网架式天线环状支撑桁架结构连续体降阶模型研究

The reduced-order continuum model of the ring-shaped supported truss structure of the mesh antenna

根据环状支撑桁架结构组成特点描述了环状桁架单元,给出了变形假设条件,并基于梁模型得到了环状桁架等效多边形结构。计算了等效多边形单元及其对应外接圆环单元的动能和应变能,利用能量等效原理分别推导了等效多边形结构和其外接圆环结构的弹性模量与密度之间的关系表达式,从而计算得到了两者频率比表达式,综合利用有限元和理论方法对比了等效多边形结构和对应圆环结构的低阶振型和频率。研究结果表明,当单元数目大于30后,采用连续体降阶圆环模型简化等效多边形结构对环状支撑桁架结构进行动力学分析是合理的。

The truss element is described according to the structural composition characteristics of the ring-shaped supported truss,and the deformation assumptions are given.The equivalent polygon structure of the ring-shaped truss is obtained based on the beam model.The kinetic energy and strain energy of the equivalent polygon unit and its corresponding circumscribed circular ring unit are calculated.The relational expressions between the elasticity modulus and density of the equivalent polygon structure and the cir-cumscribed circular ring are derived by using the energy equivalence principle.Thus,the expressions of the frequency ratio are ob-tained.The modal shapes and frequencies of the equivalent polygon structure and the corresponding ring structure are compared by using the finite element method and the theoretical method.The results show that it is reasonable to use the continuum ring model to simplify the equivalent polygon structure for the dynamic analysis of the ring truss structure when the number of elements is more than 30.