinearity modeling is summarized and the research direction is predicted.

Abstract:The dynamical model of a twodegreeoffreedom vibroimpact system with two motion limiting constraints was established, whose sticking conditions were given. The analysis shows that there exist sticking motions. According to the shooting method, the unstable periodic motion of vibroimpact, i.e. the fixed point of Poincaré section, was solved by the method of varied step and gradual iteration. Hopf bifurcation and perioddoubling bifurcation were analyzed under certain parameters by numerical simulation. At the same time the quasiperiodic responses of the system represented by invariant circles in the projected Poincaré section of twodegreeoffreedom system with two motion limiting constraints were obtained by numerical simulations. As the controlling parameter varied further, the routes of the twodegreeoffreedom system with two motion limiting constraints to chaos via quasiperiod bifurcation and perioddoubling bifurcation were investigated respectively.

Abstract:The dynamical behavior and traveling wave solutions of DegasperisProcesi equation were studied by using bifurcation theory of dynamical system and qualitative theory. Based on the character of integral system and exploiting the energy of Hamiltonian system, the phase portraits were plotted by using the Maple. The relation between the parameter and the type of different traveling wave solutions was revealed, the bifurcation values of different traveling wave solution were given, and the reason for peakon was shown. Under different parameter conditions, exact traveling wave solutions were also given. The numerical simulation shows the correctness of the theoretical analysis.

Abstract:The chaotic attitude motion of a spacecraft with three rotors subjected to small external perturbation torques was investigated. By using the Deprit's canonical variables, the Hamilton structure of the system was established. Melniklv's method was carried out to predict the transversal intersections of the stable and unstable manifolds and to achieve the conditions of the occurring of chaotic motion. The study shows that the range of the excitation frequencies, which excite the occurring of chaotic dynamics, decreases as the momentum moment of the wheels increases. Finally, the numerical simulation of phase space shows the reliability of the theoretical analysis.

Abstract:The bifurcation and chaotic behavior of a parallel platetype structure with nonlinear elastic support in axial flow were investigated. By assuming that all the plates have the same deflections at any instant, and considering the effect of cubic elastic spring on the platetype beam, the partial differential equation of the system was transformed to the firstorderstate equation. Based on this, numerical simulations show that the parallel platetype structure has rich nonlinear dynamics. The complex bifurcations and chaotic motions were detected by analyzing several key system parameters, and the route to chaos was shown to be via classical perioddoubling bifurcations.

Abstract:The finite segment method, a discrete coordinate method for a flexible beam, was extended to a regular flexible plate，which is regarded as a multirigid bodies system with many compliance (stiffness、damping) joints. The basic idea and theoretical background of the discrete coordinate method were expounded, and the dynamic equation was built by NewtonEuler method. In virtue of finite element software and dynamic simulation program, this paper proved that the discrete coordinate method can be used for dynamic analysis of multibody systems with regular flexible plate undergoing nonlinear deformations.

Abstract:There is a good property of topology conjugated between the dynamics system and the symbolic dynamics. In this paper, dynamic frame partition method, which is used to transform the time series of the dynamical system into the symbolic time series, is proposed. We compute the LempelZiv complexity value of the symbolic series. And then the intrinsic complexity of the system can be made qualitative analysis. At last, a numerical simulation result indicates that the proposed method can describe the complexity of the dynamics system and can qualitatively estimate the property of the system.

Abstract:An improved Bingham model was proposed to describe the force of a MR damper, whose primary resonance for the singledegreeoffreedom (SDOF) was researched under the condition that the spring deformation was comparatively great. The analytical solution of the system was obtained by using the Averaging Method, whose effectiveness was verified through numerical simulation, and the effects of all the physical parameters on the amplitudefrequency curves were also studied so as to control the primary resonance effectively. In addition, the amplitude comparison between the traditional damper and the MR damper in the primary resonance was presented, which showed the performance of MR damper in vibration control was better.

Abstract:Maglev system is nonlinear and unstable essentially. It is complicated to design a stable system, especially when the system is under largescale disturbance and parameter variance, which make the system lose stability and emanation easily. Theoretical analysis and experiments show that this phenomenon is due to the HOPF bifurcation in the mathematical model. This paper gives an adaptive control law, which adjusts PID control parameters of the nonlinear system according to the HOPF bifurcation. Through discrimination of the disturbance and object parameters, the controller adjusts the feedback coefficients to make the system far from the HOPF bifurcation point and maintain the stability of the magelv system. Simulation result by changing mass suddenly indicates that adjusting proportion gain parameter using this method can magnify the state stability range of the maglev system and reject the selfexcited vibration efficiently.

