Abstract:Based on dual variable principle, a symplectic algorithm for solving optimal control problem of nonlinear dynamic system was proposed. State variables at left end of time interval and costate at right end of time interval were taken as independent mixed variables, and the state and costate variables inside the time interval were approximated by Lagrange interpolation. Nonlinear optimal control problems were replaced by nonlinear equations through dual variable principle, and the symplectic algorithm for solving nonlinear optimal control problems can be obtained at the same time. Numerical simulation shows the precision and efficiency of the proposed algorithm.

Abstract:The Hamiltonization of Birkhoffian systems was studied .A new method and the corresponding conditions for the transformation of Birkhoffian systems into Hamiltonian ones were presented. The approach to the construction of Hamiltonian for the Birkhoffian systems by means of the gauge transformations and the transformations of the variables was given.It was pointed out that Hamiltonization for all second order regular Birkhoffian systems can be realized.Two examples were given to illustrate the application of the results.

Abstract:The vibration faults of aeroengine highpressure compressor rotor blade were analyzed. The highintensity sound waves contained in the high-strength noise generated by the compressor in a non-normal working condition one of the reasons for rotor blade excitation resonance or flutter. By theoretical analysis and experimental verification, the following conclusions were obtained: If the high stress caused by mechanical excitation and aerodynamic excitation and the superposition of the resonance stress caused by sound waves together affect the rotor blade, it can produce cracks and damages.

Abstract:The feedback maximization of reliability of simple power systems under random perturbations was studied.The stochastic averaging method for quasi non-integrable Hamiltonian systems and stochastic dynamical programming principle were applied to derive the dynamical programming equation for the maximization of conditional reliability function and that for the maximization of mean first passage time.The optimal control, the conditional reliability function and mean first passage time of uncontrolled and controlled power system were obtained by solving the corresponding final dynamical programming equations.The proposed method was verified by using Monte Carlo simulation.

Abstract:Based on the characteristics of the separable exponential matrix and the 2N-type algorithm, a fast precise integration method for the separable exponential matrix was proposed. The key idea is that the blockmatrix is computed based on the submatrix of the separable matrix,thus increasing the reserved item numbers in the Taylor series expansion and decreasing iterative times. On the one hand, the programming is easy. On the other hand, the numerical examples show that the method presented for the large dimension separable exponential matrix can reduce the computation and storage amount and greatly improve the calculation efficiency.

Abstract:The differential equations expressing the relations of velocity components and streamfunction for incompressible two-dimensional flow are typical one-degree-of-freedom Hamiltonian system. The streamfunction is expanded in Taylor series. The streamline patterns and their bifurcations are examined using methods from nonlinear system dynamics. Based on the small parameter canonical transformations in the physical flow plane, the normal form expressions of streamfunction and simplified differential equations are derived for the degenerate critical points. Some general characteristics of the simplified system are analyzed.

Abstract:Topological structure of multibody systems can be formed by dynamically assembling joints in the system. Based on this fact, this paper present a method by which not only the cut joints can be selected automatically but also the regularly labeling of bodies and joints can be done automatically. With the presented method, joints coordinates can be used to formulate the equations of motion while the manual selection of cut joints is no longer necessary, therefore errors in data input procedure are obviously reduced.

Abstract:The codimension-2 bifurcation in a three-dimensional differential system derived from the famous Chen system was investigated.At first, the equilibrium discussed in the original system was translated to the origin of the coordinates of the new dynamical system by the change of variables.Then the parameter conditions for the codimension-2 Bautin bifurcation were presented by analyzing the Jacobian matrix of the corresponding system.Bifurcation diagrams of the aforementioned system, which demonstrate the Bautin bifurcation, were obtained by numerical simulations.It is shown that the numerical results agree very well with the analytical ones, thus validating the theoretical analysis.

Abstract:Under different parameter conditions, Chua’s oscillator may display two types of coexisted singlescrolled periodic oscillations which are symmetric to each other, or behaves in single doublescrolled periodic oscillation with symmetric structure. With the variation of the periodic excitation, the two coexisted periodic solutions may evolve to two symmetric chaotic attractors respectively. Periodic windows as well as perioddoubling sequence can be observed in the evolution. Furthermore, for relatively low frequency related to the excitation, the two coexisted chaotic attractors may interact with each other to form an enlarged chaotic attractor, and the trajectory may be around the two subattractors in turn for relatively long time. While for the doublescrolled periodic oscillation, the periodic excitation may cause two coexisted quasiperiodic movements, which may interact with each other to form a single quasiperiodic oscillation and finally evolve to a doublescrolled chaotic attractor.

Abstract:Based on the principle about suppression of chaos with parametric nonresonant drive in the Lorenz system, the detection of weak periodic pulse signals in strong noise was realized. Periodic pulse signal, whose frequency is much more larger than the system characteristic frequency, was introduced as the system internal drive signal. According to the parametric equivalent relation obtained by the averaging method and renormalization method between the controlled Lorenz system and the original system, the critical value of detection parameter was determined. Simulations results show that rather low signaltonoise ratio in detection can be obtained by the proposed system. This method can predict the range of parameter threshold by theoretical analysis result. The detection scheme is simple and feasible, which is fit for generalization and application in object detection and fault diagnosis.

