Abstract:This article introduced a new Lorenzlike system of threedimensional quadratic autonomous ordinary differential equations. For theoretical analysis, the Lyapunov criterion was applied to study the stability of the equalibria of the system. Based on this, numerical simulations indicated that the considered system may display abundant dynamical behaviour, such as chaotic and various periodic motions. Moreover,the effect of two key parameters on the stability of the system was investigated,and the forming mechanism of the chaotic attractor was studied via constructing a controller of the system.

Abstract:A typical dynamics system, van der PolDuffing equation with two time delays,was studied. The key aim was to study amplitude control of limit cycle in van der PolDuffing system by using time delays feedback controller. 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. The stability of normal solution was analyzed, and the Hopf bifurcation condition of the controlled system was obtained. Numerical method was utilized to testify the theoretic results,which indicated the numerical results were in good agreement with the theoretical results.

Abstract:This paper discussed the stability of a thin elastic helical rod with noncircular cross section in relaxed state, i.e., the stability of a rod with intrinsic curvature and twisting. Based on the Kirchhoff's kinetic analogy,the dynamical equations of the elastic rod were expressed by the Euler's angles.Neglecting the small force of inertia caused by the linear acceleration,only the inertial effect of the rotation of the cross section was considered,which made the Euler's equations closed. We proved that the Lyapunov's stability condition in first approximation was satisfied for the helical rod in relaxed state in the spatial domain, as well as in the time domain. Therefore the extensive and stable existence of a thin elastic rod with helical configuration in the nature can be explained theoretically. It was also noticed that a helical rod with negative Poisson ratio can be unstable.

Abstract:The dynamics of a class of impulsive dynamic systems with impulsive state feedback control was studied. A Poincare map was constructed to discuss the bifurcation of periodic solution,and the sufficient conditions for the existence and stability of semitrivial periodic solution and positive period1 solution were obtained. The qualitative analysis and numerical results show that a positive period1 solution bifurcates from the semitrivial periodic solution through a fold bifurcation, a positive period2 solution bifurcates from the positive period1 solution through a flip bifurcation, and the chaotic solution is generated via a cascade of flip bifurcations. The superiority of the state feedback control strategy was also discussed.

Abstract:Starting from a special PainlevéBacklund transformation and a multilinear variable separation approach, the (2+1)dimensional generalized BorerKaup(GBK) system was analyzed,and a general variable separation excitation with some arbitrary functions for the (2+1)dimensional GBK system was derived.Based on the derived variable separation excitation and by selecting the arbitrary functions in the exact solution appropriately, such as certain localized functions and multivalued functions, a new type of solitary wave, i.e., a semifolded localized structure with practical meaning like ocean surface waves for the GBK system was constructed, and its evolution property of the novel localized structures was briefly discussed. The results show that it is completely elastic interaction,because the semifolded localized coherent structures are completely preserved,and their initial velocities, wave shapes and amplitudes are preserved after collision.

Abstract:When a mine hoist is lifting a heavy weight, the natural frequency of the system varies slowly with the changes of mass and stiffness. So the mine hoist system is an oscillatory system with slowly varying parameters if the mass of steel rope is taken into account.The multiple scales method of KuzmakLuke was firstly applied to obtain the periodicity condition of solutions of strongly nonlinear oscillators with generally nonlinear spring, and then Jacobian elliptic functions were used to express the leading order approximate solutions of quadratic and cubic nonlinear oscillators. Secondly, the obtained results were applied respectively to mine hoist systems with slowly varying mass and with quadratic or cubic nonlinear spring. Finally,the theoretical results were used to deal with certain mine hoist systems, and comparisons of asymptotic solutions with numerical solutions of two examples showed the efficiency of the proposed method.

Abstract:Based on the theory of large deformation and using the differential geometry.The paper derived the relationship of strain and displacement for spatial curved beams,taking into account the longitudinal strains and torsion strains,but neglecting the effects of shear, moment of inertia and warping.The Hamilton variation principle was used to derive the nonlinear dynamics equations of spatial curved beam under threedisplacementfreedom and threerotationfreedom,which can be degenerated to linear dynamics equations of planar circular arch,and their results were compared with the results in literatures. The nonlinear dynamics equations provide a reliable foundation for analysis of the nonlinear dynamics of curved beam.

Abstract:Based on the macroeconomic ideas of Goodwin and Puu, this article derived a generalized nonlinear dynamical business cycle system.First, the numerical methods were used to investigate the global bifurcation behaviors of the system depending on certain parameters. Then, by means of the largest Lyapunov exponent, the variations of the dynamical characters during the bifurcation were discussed.Through the bifurcation figures,we found the perioddoubling bifurcation route to chaos within some parameter intervals,and there were several periodic windows embedded in the chaotic domains. Besides, the increase of “accelerator" value can improve the cyclical motion of economics. Finally, the potential applications of the dynamical properties by bifurcation and chaos analysis to understanding economic fluctuations were introduced.

