Nonlinear Mechanics Behaviors Of The Shallow Reticulated Spherical Shell With Rectangle Underside

In this paper, nonlinear mechanics behaviors of the shallow reticulated spherical shell with rectangle underside is studied. The state of interior of country and overseas are introduced. Dynamical character of the shallow reticulated spherical shell is 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 quasi-shell method is selected, shallow reticulated spherical shell is transformed into continuous shell, then nonlinear dynamics governing equations are elected, boundary conditions are given. The nonlinear bending problem of the shallow reticulated spherical shell, nonlinear natural frequency problem of the shallow reticulated spherical shell, nonlinear dynamics stability problem of the shallow reticulated spherical shell, bifurcation problem and chaos problem of the shallow reticulated spherical shell are studied.First, the research meaning of reticulated shells, bifurcation, chaos are introduced. In the following the condition of interior of country and overseas are also introduced.Second, nonlinear dynamical stability of the shallow reticulated spherical 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.Third, the nonlinear bending problem of the shallow reticulated latticed shells is studied. Supposing the displacement function of the shallow reticulated 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.Forth, the nonlinear natural frequency of the shallow reticulated latticed shells is solved. According to the nonlinear dynamical equation and compatible equations of the shallow reticulated latticed shells, using energy variation equations, the nonlinear natural frequency of the shallow reticulated latticed shells is obtained under the clamped and free boundary conditions by integraling energy variation equations. The figures of the characteristic curves of the natural frequency are pointed based on the characteristic relationships of the natural frequency.At last, In order to discuss motion, a kind of nonlinear dynamical free oscillation equation of the shallow reticulated spherical shell is solved. A accurate solution to the free oscillation of the shallow reticulated spherical shell is obtained. Then Melnikov function is solved. The bifurcation conditions of free oscillation are given by the Floquent exponent. Then Melnikov 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 existence of chaos motion.