受边界载荷的大型环形桁架天线结构非线性动力学研究

Nonlinear dynamics of large circular annular truss antenna structures subjected to boundary loads

将展开锁定的大型环形天线简化为等效圆柱壳结构,并考虑前后索网对环形桁架的作用力,进而研究了其在一种特殊边界条件下呼吸振动的分岔和混沌.本文考虑热应力的影响,基于一阶剪切变形理论和von-Karman几何非线性关系,运用Hamilton原理推导出等效圆柱壳的偏微分形式的运动方程.并考虑将圆柱壳的一条母线固定,两端自由的特殊边界条件,利用Galerkin法将偏微分方程离散为常微分方程.运用Runge-Kutta法,对特殊边界条件下的等效圆柱壳进行数值仿真,获得系统的分岔图、最大Lyapunov指数曲线、三维分岔图、时间历程图、相图和庞加莱截面.

This paper investigates the bifurcation and chaos in breathing vibration of a circular truss antenna that has expanded subjected to heating load.The circular antenna is reducing to a continuum circular cylindrical shell,and considering the loads that come from cable net structure.By using the first order shear deformation theory,geometrical non-linearity strain-displacement relationship and Hamilton＇s principle,the nonlinear partial differential equilibrium equation of the system are deduced.Galerkin method is utilized to obtain the nonlinear ordinary differential governing equations of the cylindrical shell under the specific boundary conditions that one generatrix of the cylindrical shell is clamped and both ends of the shell are free.Using Runge-Kutta method for numerical simulation of equivalent cylindrical shell under special boundary condition,the bifurcation diagram of system and the largest Lyapunov exponent curve,three-dimensional bifurcation diagram,time history diagram,phase map and Poincare section can be obtained.The influences of radial line load and in-plane load on vibration characteristics of the continuum circular cylindrical shell are studied.