Abstract:The small parameter perturbation approximation is applied quite often in applied mathematics and mechanics. There are tremendous conservative system analyses in physics and applied mechanics, and one of the most important characteristics of a conservative system is its symplectic conservation. The present paper emphasizes that the symplectic conservative behavior should be considered in small parameter perturbation approximations. The strip domain structural analysis is considered, and we gave both the perturbation solutions with the displacement method, which is symplectic conservative, and the perturbation solutions with the corresponding transfer symplectic matrix method, which is symplectic nonconservative.

Abstract:By using the relationship between the adjoint equation and the linearized equation of the motion system, and by using the wellknown result that divergence expressions are characterized by annihilation under the full Euler operator, a multiplier method was adopted to construct the conserved quantities of the motion equations. The Lagrange function of the motion system is not necessary for this method. The FokkerPlanck equation was given to illustrate the application of this method, and its infinite conserved quantities can be obtained easily by using this method.

Abstract:The rectangular plate undergoing overall motions was investigated. The dynamic equations were derived through the Finite Element Method and Lagrange equations. Different from the conventional linear modeling method which employs three Cartesian deformation variables, the present modeling method used two nonCartesian variables along with one Cartesian variable to describe the elastic deformation. Therefore the dynamic stiffness terms was captured. The numerical study demonstrated that the equations of motion presented here are more reliable and accurate than the traditional dynamic equations. Some errors will appear if the assumption modal method is used to describe the deformation of flexible plate undergoing overall motions.

Abstract:By utilizing the trial function method, a class of nonlinear partial differential equations (PDEs for short) that are hard to be solved by the usual ways can be reduced to a set of algebraic equations, which can be easily solved, and their related coefficients can be easily determined by the undetermined coefficients method. Then, the exact analytical solutions to the class of nonlinear PDEs were successfully derived. Moreover, the method was applied to the Burgers equation, the KdV equation and the KdV-Burgers equation and the results were in very good agreement with those given in the reference. The method may be generalized to construct the solutions of other nonlinear PDEs.

Abstract:This paper presented a new semidiscrete central scheme for hyperbolic system of conservation laws. By using the fourthorder CWENO reconstruction, the new scheme has properties of higher order accuracy and high resolution for discontinuities. Because the new scheme has less dissipation, which is independent of timesteps, than the staggered central scheme, it can be efficiently used with timesteps as small as the requirement of the numerical stability.

Abstract:First this paper established the dynamic equation for a typical flexible cantilever impact system by the Euler-Bernoulli principle, and gave the corresponding model analytical method. Then, based on some assumptions and definitions, the reducedorder model was given, which can embody the main characteristics, and the eigen-value of the system can be expressed deeply. Finally, the presented method was applied to the reducedorder process of the flexible cantilever impact system, and the method was illustrated by a corresponding numerical example. The results showed that the dynamic characteristics of the system can be exactly simulated by few modes, which provides a foundation for studing the control problem of the flexible impact system.

Abstract:This paper investigated the chaotic motion for a nonlinear viscoelastic pile subjected to a periodical axial force considering the ground soil motion. The material of the pile was assumed to obey the nonlinear Leaderman viscoelastic relation. The equations for the ground soil motion satisfying the Winkler condition and the equations for the transverse motion of pile were derived as the coupled nonlinear integropartialdifferential equations. The equations were simplified into ordinary differential equations by the Galerkin method. Numerical results indicated that there were lots of dynamical behaviors including chaotic motion in the viscoelastic piles.

Abstract:In elasticstatic mechanics there are the least potential principle and the least remaining principle, which is only applicable to the situation of the stable and equilibrium state. But generally speaking there are no stable and equilibrium state in dynamic problems, so it is worthwhile considering carefully whether there is the least potential principle in the dynamic field. This paper studied the possibility of the least potential principle existing in dynamic problems, and derived the least potential principle and the least remaining principle based on the least work consumption principle, which get rid of the limitations of “equilibrium" and “stable state". The practical calculating examples were proposed and the results were correct. So in linear elastodynamics there also exist the least potential principle and the least remaining principle in instantaneous sense, which have different physical meaning. The physical meaning of the former is to take “the minimum of all probable value meantime" at any moment in the dynamical process，and the latter is to take “the minimum" in the whole dynamical process. That is to say, the former is “the minimum at that time" and the latter is “the minimum in the whole process". These two variational principles may become the theoretical foundation for all sorts of variational direct solving methods in linear elastodynamics.

Abstract:On the basis of eletromechanical dynamics and electrical theory, we established a uniform mathematic model for a generator set power network. This model was a nonlinear differential dynamic system that had 27 dimensions. It consisted of the following 5 parts: the mechanical torsional equations, the synchro generator transient process equations, the prime motor torsion allocating and speed modulation control equations, and the field excitation modulation control equations. We used the series capacitor Xc and the resistance R of the transportation line as the bifurcation parameters and derived the area figure of destabilizing parameters from computing. At the point where two pairs of pure imaginary eigenvalues occured, we reduced the dimensions of the system through central manifold theory. Then, using the multiparameter stability theory and unification technique, we solved the reduced equation and obtained the bifurcation equations and their solution. Finally, we obtained the diagram of bifurction parameters, dynamic characters in four parametric areas, and the result was verified by numerical calculation.