Abstract:An analytical solution for the coefficient of restitution of a mass colliding with a slender rod or beam was presented. The colliding body was regarded as the attachment of the target, so the problem was transformed into a normal vibration problem using DMSM (Direct Mode Superposition Method). The separation moment was obtained by setting the impact force as zero. It can be concluded that,when only elastic impact is considered, the coefficient of restitution is determined by not only the material property of the target, but also the mass ratio of the colliding body to the target, and the boundary condition of the target. However, the initial velocity has no effect on the coefficient of restitution.

Abstract:Based on the deformation hypothesis of Timoshenko's plates and the Boltzmann's superposition principles for linear viscoelastic materials, the nonlinear equations governing the dynamical behavior of Timoshenko's viscoelastic thick plates with damage were derived,and the Galerkin method was applied to simplify the equations. The numerical methods in nonlinear dynamical systems were used to solve the simplified systems. It could be seen that there are plenty of dynamical properties for dynamical systems formed by this kind of viscoelastic thick plates with damage under a transverse harmonic load. The influences of load, geometry and material parameters on the dynamical behavior of the nonlinear system were investigated,and the effect of damage on the dynamical behavior of plate was discussed.

Abstract:Based on the general approach of Incremental Harmonic Balance method (IHBM), the behavior of nonlinear dynamic stability for viscoelastic plates subjected to inplane periodic excitation was investigated by converting the integrodifferential governing equations to differential ones. The dependence of the downward shift and contraction of principal instable regions on the viscose parameters of standard linear solid and vibration frequency of plates was examined. A simplified approach of direct application of Incremental Harmonic Balance method to integrodifferential equation of motion was given, and this approximate method was validated through the comparison of results obtained respectively by two kinds of application of IHBM.

Abstract:The finite element transfer matrix method was applied to analyze the natural vibration characteristics of some slender rocket/projectile,which was validated by experimental data.The finite element transfer matrix method has not only the merits of finite element method, such as flexible model and wide application, but also the advantages of low matrix order and fast computation of transfer matrix method. So it can be used to easily analyze the vibration characteristics of rocket/projectile with complex variant sections. Stiffness matrices and mass matrices that are essential to simulate can be obtained directly by commercial finite element software.

Abstract:Taking into account the influence of structural deformations on electromagnetic field,assuming that the beam's deformations are small,and regarding the change of current direction after beam's deformations as current vector's stiff rotation, the natural lateral vibration control equation of beam carrying electric current in magnetic field was established. The equation indicated that the beam's natural lateral vibration was a typical issue.The perturbation method was employed to get the control equation's approximate solution.The analytical expressions of beam's natural lateral vibration frequency and displacement were derived.The main factors, such as the distance of wire and beam, the quantity and direction of current, and the length and radius of beam,which affect the natural lateral vibration of beam carrying electric current,were discussed with an example,and some valuable conclusions were obtained from the example.

Abstract:With the Laplace transform method, the analysis methods of impacting process of linear system were discussed. First, the impact model of the linear system was built,and the basic analysis principle and calculation formula were derived. At the same time, the convolution integral formula was also given. Second, the subsystem's transfer functions,which include mass, elasticity bar, cantilever beam,et,were derived. Lastly,the validity of this analysis method was validated by examples. The results indicated that both system's dynamic characteristics and pre-impacting motion state affected the impacting process and impacting result strongly,and the impacting restitution coefficient can't reveal kinetic phenomenon in impacting process. Compared with other methods, this analysis method have some advantages such as specific conception, higher numeric computing efficiency, and more analytic results.

Abstract:We integrated vibration mode vector with vector space cosine factor conception,and put forward a new quantitative index ，which can judge the entire correlation degree of computational and experimental models. Based on the index's property, we gave a method to confirm dynamic computational model's part parameters. Finally，the example indicated the index could better express the correlation of two models，and the method could be applied in practical engineering.

Abstract:The acoustic band gap structures for rectangular arrays system made of elliptical water cylinders surrounded by a mercury host were investigated by plane wave expansion method. Multiple, complete acoustic band gaps were found for different elliptical cylinder radii and rotating angles. When lattice constants a1=4cm，a2=3.2 and filling fraction F=0.35, there is only one complete band gap and the corresponding width is 0.453 for rotating angle being 0, but there are three complete band gaps and the corresponding widths are 0.458, 0.023 and 0.062 respectively for rotating angle being π/4. It can be concluded that, in such a simple twodimensional inhomogeneous system of liquids, the acoustic band gap structures are affected by the filling fraction, the shape of elliptical cross section,and the rotating angle

Abstract:Traditional PID control has been widely used in real applications. But for traditional PID control, mathematical model must exist when adjusting PID parameters, and the parameters are constant after adjusted. However, in real systems, when the system state and parameters change and become uncertain, system performance cannot keep in the best state. For the purpose of improving system performance of PID control and making use of the existing study fruit of PID control, BP neural network was used for adjusting PID parameters. After simulating, the results show that the algorithm based on BP neural network adjusting has better control characteristics than those of traditional PID and BP neural network.