Abstract: Based on the symplectic theory in applied mechanics, some characteristic theories, such as the symplectic Gramme-Schmidt orthogonal algorithm, the independence between symplectic eigensolutions, precise integration method for the problem with two end boundary conditions, etc. were employed to analyze the energy band structure of Timoshenko beam and the wave scattering in the beam which was connected with a rigid scatterer.
Abstract: The solutions to the fractional FornbergWhitham (FFW) equation and the modified FFW equation generated by change of one nonlinear term uux with u2ux were presented. The fractional variational iteration method (FVIM) was used, in which the Lagrange multiplier was determined with the variational function and the Laplace transformation. Two cases were discussed respectively for the FFW equation because the order of time differentiation was determined through comparison of the two derivatives’orders in the fractional differential equation. Finally, two numerical examples of the FVIM solution were given. The computational results demonstrate the high efficiency of the presented method.
Abstract: An entropy-consistent flux scheme was developed for the shallow water equations. To offset the entropy increase with cubic order of the shock strength across shock waves, the term of absolute value of the characteristic velocity difference was added into the entropy stable flux, so as to achieve entropy consistency. The new numerical difference scheme featured extreme simplicity, high efficiency, and none additional artificial numerical viscous terms. Numerical experiments of the proposed scheme adequately demonstrated these advantages. The new scheme successfully simulates both the circular shock water wave propagations and the vortices formed on both sides of the breach in different kinds of dam break problems, thus makes a better method to solve the shallow water equations.
Abstract: Due to uncertainty and nonrepeatability in the indirect observation of space plasma, and limitation of the passive experiment, in order to describe the dynamic characteristics of the space plasma particle motion accurately, a nonlinear motion model of a single space plasma particle was proposed. By dint of Mawhin’s continuation theorem, the existence of periodic solutions to a class of nonlinear problems was discussed, and in turn, the homoclinic orbit of the motion model for a single space plasma particle was investigated. A new result about the existence of the homoclinic orbit was obtained. The result provides a better basis for observation and theoretical study in space environment.
Abstract: In order to depict the space maneuvering more precisely, some new non-Keplerian theories and methods are required to meet the complex demands of space operation in the future. According to the similarity analysis between the spacecraft precessional motion and gyroscopic precession, the concept of gyroscopic effect produced during the non-Keplerian motion of spacecrafts around the earth was presented. A mathematical model of the gyroscopic effect was established based on the spacecraft dynamic equation, and the spacecraft motion under the gyroscopic effect was investigated. Then a new non-Keplerian orbit theory and method to realize better space maneuvering is provided.
Abstract: Based on two sets of dynamic equilibrium differential equations for plates under initial load effect, which were respectively expressed as general and polar coordinate forms to fit different boundary conditions. The approximate solutions of fundamental frequencies under initial load effect for the simply supported rectangular plate, the clamped rectangular plate, the simply supported equilateral triangular plate, the clamped elliptic plate, the clamped circular plate and the simply supported circular plate, were derived with the Galerkin method. These approximate solutions were verified with the finite element method under initial load effect, which clearly illustrated the initial load effect and corresponding factors that influence the plates’ fundamental frequencies. Initial load effect on fundamental frequencies of the above 6 typical plates was analyzed with these solutions. Due to initial load effect, bending stiffnesses of the plates increased, and their fundamental frequencies rose. The key physical factors governing the initial load effect on the plates are the initial load magnitude，the ratio of span to thickness and the boundary conditions, etc. The bigger the initial loads and the smaller the bending stiffnesses of the plates are, the higher the initial load effect on the fundamental frequencies is. This initial load effect is obvious and should not be neglected in the design and analysis of plates.
Abstract: The slip line equation for circular tunnels had been solved by Soviet scholars in the middle of 20th century, and widely used in China. But the assumption that the angle between the slip line and the velocity vector was 45°-φ/2 in the derivation had been wrong. Theoretically, that angle was related to the flow rule adopted. The plastic slip line equation of circular tunnels and the formula of horizontal fracture depth were derived based on both the associated flow rule and non-associated flow rule. Proved by previous model test, the slip line solution based on the non-associated flow rule is recommended for application.
Abstract: An SIR vector-borne epidemic model with distributed delay and nonlinear incidence was established, the basic reproduction number determining the uniform persistence of the disease was found. When the basic reproduction number was not greater than 1, the disease died out finally; when the basic reproduction number was greater than 1, the model had a unique endemic equilibrium, and the disease uniformly persisted in the population. By constructing Lyapunov functional, it was proved that, under certain conditions, the endemic equilibrium was globally stable in the feasible region only when it existed. In addition, the non-uniqueness of the suitable Lyapunov functionals was shown for proving the global stability of the endemic equilibrium.
Abstract: A stochastic SI epidemic model was proposed with double noises. With the stochastic averaging method and nonlinear dynamic theory, the SI epidemic model was simplified. According to the Lyapunov exponent and singular boundary theory, some new criteria ensuring the model’s local and global stochastic stability were obtained. By dint of the Lyapunov exponent of invariant measure and the stationary probability density, the stochastic bifurcation of the model was explored. Results show that the system under the effect of random factors becomes more sensitive and more unstable.
Abstract: A 3-dimensional numerical model for elastic uniform tube vibration induced by cross flow was proposed based on the finite volume method and finite element method combined with dynamic mesh technique. The model presented a 3-dimensional fully coupled approach to solve the fluid flow and the structure vibration simultaneously. First, the capability of various mesh discretization forms and different turbulent models in prediction of turbulent flow characteristics was investigated through computation of turbulent cross flow around a rigid tube, and the CFD model for flow induced vibration was obtained. Second, based on the flow induced vibration model, the phase difference between fluid load and vibration displacement was also studied, and the results indicated that the difference was caused by the fluid load. Meanwhile, the results of 1-way coupling calculation were compared with that of 2-way coupling. Finally, the wake characteristics were analyzed with some time-averaged parameters including pressure distribution on the tube surface, flow velocity and separation angle in the wake of the vibrating tube.
Abstract: The nonlinear chaotic autonomous 3-dimensional system is algebraically simple but could generate complex chaotic attractors. The chaotic system was demonstrated through theoretical analysis and numerical simulation，and the range of the parameters which could induce the system to be unstable was analyzed. The dynamic characteristics of the system are revealed with bifurcation diagram and Lyapunov exponent spectrum.