扁锥面网壳的非线性力学行为

【作者】 韩明君；

【导师】 王新志； 邱平；

【作者基本信息】 兰州理工大学 ， 工程力学， 2005， 硕士

【摘要】 论文主要研究了三向网格扁锥面网壳的非线性力学行为。介绍了网壳发展的国内外现状,针对扁锥面网壳在静态和动态方面作了较为系统的分析和计算。基于板壳非线性动力学理论,采用非线性动力学中的现代数学分析方法,运用连续化拟壳法思想,将网壳转化为连续壳体,建立了非线性动力学控制方程,合理的确定了边界条件和初始条件。分析了三向网格扁锥面网壳的非线性固有频率问题,动力稳定性问题,分岔问题,混沌问题。 在第一章绪论中主要介绍了网壳、分岔、混沌研究的意义,然后介绍了网壳研究的国内外进展状况。 在第二章中主要研究了扁锥面网壳的非线性固有频率问题。在圆形三向网架大挠度方程中,再加上三向网架中截面方程和初始挠度就得到三向网格扁锥面网壳的大挠度方程。主要研究了扁锥面网壳的非线性固有频率问题。根据薄壳非线性动力学理论,用拟壳法给出扁锥面网壳的非线性动力学控制方程。选取扁锥面网壳中心最大振幅为摄动参数,用摄动变分法进行求解。一次近似得到了扁锥面网壳的线性振动时的固有频率,二次近似得到了扁锥面网壳的非线性固有频率。 在第三章中主要研究了扁锥面网壳的非线性动力稳定性问题。由扁锥面网壳的非线性动力学变分方程和协调方程,在固定夹紧的边界条件下,用Galerkin方法得到一个含二次非线性微分方程。为了讨论混沌运动,对一类非线性动力系统的自由振动方程进行了求解。对于扁锥面网壳的非线性动力学的自由振动方程,给出了准确解。继而求出Melnikov函数,给出了发生混沌的临界条件,通过数字仿真和Poincare映射图也证实了混沌运动的存在。更多还原

【Abstract】 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.更多还原