Abstract:The differential equations of motion of high order nonholonomic systems constructed by utilizing the general methods not only lack the symplectic structure and Lie algebra structure of holonomic systems, but also lack the self adjoint nature of holonomic systems. In this paper, the high order nonholonomic system was transformed into first order kinetic system by using the reduced order method, which was self adjointized by making use of the Cauchy Kowalevski theorem, then the generalized Birkhoffian equation of high order nonholonomic system was obtained. This will provide a new method for researching a number of high order nonholonomic system's problems, such as the geometry and algebraic structure, geometric numerical integrator and engineering applications, etc.

Abstract:The Nonlinear Generalized Minimum Variance (NGMV) controller introduced in this paper is an optimal control strategy for a class of nonlinear plants. It is assumed that the plant model can be decomposed into a set of delay terms, a stable input nonlinear subsystem and a linear subsystem which can be represented in either polynomial or state space forms. The optimal controller is obtained by minimizing the variance of the generalized signal consisted of error weighting, state weighting and control signal weighting. The controller is easy to compute and the resulting nominal closed loop system is stable. The controller can be represented in the Smith predictor form while the system is open loop stable. In this paper,the development of Nonlinear Generalized Minimum Variance control theory is reviewed in details. Next, NGMV controller design methods for the systems in both state space form and polynomial form are introduced. Finally, future work directions as well as challenging research problems in this area are addressed.

Abstract:A completely decoupled method for subsystem controller's design was given based on the comparison equations' stability criterion of linear interconnected large scale system. This method constructs a vector Lyapunov function to ensure the stability of the comparison equations. And the controller's design is converted to solve a set of linear matrix inequalities. Then these controllers are used to stabilize the large scale system. Compared with those methods based on scalar Lyapunov function, this method reduces the control algorithm's computing and difficulties, due to independent design for each subsystem controller. The simulation results show the feasibility and effectiveness of this method.

Abstract:This paper concerned the issue of controlling a new chaotic system to its equilibriums. Based on adaptive sliding mode variable structure control method , this proposed control scheme, even if the presence of input saturation and external disturbance, can also be the state of the chaotic system asymp totically driven to a appointed equilibrium point. The control scheme is robust for outer perturbation. Numerical simulation illustrates the effectiveness of the proposed adaptive sliding mode variable structure controlscheme.

Abstract:Based on the stability theory of the dynamical system, the theorem of generalized projective synchronization (GPS) for any autonomous chaotic systems was proposed, where suitable nonlinear feedback controllers were designed. The choice of the function is more feasible and flexible, because it can either be the linear function or nonlinear one. One can also improve the speed of GPS by adjusting the parameter. Numerical simulations illustrate the effectiveness of the theorem.

Abstract:The frequency response of a periodic beam with a propagating disturbance was studied by using the multi reflection method. A propagating disturbance is incident upon a discontinuity and gives rise to transmitted and reflected waves. At first, the wave field of segment considering incident disturbance was set up between two discontinuities due to multiple reflections. Then, wave field was set up when wave transmission took place in two coordinate directions. The first correction terms on segment are due to the leftward propagating components on all segments to the right of the segment when only leftward propagation is permitted, and the second correction terms on segment are due to the rightward propagating components on all segments to the left of the segment. So all of the transmitted and reflected waves of given flexural wave incident upon the beam at some specified location were found and superposed. The relation between the wave field of incident waves and the wave field of resulting waves on any segments was expressed. The propagating constant and iteration times of wave field of periodic beam were determined.

Abstract:The flow field of 3-D rotor-seal system was developed, and the characteristics of compressible gas flied for the system were researched by Computational Fluid Dynamics (CFD) technology. The empirical parameters and experimental parameters of the Muszynska gas exciting force model were further identified by the computational results, which made it more suitable for the rotor-seal system. The nonlinear dynamic analysis of the rotor-seal system applied the power series model of the rotor-seal system obtained by power series expansion. The multiple scale method was used to obtain the bifurcation equations of the rotor-seal system in the 1:2 subharmonic resonance case. Based on the singularity theory and Hopf theory, the 1:2 subharmonic resonance transition sets and the existing condition of the supercritical Hopf bifurcation and subcritical Hopf bifurcation were obtained. The subcritical Hopf bifurcation of the rotor-seal system was inhibited by parameter control to improve the system stability.

Abstract:A split flow traffic flow lattice model on the road crossing was proposed, and the sufficient and necessary conditions for keeping the model's linear stability were derived. The MKdV equation was derived from the models near the critical point. By using the kink and anti kink solutions of the MKdV equation, the traffic jam was described. It is found that the coexisting curves decrease with the increasing of the rate of lane changing. Therefore, it plays stability role in heightening the traffic flows in main lane.

Abstract:This paper presented a nonlinear analysis for Nakamura's model to investigate the influence of parameters, including the weight of pedestrians, the ratio of synchronized pedestrians, the function describing how pedestrians synchronize with the bridge natural frequency, etc. on lateral vibration amplitude of a footbridge. Theoretical analysis and numerical simulations indicate that the function describing how pedestrians synchronize with the bridge natural frequency may not be equal to 1.0 and can be far away from 1.0 even though the lateral vibration is excessive. The results are helpful for the application of Nakamura's model in engineering practice and can provide references for field measure.

