Papers by Author: Shan Yuan Zhang

Abstract: A nonlinear waves equation of an elastic circular rod taking account of finite deformation and transverse Poisson effect is derived by means of Hamilton variation principle in this paper. Nonlinear wave equation and corresponding truncated nonlinear wave equation are solved by the hyperbolic tangent function and cotangent function finite expansion method. Two different types of exact traveling wave solutions, the shock wave solution and the solitary wave solution are obtained. The necessary condition of these solutions existence is given also.

Abstract: The dynamic buckling of composite bars subject to axial rigid body impact are simulated using the finite-element software ABAQUS6.8. The critical velocity and the bifurcate time are obtained by stain-time curve and effects of fiber angle and impact velocity on dynamic buckling behavior of composite bars are also investigated. The results indicate that the ply angle and impact velocity have an influence on dynamic buckling of composite bars.

Abstract: Using the logarithmic hoop strain，a nonlinear dynamic equation governing the axisymmetric radial motion of an axially compressed cylindrical shell subjected to radial disturbance is derived. By means of Bubnov-Galerkin approach the partial differential equation can be transformed into an ordinary differential equation containing second-order nonlinear term. The qualitative analysis indicates that the autonomous dynamic systems corresponding to two cases of pre-buckling and post-buckling has the form-same homoclinic orbits and two orbits locate different positions on the horizontal axis of phase plane. The threshold condition for the occurrence of Smale horseshoe-type chaos in disturbed system is obtained by Melnikov’s method. Finally, the bifurcation diagram, time-history curve, phase portrait and Poincare’s map are calculated.

Abstract: Chaotic motion of symmetric laminated composite arch with two hinge supports under transverse periodic excitation was investigated. The nonlinear dynamic equations of the arch are changed into the square-order and cubic nonlinear differential dynamic system by Galerkin method, and its homoclinic orbit parameter equations are also acquired. The critical conditions of horseshoe-type chaos are obtained by using Melnikov function. The influence of loading frequency on chaotic region are analysed by numerical calculation. The motion behaviors of system are described through the bifurcation diagrams, the time-history curve, phase portrait and Poincaré map. The results are given as follows. The influence of loading frequency on chaotic region are significant. When the height of arch reach some value, the system can occur horseshoe-type chaos. The system of symmetric laminated composite arch under transverse periodic excitation may occur steady motion and chaotic motion.

Abstract: The motion equation of nonlinear flexural wave in large-deflection beam is derived from Hamilton's variational principle using the coupling of flexural deformation and midplane stretching as key source of nonlinearity and taking into account transverse, axial and rotary inertia effects. The system has homoclinic or heteroclinic orbit under certain conditions, the exact periodic solutions of nonlinear wave equation are obtained by means of Jacobi elliptic function expansion. The solitary wave solution and shock wave solution is given when the modulus of Jacobi elliptic function in the degenerate case. It is easily thought that the introduction of damping and external load can result in break of homoclinic (or heteroclinic) orbit and appearance of transverse homoclinic point. The threshold condition of the existence of transverse homoclinic point is given by help of Melnikov function. It shows that the system has chaos property under Smale horseshoe meaning.

Abstract: Taking into account the nonlinear constitutive relationship and transverse Poisson effects, the propagation characteristic of nonlinear wave for one-dimension elastic thin rod is studied. With the help of Mathematic, two traveling wave solutions for this nonlinear wave equation are obtained by sine-cosine function method, which include the shock wave solution and the solitary wave solution. The necessary condition of these solutions is given also.

Abstract: Some experimental results of the free-free tubes laterally impacted by the missile were given and the finite element program LS-DYNA was used to simulate this dynamic response process. The instantaneous deformation of the circular shell given by experiments and computer simulation were compared and discussed. It can be seen that when the impact occur the local dents firstly appear at the beginning of impact. With time increase, the depth of the dents increase, the scope of the deformation of the tube wall is enlarged; the total stiffness of the cross-section of the tube is weaken and decreases at the impact point, the beam-like bending deformation take place and the rigid-body translations occur. Through the computer simulation the exchanged energy between the missile and the tube were acquired. The impact energy of the missile is transferred to internal energy and kinetic energy of the tube. The ratio of the internal energy with the kinetic energy of the tube is great for the weakness rigidity of the tube wall, which is opposite to that of a free-free beam. This research made us deeply understand the character of the response when studying the elastic-plastic behavior of the free circular shell under intense dynamic loading.

Abstract: The experimental studies on the dynamic buckling of the perfect bars with three kinds of lengths under impulsive axial compression were completed and the boundary condition of clamped-fixed was realized firstly in present studies. The time-history curves of axial strain of bars under different impact velocity were recorded. According to the magnitudes of the axial strain and bifurcate time, the quantitative relation of dynamic buckling load and critical bifurcate length are achieved; according to the curves recorded, the lateral velocity of bars are computed also. The experimental results show that the dynamic buckling load of the bar is distinctly greater than the static one, the front of stress wave can be regarded as fixed and the effect of the axial stress wave in the dynamic buckling of bar must be considered.