Abstract:A hybrid control method was proposed to control the vibration of a spacecraft flexible structure by combining CMAC neural network (NN) and PID control method. Firstly, based on the given dynamic equation of the system, the neural network algorithm was obtained by using the concrete characteristics of CMAC neural network. Then, PID control method was introduced into the control system. The above processes form a hybrid control method, which combines the merits of CMAC neural network and PID control method. Finally, the numerical simulation of the complex flexible spacecraft showed that the proposed method was effective.

Abstract:This paper suggested a novel solution for the non-linear vibration equation of a pendulum. From the relevant differential equation and the initial condition for the problem, there are some derivative properties, which include the maximum displacement, the maximum velocity, the initial acceleration and the trajectory on the phase plane. The studied approximation motion for a pendulum was expressed in the form of Fourier series, in which the circular frequency was also an undetermined value. Let the approximate motion to be close to those derivative properties, the involved Fourier coefficients as well as the circular frequency can be evaluated, in which the four-parameter method and fiveparameter method are used. It is found that the results obtained from the fourparameter method have a high accuracy, and that the results obtained from fiveparameter method has a very high accuracy．

Abstract:A fuzzy neural network was proposed for robotic tracking control. This fuzzy neural network used the Bspline basis function as membership function whose shape can be adjusted on line. The proposed network has better learning and adaptive ability. The simulation results showed that the proposed network can be applied to robotic tracking very well with good performance.

Abstract:The gas gun is well applied in the ballistic environment simulation of weapons by its excellent performance. In the paper, the launching environment parameters are analyzed firstly, and the characteristic value is found. And then the internal ballistic model of the gas gun is established by applying the similar theory of gas kinetics. Finally, the model is simulated on the computer and analyzed. The conclusions in the paper afford theoretical foundations for the following construction design of the gas gun, choosing of the according equipments and adjusting of the parameters of the gas gun.

Abstract:The testing of structural modal parameters is an important basis of dynamic response analysis and structural damage detection. Modal parameters of real structure are usually tested by ambient excitation. The sensor placement affects testing accuracy during this detection. The affection of sensor placement on structural parameters testing are studied by finite bandwidth white noise vibration experiment. The experimental result shows that optimal sensor placement can improve testing accuracy of structural modal parameters.

Abstract:An attempt is made to extend the General Differential Quadrature Rule (GDQR) to the analysis for flowinduced vibration of curved pipes conveying. Based on the equation of in-plane vibration of curved pipes conveying fluid, the GDQR is applied to discretize the pipe modal, leading to a set of equations for the fluidconveying pipes' dynamic behaviour. Calculations of natural frequencies and critical fluid velocities by GDQR show reasonably agreement with the analytical solutions. Further, this paper investigates the typical dynamic responses of a clampedclamped curved pipe conveying fluid. As a result, the represented research shows that the GDQR can deal with these curved pipe models easily with satisfactory computation precision. Therefore, the application of GDQR for nonlinear vibrations of pipes conveying fluid will be the subject of further study.

Abstract:By using the Finite Element Method (FEM)，the nonlinear thermal vibration characteristics of composite laminated plates under linear temperature field were investigated. Based on the eigenvalue buckling analysis method, the bifurcation point of an ideal linear elastic structure was estimated. And the critical buckling temperature distribution and the lowest nature frequencies of composite laminated plates with different layers and orientations were also calculated and analyzed. Moreover, the general regularities of temperature effect on the thermal vibration characteristic of the composite plate structure were summarized. All these conclusions will give guidance on structure design and heatresistant design.

Abstract:First, a uniform viscous and incompressible flow past a circular cylinder was simulated by using the Ansys/Flotran CFD software, then the induced vibration for a viscous flow past a circular cylinder supported by elastic spring and dash pot was simulated with the Ansys/Flotran CFD software and stepwise integration. The lift forces and transverse responses were analyzed with the fast fourier transform(FFT). By analyzing the calculation results, some useful conclusions were given, which may be used in the designing of equipments with viscous flow past a circular cylinder supported by elastic spring and dashpot.

Abstract:Firstly, we discussed the general design principle of an ecoplaner qualitatively. Then, we applied the linear modification approximation theorythe method of NewtonRaphson to perform the kinematics analysis on the hanging system of the scarification mechanism of the ecoplaner and discussed its pit shape. Finally, we carried out the numeral simulation on the pit shape and the ElastoDynamics with the business software-MATLAB.The results were helpful for the designer to have more distinct knowledge about the mechanism motion property and the structure property of the developed product prototype before formal production, and therefore raising the successful rate of the product development.