Abstract:The perturbation approximation should be symplectic conservative. The FEM displacement method is naturally symplectic conservative, the mixed energy representation is also shown symplectic conservative. The stiffness matrix, as well as the mixed energy matrix, perturbations based on the Taylor series expansion are all proved symplectic conservative. However, the Taylor series expansion perturbation for the symplectic transfer matrix is not able to reach symplectic conservative. The symplectic conservative perturbation for a transfer symplectic matrix should be based on the canonical transformation method. Although, the perturbation methods of the stiffness matrix, of the mixed energy matrix and of the transfer symplectic matrix multiplicative perturbation are all symplectic conservative, however, they are not identical. Therefore, numerical comparison is given for an example.

Abstract:Based on the basic equations of free vibration of thin plate, the Hamilton canonical equations were obtained. By variable selection of moment, equivalent shear force, rotation angel and deflection forming dual variables, the analytical solutions for free vibration of thin plate were obtained under different boundary conditions, which were divided into symmetrical and asymmetrical about xaxial. The computational example of a quadrilateral rectangular plate bending was given, which demonstrated the effectiveness of the proposed method, thus extending the application of Hamilton system.

Abstract:Symmetric systems can be transformed into uncoupled subsystems by using the group representation theory, which can reduce the computational effort required for Ｈ２　and Ｈ∞ control of the systems, especially for large scale systems whose controllers are synthesized directly for subsystems with lower dimensions. This paper presented several computational problems in Ｈ２　and Ｈ∞ controllers design to demonstrate the point that the use of symmetry can decrease the computational requirements, e.g. computation of control systems norm and solutions of Lyapunov equations and Riccati equations.

Abstract:The intent of this paper is to study the motion of a kind of hydric nonholonomic systems.The motions of the system can be divided into three stages.The first stage is the continuous motion of a holonomic system.The second stage is an impulse motion.The third stage is the continuous motion of a nonholonomic system.The initial conditions of the last stage are detemined by the final condition of the preceding stage.An example is given to illustrate the application of the result.

Abstract:This paper studied the van der Pol equation with two time delays, particularly the amplitude control of limit cycle in van der Pol system with time delays. The perturbation method was used to obtain the relation equation between amplitude and timedelays. Based on the equation, the controlling of time delays to amplitude were discussed. Then numerical method was utilized to testify theoretic result.

Abstract:A new homotopy technique based on the parameter expansion (PEHAM) was proposed to strongly nonlinear oscillation. By means of the technique of parameter expansion and the theory of homotopy, we transformed the original nonlinear dynamical system into a set of linear differential equations which can be solved easily. This method is a more general one in which the magnitude of the nonlinear need not be a small parameter. A typical cubic system in the form of oscillator was employed to show its feature. Not only the zeroth and firstth approximation of the conservative Duffing oscillator but also the approximate period were obtained by the method. The results verify that when　αis not a small parameter, even when α→∞,the relative error between the exact period and the approximate period exceeds no more than 3% . The analytical results obtained by the method agreed well with the numerical result obtained by the forth order RungeKutta method.

Abstract:This paper discussed the chaotic phenomenon of equilibrium of a thin elastic rod with noncircular cross section under the action of torques on both ends. The equilibrium equations of the rod were written on the basis of Kirchhoff's kinetic analogy. The chaos was caused by the small periodic variation of the bending stiffness of the rod. The Melnikov's method was applied to predict the existence of the chaos, and the Poincaré sections, as well as the phase trajectory were given as numerical verification. It was shown that the rod had a chaotic configuration in the sense of Smale horseshoe. The geometric shapes of the rod with chaotic and regular behavior are presented.

Abstract:Based on the food chain relationship of nutritionautotrophyzooplankton, and considering biochemistry mechanism of biology growth and complementarities of animalcule decomposition, we set up a dynamical Nutrition-Phytoplankton-Zooplankton model, and analyzed the dynamical stability of the model solution by using modern nonlinear theory. The results indicate that the stability of the model will change or even bifurcate when the parameters change.

Abstract:Considering the environmental damping, this paper investigated the chaotic vibrations of a KelvinVoigt type curved pipe conveying fluid subjected to motionlimiting constraint. Numerical simulations indicate that the chaotic vibrations can be induced for certain parameter values of the curved pipe conveying fluid, and the environmental damping and viscoelastic coefficient greatly affect the dynamic responses of the curved pipe. The results provided a reference for tubing and design of pipe system in engineering applications.

Abstract:The design principle and realization of a real FFT algorithm were proposed. In the proposed algorithm, real FFT computation of 2N points were transformed to complex FFT computation of N points according to the symmetry of input serial at first. Then after properly processing the N complex outputs of FFT, the 2N FFT complex outputs of original real inputs were gotten. The proposed algorithm can almost half reduce the operation time of FFT and resolve the conflict between the request of real-time operation in digital signal processing system and the lots of accounting in FFT. The software design of real FFT based on TMS320VC5402 DSP was given. The code length and operation time of the real FFT with 16, 32, 64, 128, 256, 512,1024 points were compared with that of complex FFT. The experiment results proved the correctness of the method.

