Abstract:The dynamics of a thin elastic helical rod with circular cross section in relaxed state, i.e., the dynamics of a rod with intrinsic curvature and twisting, was discussed. Based on the Kirchhoff's kinetic analogy, the dynamical equations of the elastic rod were expressed by the Euler's angles. The inertial effects of the linear and angular accelerations of the cross section were considered. The stability in spatial and time domain of a helical rod with circular cross section in relaxed state was discussed in the sense of first approximation. We proved that the stability conditions were satisfied in the spatial domain, and in the time domain when the wave number was larger than 1. The propagation of the elastic wave of bending/twisting deformation was discussed, and the relationship between the propagation speed and the wave number was obtained.

Abstract: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.

Abstract:Robust control laws were proposed for the stabilization of nonholonomic wheeled mobile robots moving on an uneven surface,which was not exactly known.The proposed control laws rendered the closed-loop dynamic system practically stable and robust with respect to the effect of the gravity introduced by the uneven surfaceQuadratic surfaces with unknown but bounded coefficients

Abstract:By introducing a new transformation, a nonlinear second-order partial differential equation—Burgers equation can be converted to a nonlinear first-order equation, which can be solved directly. Furthermore, the new exact analytical solutions of the Burgers equation can be derived, and the results obtained are in good agreement with those given in other papers. This method can also be used to solve other nonlinear partial differential equations.

Abstract:A nonlinear feedback controller was designed for a four-dimensional hyperchaotic LC oscillator system. It was proved theoretically that the controller can make the controlled hyperchaotic LC oscillator system track any given reference signal at exponent rate. And the diverse structure synchronization between the LC oscillator system and different dimensional chaotic system was achieved. Numerical simulations verified the validity of the controller.

Abstract: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.

Abstract:Algebraic criteria for the periodic oscillatory synchronization of the generalized Lienard systems were derived based respectively on the stability theory of linear time-varied systems, Lyapunov direct method and Gerschgorin disc theorem. It was proven theoretically that the synchronization criteria based on Lyapunov direct method were more flexible than the criteria based on Gerschgorin disc theorem, and the criteria obtained by choosing proper Lyapunov function were more flexible than the criteria based on the stability theory of linear time-varied systems. Rayleigh-Duffing equation as a numerical example verified the theoretical results.

Abstract:By numerical simulation method, we studied the Host-Parasitoid model, which was a nonlinear discrete system to describe the interaction between the population of herbivorous arthropods and their insect parasitoids. Many forms of complex dynamics were observed, including the periodic bubbles, pitchfork bifurcation with period-doubling cascade, Hopf bifurcation and intermittent chaos. The nonlinear characteristic of the system was discussed in detail and illustrated by periodic or chaotic attractors, basins of attractors with fractal boundaries. All the methods confirmed the passing of the system from regularity to chaos. The effect of the parameters change in the system could be found in the bifurcation diagrams and the phase graphics near the Hopf bifurcation point. Finally, the system could be controlled from chaos to different periodic orbits effectively by using the parameters open-plus-close control law.

Abstract:Based on the synchronization by single-variable drive method, and applying the adaptive control theory, we studied the synchronization of Liu chaotic system in the condition that one or more uncertain parameters existed, and deduced the sufficient conditions of asymptotic stability for error systems with different unknown parameters using Lyapunov function. Simulation results showed that the adaptive controllers can quickly identify system parameters and synchronize two Liu chaotic systems.

Abstract:The internal resonance of strongly non-linear autonomous systems with multi-degrees of freedom was analyzed on the basis of modifying the KBM method, and the amplitude of limit cycles and the approximate solution were obtained. Compared with KBM method, the characteristic of the present method was that the term included in the approximate solution was a nonlinear function of time instead of a linear function, which could increase the accuracy and be used extensively. An example was given, whose approximate solution and phase-space trajectories were obtained. The results computed by this method were in pretty good agreement with the numerical results, and the accuracy of the present method was very good.

Abstract:The long-based undulatory fin of an Amiiform fish G.niloticus was investigated. A simplified physical model was brought forward, which was composed of N equal thin rods and a rectangular elastic membrane connecting them together. We established a kinematic model of the long-based undulatory fin on the basis of analyzing the long-based dorsal fin locomotion and considering the fluid-structure interaction. Further, the equilibrium equations of the undulatory fin were obtained by applying the membrane theory of thin shells, which took into account the geometrical non-linearity of the structure. The thrust and propulsive efficiency of the long-based fin undulating can be analyzed by applying the derived kinematic model and the equilibrium equations of the undulatory fin.

Abstract:The fuzzy logical control strategy for the parallel-type hybrid vehicle was put forward, and the models of the main components were established．By using the mimic environment of ADVISOR2002, the comparison between the fuzzy logic control strategy and the electric-assisted control strategy were conducted. The result shows that the fuzzy logic control strategy can improve the dynamic,fuel economy and emission．

Abstract:Considering the influence of electromagnetic field on the structural deformation, and supposing that the wire’s deformation was small, a natural lateral vibrant control equation of wire carrying electric current under the periodical excitation in the magnetic field was established by chord modeling. The critical condition to chaotic motion of the wire carrying electric current in the magnetic field was researched with Melnikov Method and Galerkin Principle. And factors such as string tension, string distance and current that affected the chaotic motion region were discussed. The results showed that the chaotic motion region of wire carrying electric current increased with the increasing of string tension and string distance respectively, and decreased with the increasing of electric current when the electric current was below a certain value.

Abstract:In structural dynamic testing and damage detection, the low-order modal information of a structure can be easily obtained, which reflects mostly the global behavior of the structure rather than the local characteristics of the structure. By using the theoretical and experimental modal analysis, this paper investigated the high-order modal properties of the frame structures and the relationship between the high-order modal parameters and the local characteristics of the frame structures in order to implement damage diagnosis of the structures. The theoretical modal analysis showed that there was a dense high-order mode section and the high-order modes behaved the local characteristics in the frame structures. A local exciting method was used to obtain the high-order modes information on a reinforced concrete frame model by the experimental modal analysis method. It was known from the testing results that the stiffness change of a column in the frame structures could be detected by the maximum energy high-order modes.

Abstract:Based on the analogies between plane elasticity and thin plate bending problem, the thin plate bending under symplectic geometry form was solved by direct method. For thin plate with different boundaries, first the order of the governing equations was decreased to form a dual equation set, then the variable separation method was used, so the problem was transformed into an eigen-value problem. The following methods such as eigen-function, symplectic orthogonal relationship and symplectic expansion method were usded to obtain the analytical solutions of the thin plate. The numerical example shows that the method is effective and converges fast.

Abstract:The dynamical characteristics for the coupled pendulum and beam system were studied. The nonlinear characteristics, including geometrically nonlinear and physically nonlinear, were not considered in the beam and pendulum. But the nonlinear items were found in the coupled vibration equations derived from structure dynamics. Using the perturbation method, the dynamical response and bifurcation were studied. Using the software MATHMATIC, the responses of point near the bifurcation point were obtained.

Abstract:Sound field in a car’s irregular enclosed cavity under structural excitation was researched by the advanced Trefftz analytic method. Combining with the acoustic structure coupling and using a weighted residual formulation to deal with the boundary condition, the analytical solution expression of the progressional expanded wave function was obtained, and the prediction analysis solution at mid-low frequency was given. The active noise control model for the cavity was established. The feasibility of the method was proved by mathematical simulation result using Matlab.