环形桁架结构径向振动的等效圆环模型

发布时间：2018-10-31 19:34

【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.
[Abstract]:The dynamic performance of ring truss structure is very important to the working state of the whole antenna in the large ring grid deployable antenna. For large space truss structures, based on the idea of continuum equivalence, simplifying its dynamic model to simple elastic continuum model has been a hot topic in dynamic research. The annular truss structure is regarded as a circular periodic structure composed of repeated plane truss elements. On the basis of the equivalent beam model of periodic truss element, In this paper, the radial vibration of annular truss structure is analyzed by using an equivalent ring model, which does not take into account shear deformation and moment of inertia, and the partial differential equations of motion of the equivalent ring model are solved analytically. First, the fourth order partial differential equations describing the radial vibration of a circular ring are reduced to the first order partial differential equations by variable substitution, and then the reduced partial differential equations are transformed into ordinary differential equations by Laplace transformation. The analytical expression of the dynamic response of the equivalent ring model in complex frequency domain is obtained by using the Green function solution of the differential equations, and then the characteristic equation of the natural vibration of the equivalent ring model and the expression of the transfer function are obtained. Finally, the natural frequencies, modes and transfer functions of the ring truss finite element model and the equivalent ring model are compared and analyzed by numerical examples. The feasibility of applying the equivalent ring model to the radial vibration analysis of the annular truss structure is verified.
【作者单位】：南京航空航天大学机械结构力学及控制国家重点实验室;
【基金】：国家自然科学基金重大项目(11290153) 江苏高校优势学科建设工程资助项目
【分类号】：V414;V443.4

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