Mode Superposition Method In Elastic Impact Problem And Numerical Study In Hamiltonian System Of Related Problems

The impact problems of structures have wide engineering background and are of important theoretical significance and research worthiness. This dissertation mainly deals with .the dynamic impact problems of several structures based on Direct Mode Shape Superposition Method (DMSM), and some related problems in Hamiltonian system are also discussed. The main concerned contents of the results may be summarized as follows:1. The paper presents exact analytical solutions of longitudinal impact analysis for slender conical rods struck by a particle. A new method is proposed for analysis of impact between particle and conical rod with or without supports of spring, in which the superposition method is used and the response of the rod is presented. These analytical results are exact and can be used to validate the numerical methods or other analytical results. The numerical examples show that one of the advantages of the present method is that the analytical form is much simple. It is also found that some variables describing the geometrical shape of rods play an important role in impact dynamic system.2. Impact problem of non-uniform rod or multi-step rod structure are systematically analyzed. The mass and the stiffness are considered as two independent functions. For several formations of the function, the fundamental equation is transformed into constant differential equation after proper transformation, and the basic solutions are obtained. Then the frequency equation and impact forced are gained by using DMSM. Futermore, for the impact problem of a structure of a loaded rod coupled with a spring-mass system, the response of the system is revealed. Some factors have effect on values of the system's frequency and the effects are shown, then the responses of the rod structure are given at different moments.3. The problem of particle colliding at an aribitray location on the beam is analyzed. Suppose that the displacement function of the two parts separated by the impact point, and the analytical solution is obtained by using DMSM. The impact problem of a mass colliding with a composite beam is also considered. Based on the bending-torsion coupled dynamic model of Timoshenko beam, the results of dynamic response and impact force are presented by using DMSM for the problem of a moving rigid-body impacting at a cantilever's end. The rigid-body and the beam are regarded...