Abstract:Based on the mathematical description of current regulator, SPWM and PM motor, the mathematical model of a brushless DC motor system was proposed directly and transformed to a similar Lorenz system by applying the nonlinear affine transformation and the scaling transformation theory. The stability and attractor of the system were analyzed, and the relationship between the system operation condition and the direct current input was obtained. The stability of the three equilibrium points was analyzed by calculating the eigenvalues of the Jacobi matrix, which revealed that the Hopf bifurcation resulted in the strange attractor. Finally, numerical simulations were presented, and the results showed the validity of the theoretical analysis.

Abstract:Robust vibration control of flexible appendant structures on a rigid base was investigated. The Structured Singular Value(μ) theory was applied to design a robust vibration controller, and piezoelectric patches were used as actuators and sensors. Output multiplicative uncertainty structure was adopted to depict the discrepancies between nominal model and real system, and μ controller synthesis framework was formed. A flexible beam appended to a rigid base was taken as an example to illustrate the μcontroller design process. The simulation results showed that the　μ controller exhibited good performance. So, it's feasible to apply Structured Singular Value theory in vibration control of flexible appendant structures.

Abstract:The building structures with tuned mass damper (TMD) were used as research object, and a controll strategy was proposed when the output force of the TMD actuator was less than the designed controll force.The optimization method was used to search for the system controllaw under the condition that the premium of the linear matrix inequalities(LMIs) was satisfied,and the peakenergy controller was adopted for assuring the control effect.Finally,an example of 6storey building was used to illustrate the feasibility of the presented method.

Abstract:This paper regarded the threedimensionally carbon/silicon carbide braided composite as a spatial structure, which is made up of cellelements and contains matrix and fiber. The structure model of a cellelement for the threedimensionally multidirectionally braided composite was constituted geometrically and used for meshing the composite structure. Based on the cell model, we studied the dynamic behavior of the C/SiC composite cantilevered plate using finite element method. The theoretical dynamic behavior of the composite plate was also obtained and compared with the numerical result, which verified the correctness of the calculation model.

Abstract:Aimed at hardness of espial and complexity of technology in the experiment of dynamic systems, the electronic analog computer is employed to implement the transfer function and primitive operator of dynamic systems from viewpoint of control theory for the general equality between electricity and dynamics, in this way the dynamic experiment changes into electricity experiment and the ripe technology of electricity measure can be used in the simulation and experiment of dynamic systems. Based on the electronic analog computer, the electronic equivalent models of essential elements of dynamical systems are given, and the electronic equivalent analogue operation and electronic experimentation framework of typical dynamical systems are given too. The results of simulation and analog show that the method is simple and correct, and the scope of its application is wide.

Abstract:A structural dynamic propertiesbased damage identification method was proposed. The dynamic response of the uniform BernoulliEuler beam was discussed by introducing a damage distribution function, and a “damage influence matrix(DIM)" was constructed, which can show the structural modal coupling induced by damage. The method of structural damage location and assessment based on DIM was also introduced.

Abstract:A new model of cellular neural networks involving variable delays and impulses was investigated. Some new sufficient conditions for the existence and global exponential stability of a unique equilibrium of the impulsive delayed model were obtained, without assuming the boundedness, monotonicity or differentiability of the activation functions and subjected to impulsive state at fixed time. The results extend and improve the earlier publications.

Abstract:An approach for detecting the tiny damage of a structure was proposed. Based on the HilbertHuang Transform, the structural damage feature index, i.e., the variation of instantaneous frequency and of instantaneous energy, were extracted, and the dynamic response signals of the composite wingbox excited under a square wave signal were calculated. IMFs of the dynamic response signal were decomposed using EMD method, and the instantaneous frequencies corresponding to IMFs were calculated. The variation of the instantaneous frequencies can be used to judge whether or not the structure is damaged. Hilbert spectrums of the dynamic response signals were obtained using HHT method , and the instantaneous energy corresponding to Hilbert spectrum was calculated, from which the damage information, i.e. the variety quantity of instantaneous energy, can be extracted. And the relationship between the proposed damage feature index and the structural damaged degree was given.