Abstract:The structural dynamic property is determined by physical parameters such as mass, damping, stiffness and their distribution. The structural dynamic property alters when these parameters and their distribution change. So the structural dynamic response varies even if the exciting force is same. Maintaining safety and integrity of the structures requires a better understanding of relationship between structural mass distribution, damage and dynamic response. In this study, relationship between structural mass distribution, damage and dynamic response is investigated by experiments. As a demonstration, the experiment of a steel structure with different mass distribution and damage is validated. The mass distribution in the structure is simulated by column welded different dimensional mass block at the top part, and structural damage simulated by sawcutting a crack at the middle part of column. The sweepsine resonance test is applied to study the relationship between structural mass distribution, damage and dynamic response. The structural first resonance dynamic strain response is measured during experiments. The experimental results indicate that the structural first resonance dynamic strain response increase when the asymmetry of mass distribution increases. When the structure is intact, the structural first resonance dynamic strain response at inferior part of column is always bigger than that of response at middle part of column. When the structure is damage, the structural first resonance dynamic strain response at inferior part of column is always less than that of response at middle part of column.

Abstract:A mechanical model of Shenzhen Bay Bridge was established, which considered the hanging degree of cable, and the finite element software was used to simulate the displacement response of the bridge deck and tower anchor points when the seismic, wind, vehicles and other loads were acted on the bridge structure, and the dynamic characteristics of the bridge as well as the vibration solution of the connection nodal. The initial disturbance of cable under foundation excitation was revealed, and the harmonic resonance and parametric vibration of cable in the most unfavorable load case were studied. On this basis, the matching ratio of incentive frequency to cable natural frequency was analyzed, and the influencing characteristics of the nonlinear vibration for cable was obtained, which included excitation amplitude, initial force, modal damping ratio and the cable angle.

Abstract:A nonlinear coupled vibration model of cables and bridge decks and towers and its 1∶2∶1 resonance was investigated. The cable was simplified as a concentrated mass jointed by two weightless strings. The deck and the tower were both simplified as a concentrated mass that can only move vertically and horizontally, respectively. By these simplifications, a nonlinear vibration system of three degrees of freedom was established. With the application of the method of multiple scales, the condition of occurrence of the internal resonance was obtained. The validity of the analysis was verified by numerical simulation. The results show that the 1∶2∶1 internal resonance will arise under some initial condition and then the vibration energy will be transformed and exchanged among the cables, the decks, and the towers regularly.

Abstract:On the basis of comparing the suspension bridges using carbon fiber cables with those bridges using steel cables, the vertical nonlinear vibration feature of suspension bridges was studied, the approximate solutions of suspension bridges’ vertical nonlinear vibration were obtained with Galerkin principle and LP method, and the impact of temperature, amplitude and other factors on the vertical nonlinear vibration of suspension bridges was analyzed. The temperature increment will make the nonlinear vibration frequency of suspension bridges fall, and have larger impact on the timehistories curve of suspension bridges using steel cables. On the contrary, temperature change nearly hasn’t any impact on the timehistories curve of suspension bridges using carbon fiber cables, and amplitude increment will make the nonlinear vibration frequency of suspension bridges increase.

Abstract:This paper investigated the problem of chaotic attitude and reorientation maneuver for completely viscous liquidfilled spacecraft with flexible appendage. All the equations of motion were derived by using Lagrangian mechanics and transformed into the form consisting of an unperturbed part plus perturbed term in order to exploit the system’ nonlinear characteristics in phase space. We emphases on the chaotic attitude dynamics produced from certain sets of the physical parameter values of the spacecraft when energy dissipation acts to derive the body from minor to major axis spin. The orientation of the spacecraft relative to the inertially fixed angular momentum vector is unpredictable because of the occurrence of chaotic dynamics during spinaxis transition. This paper demonstrated that the desired reorientation maneuver was guaranteed by using a pair of thruster impulses. The control strategy for reorientation maneuver was designed, and the numerical simulation results were presented for both the uncontrolled and controlled spins transition.

Abstract:Applying LagrangeGermain’s theory of elastic thin plates and Hamilton formulism to study the dynamics of cantilever plates and its vibration control problem, a solution of the problem was given. Dispersion equations of propagation mode of strip plates were deduced from eigenfunction expansion method. The mode control was applied to study the active vibration control of the strip plates, and the control effect was compared to the EulerBernoulli beam. At last, the results were analyzed and discussed.

Abstract:Speed control algorithm of adaptive fuzzy is proposed based on onelevel speed adjustment braking of Automatic Train Operation system. Shrinkage factor of variable universe is used to optimize quantization factor of fuzzy controller and the scale factor is adjusted by fuzzy reasoning. It is proved that the adaptive fuzzy control algorithm can improve speed control performance, passenger comfort, operation efficiency and location parking through simulation.

Abstract:The automatic landing system based on the LQG/LTR method has good robustness, which can resist strong wind shear. This paper gave a brief introduction to the principle of the LQG/LTR method and presented an LQG/LTR automatic landing controller design for a commercial airplane. Simulation results show that the LQG/LTR method works well on nonminimal system under certain conditions. The autolanding system designed can maintain good control effect with the presence of several disturbances such as wind shear and model uncertainty, hence achieving good robust stability.