Of Shallow Conical Shells, Nonlinear Mechanical Behavior

In this paper, nonlinear mechanics behavior of the shallow reticulated conical shell is studied. The state of interior of country and overseas are introduced. Analysis and calculation of the shallow reticulated conical shell in the aspect of static and dynamical are studied systematically. According to the nonlinear dynamical theory of plate and shell, modern mathematical analytic method of nonlinear dynamic is selected, and ideology of continuous quasi-shell method is used, reticulated shell is transformed into continuous shell, nonlinear dynamical governing equations are established, boundary conditions and initial conditions are given. The nonlinear natural frequency problem of the shallow reticulated conical shell, dynamical stability problem of the shallow reticulated conical shell, bifurcation problem and chaos problem of the shallow reticulated conical shell are studied.In preface of chapter one, the research meaning of reticulated shells, bifurcation and chaos are introduced. In the following the status of interior of country and overseas are introduced.In chapter two, the nonlinear natural frequency of the shallow spherical reticulated shell is studied. The equations of middle cross section of the three-dimensional reticulated frame and initial deflection are added to the equations of three-dimensional reticulated frame, then the equations of shallow reticulated conical shell are obtained. Based on the nonlinear dynamical theory of shallow shell, the nonlinear dynamical equation of the shallow reticulated conical shell is obtained by the method of quasi-shell. The maximal amplitude in the center of the shallow spherical reticulated shell is selected as the perturbation parameter, and the problem is solved by the perturbation variation method. In its first approximate equations, linear natural frequency is obtained, in its second approximate equations, nonlinear natural frequency of the shallow reticulated conical shell is obtained.In chapter three, the problem of the nonlinear dynamical stability of the shallow reticulated conical shell is analyzed. From nonlinear dynamical variation equations and compatible equations of the shallow reticulated conical shell, under the fixed edges boundary conditions, a nonlinear differential equation with quadric items is obtained by theGalerkin method. In order to discuss chaos motion, a kind of nonlinear dynamical free oscillation equation is solved. An accurate solution to the free oscillation equation of the shallow reticulated conical shell is obtained. Then Melnikov function is solved, critical condition of chaos motion is given, and the existence of chaos motion is confirmed from digital simulation phase plans and the Poincare map too.