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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.研究了作用在等效圆柱壳两端上的径向线载荷和面内载荷对系统振动行为的影响
The large loop antenna with unlocking is simplified to an equivalent cylindrical shell structure, and the force of the cable truss on the circular truss is considered, and then the bifurcation and chaos of the respiration vibration under a special boundary condition are studied. Based on the first-order shear deformation theory and the von-Karman geometric nonlinearity, the equations of motion for the differential form of an equivalent cylindrical shell are deduced by using the Hamilton principle, and one generatrix of the cylindrical shell is fixed and the two ends are free Special boundary conditions, the partial differential equations are discretized by the Galerkin method as the ordinary differential equation.The Runge-Kutta method is used to simulate the equivalent cylindrical shell under the special boundary conditions, and the bifurcation diagrams of the system, the maximum Lyapunov exponent curve, the three-dimensional Bifurcation diagram, time history diagram, phase diagram and Poincaré section. The effect of radial line load and in-plane load acting on the vibration behavior of the system at both ends of the equivalent cylindrical shell