环形桁架结构径向振动的等效圆环模型
刘福寿，金栋平
摘要:在大型环形网架式可展天线中，环形桁架结构的动力学性能对于整个天线的工作状态至关重要。针对大型空间桁架结构，基于连续体等效的思想，将其动力学模型简化为简单的弹性连续体模型一直是动力学研究的热点。将环形桁架结构看作由重复的平面桁架单元构成的环形周期结构，在周期桁架单元等效梁模型的基础上，提出采用不计剪切变形和转动惯量的等效圆环模型分析环形桁架结构的径向振动，并对等效圆环模型的偏微分运动方程进行了解析求解。首先通过变量代换将描述圆环径向振动的四阶偏微分方程组降阶为一阶偏微分方程组，然后通过对降阶后的偏微分方程组进行Laplace变换将其转化为常微分方程组，并采用微分方程组的Green函数解法，获得了等效圆环模型在复频域下动力响应的解析表达式，进而得到等效圆环模型固有振动的特征方程及传递函数的表达式。最后通过数值算例对环形桁架有限元模型与等效圆环模型的固有频率和振型以及传递函数进行了对比分析，验证了等效圆环模型用于环形桁架结构径向振动分析的可行性。
关键词：环形桁架结构, 等效圆环模型, 拉普拉斯变换, 传递函数, 固有振动
Equivalent circular ring model for the radial vibration analysis of hoop truss structures
Fushou Liu, Dongping Jin
Abstract：In large deployable mesh antenna, the dynamic property of hoop truss is vital to the working performance of the whole antenna. For large space truss structures, the model simplification of these structures with simple elastic continuum model is always the focus of dynamics research. By regarding the hoop truss as a hoop periodic structure composed of repetitive planar truss elements, and based on the equivalent beam model of the repeated truss element, an equivalent circular ring model for the radial vibration analysis of the hoop truss structure is presented. By variable substitution, the fourth-order partial differential equations (PDEs) for the radial vibration of theffcircular ring are reduced to first-order PDEs, then the reduced PDEs are transform to ordinary differential equations via Laplace transform, Green's function method is utilized to solve the dynamic response of theffcircular ring in complex frequency domain. Furthermore the characteristic equations for natural vibration and the expression of transfer function of the equivalent ring model were derived. At last, a numerical example is used to compare the natural frequencies, mode shapes and transfer functions of the finite element model and the equivalent ring model of the hoop truss. The results verifies the feasibility of using equivalent circular ring model for radial vibration analysis of hoop truss structure.
Keyword：hoop truss structure, equivalent circular ring model, Laplace transform, transfer function, natural vibration
原文链接：http://lxxb.cstam.org.cn/CN/abstract/abstract146015.shtml
