梁式结构动力模型降阶方法及其应用  

A DYNAMIC MODEL REDUCTION METHOD OF BEAM-TYPE STRUCTURES AND ITS APPLICATION

作　　者：赵阳[1] 许博谦[1] 李晓波[1] 李玉韦 Zhao Yang;Xu Boqian;Li Xiaobo;Li Yuwei(Changchun Institute of Optics,Fine Mechanics and Physics,Chinese Academy of Sciences,Changchun 130033,China;Dalian University of Technology,Dalian 116024,China)

机构地区：[1]中国科学院长春光学精密机械与物理研究所,长春130033 [2]大连理工大学工程力学系,大连116024

出　　处：《动力学与控制学报》2021年第4期32-38,共7页Journal of Dynamics and Control

基　　金：国家重点研发计划项目(2016YFE0205000)。

摘　　要：工程项目当中常会遇到运载火箭、火车车厢和高层建筑等大型梁式结构的动力学性能分析,其计算工作量非常大,往往需要对动力模型进行降阶处理.针对这一问题,提出了面向梁式实体结构的多点凝聚法,基于梁平截面假设,该方法将结构每个截面上的有限元节点通过位移转换矩阵凝聚到该截面的多个凝聚点上,从而利用减缩基向量实现了模型的降阶.多点凝聚法还可推广应用到运载火箭液体推进剂的模拟当中,进一步提出了实体降阶法,该方法首先采用实体单元建立液体推进剂,并利用液体不可压缩和不能承受剪切应力的特性合理定义其弹性模量和泊松比这两个材料属性,随后便可利用多点凝聚法得到简化模型.算例表明,采用本文提出的模型降阶方法得到的简化模型一方面可以大幅提升计算效率,另一方面计算结果的相对误差可保证在8%以内,验证了降阶方法的有效性.In engineering projects,we often have to deal with dynamic analysis of large beam-type structures such as launch vehicles,train cars and high-rise buildings.As the computational workload is very large,model reduction is usually essential.In order to solve this problem,a multi-point cohesion method for beam-type solid structures is proposed.Based on the plane section assumption of beam theory,the displacements of FEM nodes on each cross section are approximated by the motion of cohesion points of the cross section through a displacement transformation matrix,resulting in the localized base vectors which will be used for model reduction.The method can also be applied to simulation of liquid propellant launch vehicles.The solid reduction method is then further proposed.Utilizing the characteristics that the liquid is incompressible and can’t withstand shear stress,the elastic modulus and Poisson’s ratio of the solid elements used to establish the liquid propellant are reasonably defined.Then the simplified model can be obtained by the multi-point cohesion method.Results of illustrative examples indicate that,the simplified model derived by the multi-point cohesion method can not only improve computation efficiency,but also ensure that the relative error of the results is less than eight percent.In the meanwhile,the results confirm effectiveness of the model reduction method.

关 键 词：梁式结构 模型降阶 液体推进剂 模态分析 

分 类 号：TB122[理学—工程力学]