周期胞元平面桁架结构等效动力学分析  

Equivalent continuum modeling of a kind of planar lattice truss

作　　者：柳剑波 王立峰[1] 金栋平[1] LIU Jian-bo;WANG Li-feng;JIN Dong-ping(State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics,Nanjing 210016 , China)

机构地区：[1]南京航空航天大学机械结构力学及控制国家重点实验室,江苏南京210016

出　　处：《振动工程学报》2018年第1期67-73,共7页Journal of Vibration Engineering

基　　金：国家自然科学基金重大项目(11290153)

摘　　要：基于能量等效研究了周期胞元构成的平面桁架结构等效动力学建模问题。通过相邻胞元应变协调条件,将胞元的应变场阶次降阶为Timoshenko梁对应的应变场阶次。根据周期胞元的中心位移,获得胞元应变能与动能,进而利用Hamilton原理得到平面桁架结构等效连续体动力学方程。基于等效连续体模型和有限元模型,对周期胞元桁架结构进行了固有特性分析,验证了等效连续体模型的正确性和精度。Based on energy equivalence,an equivalent dynamic model is proposed for a kind of planar lattice truss composed of periodically assembled cells.The order of strain field of the lattice truss can be reduced by using compatibility conditions be-tween the cells.The expressions of strain energy and kinetic energy are derived according to the displacement components at the cell centre.Subsequently,the dynamic equations of the equivalent continuum model of the truss are obtained by means of the Hamilton's principle.The natural vibration of the truss is analyzed via the equivalent continuum model.The comparison with the results of the finite element method shows the validity and accuracy of the equivalent continuum model.

关 键 词：结构动力学 平面桁架 周期胞元 连续体 能量等效 

分 类 号：V414.2[航空宇航科学与技术—航空宇航推进理论与工程]