Nonlinear Dynamic Behavior Of The Flat Cylindrical Shell

In this paper, nonlinear mechanics behaviors of the shallow cylindrical latticed shell is studied. The state of interior of country and overseas are introduced. Dynamical character of the shallow cylindrical shell are systematically analyzed and calculated in the aspect of strong dynamics load. It provides the theory evidence to the application of the project. According to the nonlinear dynamics theory of plate and shell, modern mathematics analytic method of nonlinear dynamics is used, and ideology of continuous qnasi-shell method is selected, shallow cylindrical reticulated shell is transformed into continous shell, then nonlinear dynamical governing equations are elected, boundary conditions are given. The nonlinear bending problem of the shallow cylindrical latticed shell, nonlinear natural frequency problem of the shallow cylindrical latticed shell, nonlinear dynamics stability problem of the shallow cylindrical latticed shell, bifurcation problem and chaos problem of the shallow cylindrical latticed shell are studied.In the preface of chapter one, the research meaning of reticulated shells, bifurcation , chaos are introduced. In the following the condition of interior of country and overseas are also introduced.In chapter two, nonlinear dynamical stability of the shallow cylindrical latticed shell is analyzed. According to nonlinear dynamical variation equations and compatible equations, under the clamped and free boundary conditions, a nonlinear differential equation with quadric items is obtained by the method of Galerkin. In order to discuss motion, a kind of nonlinear dynamical free oscillation equation of the shallow cylindrical latticed shell is solved. A accurate solution to the free oscillation of the the shallow cylindrical latticed shell is obtained. Then Melnikov function is solved. The bifurcation conditions of free oscillation are given by the Floquet exponent. Then Me\nikov function is solved by theory of residues, and the critical of chaos motion is given, besides numerical-graphic method and poincare map also confirm the existenceof chaos motion.In chapter three, the nonlinear natural frequency of the shallow reticulated cylindrical latticed shells is solved. According to the nonlinear dynamical equation and compatible equations of the shallow reticulated cylindrical latticed shells, using energy variation equations, the nonlinear natural frequency of the shallow reticulated cylindrical latticed shells is obtained under the clamped and free boundary conditions by integring energy variation equations . The figures of the characteristic curves of the natural frequency are plotted based on the characteristic relationships of the natural frequency.In chapter four, the nonlinear bending problem of the shallow reticulated cylindrical latticed shells is studied. Supposing the displacement function of the shallow reticulated cylindrical latticed shells, under the clamped and free boundary conditions, not line form relation of deflections and load is obtained by the method of Galerkin ,then character curves of load and deflections is given. This paper can be a valuable reference for engineering.