Abstract:The nonlinear dynamic behaviors of an elastic support hinged hinged uniform shallow arch with two torsional springs locating at two ends respectively under external excitation are investigated. Based on the control equation of elastic support shallow arch the multiple scale method was used for the perturbation analysis of internal resonances, and the averaging equation with its polar form was determined. The influence of the stiffness for elastic boundary, which has a one to one relationship to the corresponding coefficient in the averaging equation, can be reflected in the natural frequencies and mode shapes of arch structure via the characteristic equation. Then the 1:1 internal resonance between the lowest two modes was selected as studying object for numerical calculation. The analytical results show that there exist internal resonance forms for both cross and veer in the torsional elastic support shallow arch, further the two mode interaction induced by external excitation may lead to quasi periodic oscillation and chaotic motion when the systematical parameters are controlled in a certain range.

Abstract:The bifurcations of periodic solutions for a parametrically and externally excited rectangular thin plate with 1:1 internal resonance were investigated. First, the equations of motion with two degree of freedom of the rectangular thin plate were derived from the von Kármán equation and Galerkin's method. Then，based on periodic transformations and Poincaré map, the subharmonic Melnikov function was improved to analyze the periodic solutions of four dimensional non autonomous systems. Numerical simulations verified the analytical predictions.

Abstract:For overcoming the deficiencies of the existing bearing rotor system dynamic model, a nonlinear lumped mass model of ball bearing flexible rub rotor system is established, in which the nonlinear ball bearing force, unbalance, rubbing fault and gyroscopic effect are considered. Based on the numerical calculation and comparison, some conclusions can be obtained. The rotor system response is variable stiffness vibration of the ball bearing under low speed. Comparing with that of high speed the variable stiffness vibration of the ball bearing weaken. The influence of the rotor unbalance and rubbing fault on rotor system is strengthened gradually. The gyroscopic effect on high speed symmetric rotor response is important.

Abstract:This paper studied an initial boundary value problem for a coupled system of nonlinear abstract equations with memory term in Galerkin method. Two equations were added in view of the character of the system and the results were obtained by combing with the nature of the calculus. The convergence was studied, and the existence of a global weak solution for the abstract equations was proven.

Abstract:The static equilibrium equation of functionally graded circular plate was established by using elastic theory, and the neutral plane site of functionally graded elliptical plate was determined. On the basis, the nonlinear vibration and buckling differential equations for the functionally graded elliptical plate in uniform temperature field were derived, the approximate solution to nonlinear thermal vibration and buckling of functionally graded circular plate was obtained, and the effect of neutral plane site, gradient index and temperature on nonlinear thermal vibration and buckling of functionally graded elliptical plate was discussed and analyzed. The calculation results agreed well with the results, which verified the method. Analysis of examples indicates that the neutral plane site has certain influence on nonlinear thermal vibration and buckling of functionally graded elliptical plate in uniform temperature field.

Abstract:This paper studies the effects of various semi rigid column beam connections on the seismic response of space steel structure. Choosing the first order natural period, ratio of axial force and drift angle as the evaluation index, this paper uses ANSYS to analyze the effects of lateral and axial torsional stiffness on the seismic performance of steel structure under real earthquake wave. The simulation results show that the lateral torsional stiffness has great influence on the structural seismic behaviors. Thus, it can provide some certain reference for the design of ultra limit buildings.

Abstract:This paper studied the attitude stabilization of a 3D rigid pendulum with sliding mode control method. The 3D rigid pendulum consists of a rigid body supported by a fixed and frictionless pivot with three rotational degrees, acted on by a constant gravitational force. Considering the attitude control of the 3D rigid pendulum at equilibrium position, this paper has designed a sliding mode controller and analyzed the asymptotic stability of angle velocity and attitude. Then the sufficient conditions of the sliding parameters were gained according to the Lyapunov direct method, and numerical simulation results show the validity of the controller.

Abstract:Singularity disposing, salient point gaining and random error weakening are key processes for estimating precision during the data processing for ballistic trajectory. Firstly, the predominance of wavelet transform on dealing with singularity, salient point and random error, was used to conduct a decomposition, fusion and reconstitution of the observation data base on wavelet transform , which can eliminate singularity, identify salient point and weaken random error. Secondly, the B spine function with knots free distributing was used to describe the missile movement state, which makes the principle of the trajectory determination process become a nonlinear optimization problem of multi model fusion with the parameters of missile trajectory expression coefficients and observation system error coefficients. By introducing the model structure to determinate the selection rule of optimal fusion weight, the optimal estimation for the to be estimated parameters was obtained, and more the precise trajectory determination was gained. Finally, the simulation calculation shows that this method has some advantages in disposing singularity, gaining salient point and weakening random error, which can reduce the calculation amount and increase the ultimate precision of trajectory determination effectively.

Abstract:Replacing the decentralized control, the distributed control, is used for the networked system in order to achieve the exchange of information between the subsystems and to improve its performance. Based on the Lyapunov function method, the optimization algorithm for the maximal permissible time delay were derived in the case of a communication signal delay, and the stability criteria of the whole networked system were proposed respectively for the decentralized control and the distributed control . A simple networked system and the corresponding numerical simulation was couducted. By using the proposed theory. The results show that, compared with the traditional decentralized control, the network distributed control can improve the convergence rate of stability of the entire networked system.