Abstract:A thirdorder semidiscrete centralupwind scheme for hyperbolic conservation laws was presented. The method was based on combining the thirdorder weighted essentially nonoscillatory reconstruction with the semidiscrete centralupwind numerical flux. The resulting scheme retained the main advantage of central schemessimplicity, and the numerical results showed the highresolution of the method.

Abstract:We investigated the stationary probability distribution (SPD) and the mean and normalized variance of the steadystate properties of a bistable Duffing model subjected to the additive and multiplicative colored noises with a colored crosscorrelation for different correlation times. The expression of SPD was obtained by using the unified colored noise approximation. Through analyzing the effects of the SPD and the mean and normalized variance, we found some new nonlinear phenomena absent for white noise: the additive noise intensity, the crosscorrelation intensity and correlated time between multiplicative and additive noise can induce nonequilibrium phase transition.

Abstract:The analytic solution of the eigenfrequencies and models of a rectangular thin plate with completed clamped supported was derived by the symplectic geometry method. Firstly, the basic dynamic equations for the elastic thin plate were transferred into Hamilton canonical equations. And then the whole variables were separated. Finally, according to the eigenfunction expansion method in the symplectic geometry, the explicit solutions of the eigenfrequencies and models of the rectangular thin plate with completed clamped supported were obtained. Because only the basic dynamic elasticity equations of the thin plate were used, it does not need to select the deformation function arbitrarily. Therefore, the solution is reasonable and theoretical. Moreover, some numerical results were presented to demonstrate the correction of formulations.

Abstract:This paper studied a circular plate's impact force under impact of a mass The formula for the plate's impact force was deduced by using the Galerkin Principle and Laplace Transform. At the same time, the factors that affect the impact force such as the circular plate's radius and thickness, the absorption cushion's stiffness, the altitude of the dropping mass as well as the mass's weight were discussed, and the curves of the impact force versus time were presented for the numerical example. The examples indicated that the above method of calculating the impact force was not only more correct than the conventional contact theory of Hertz, but also more simple and easy to be applied by engineers.

Abstract:A forced vibration system will approach its maximum vibration amplitude at resonance, if the resonant frequency has to be passed. This peak amplitude can be reduced by means of phase modulation technique, whose mechanism is that the increase/decrease of vibration amplitude is closely related to the phase difference between the response and excitement, and the phase difference can be modulated by controlling the course of excitement frequency. Experimental verification was conducted with a cantilever beam subjected to pulses excitement. For the given maximum rate of increasing the excitement frequency, the maximum vibration amplitude of the cantilever was reduced about 18 % with phase modulating during the passage of the first resonant frequency.

Abstract:The structure damage detection method uses the changes in dynamic parameters between the intact and damage states to evaluate and localize damage directly, fast and inexpensively. This paper adopted the curvature mode shape to investigate the damage in frame structure. The Finite element analysis was used to obtain the displacement. By using the central difference approximation, the curvature mode shapes were then calculated from the displacement mode shapes. Numerical simulation results show that the changes of curvature mode shapes are sensitive to the damage in the frame structure. Thus, the curvature mode shapes can indicate the presence of damage and its severity, and locate damage at the same time. Curvature mode shape is also suitable for detection of multiple damages. The experimental result further verifies its sensitivity to structural damage.

Abstract:Based on the characters of parafoil homing trajectory, SerretFrenet frame was used to describe the shortest distance from the current position to the trimming trajectory. Then, using the theory of small disturbance linearization, it showed that the error equations were time invariant. The transform function between the control and the position error could be found from those error equations, and could be used to design the trajectory controller directly. The position errors and velocity errors which are inputs to the trajectory controller could be solved by analytical method, which greatly simplify computation. The effectiveness was testified by the result of example.

Abstract:A new surface treatment was proposed to attenuate the undesirable axial symmetrical vibrations of a cantilever cylindrical shell. The proposed treatment relies on, in its operation, the use of the attraction arrangement magnets in the clamped end and on the constraining layers root . The interaction between the magnets and the viscoelastic layers aims at enhancing the energy dissipation characteristics of the damping treatment. This new treatment will be called Magnetic Constrained Layer Damping (MCLD) treatment. The analytical model of the axial symmetrical vibration of the cantilever cylindrical shell treated with fully MCLD has been derived. The longitudinal and circumferential force equilibrium equations in terms of the axial displacement u30 in constraining layer and radial displacement w and the constant c were derived. Since the dynamic magnetic force resulting from the variation of u30 can be incorporated into the boundary conditions, the developed model can describe the dynamics and the damping characteristics of the structure with MCLD .Also the performance characteristics of the MCLD was compared with the corresponding performance of the conventional Passive Constrained Layer Damping (PCLD). The obtained results indicate that using the fully MCLD treatment can simultaneously suppress vibration for the first several modes of the cantilever cylindrical shell.