摘要
为了快速预报梁耦合结构的动力学特性,本文将梁的精确解析公式与有限元分析软件的前处理功能相结合,提出了一种高效动力学分析方法。基于梁结构控制微分方程,推导了梁单元的精确动力学刚度矩阵;利用ANSYS Mechanical APDL平台建立了梁耦合结构的几何模型,并对其进行单元离散,获取结构的单元和节点信息。与有限元方法的离散策略不同,由于本文方法采用了精确的动力学刚度单元,每根梁仅需离散为一个单元;将单元和节点信息导出,并在数值计算软件中与梁单元的动力学刚度矩阵进行组装,构建了耦合结构的整体动力学方程。在此基础上,求解了多种梁耦合结构的强迫振动响应,并将计算结果与ANSYS的仿真值进行了对比。结果表明:相比于传统有限元方法,本文方法显著减少了计算所需单元和节点数量,提高了计算效率。
To quickly predict the dynamic characteristics of beam-coupled structures,an efficient dynamic analysis method is proposed in this paper by combining the accurate analytical formula of a beam with the preprocessing function of a finite element analysis software.Using the governing differential equation of the beam,its exact dy-namic stiffness(DS)matrix is derived.Then,the geometric model of the coupled beam structure is established u-sing the ANSYS Mechanical APDL platform,and element discretization is conducted to obtain the element and node information of the structure.Unlike traditional discretization strategies of the finite element method(FEM),the proposed approach employs an exact DS element,where each beam only needs to be discretized into one element.Subsequently,the element and node information are exported and assembled with the DS matrix of the beam in the numerical calculation software to construct the dynamic equation of the coupled structure.On this basis,the forced vibration analysis of various coupled beam structures is conducted,and the results are compared with those from ANSYS.Compared with the conventional FEM,the proposed approach significantly reduces the number of elements and nodes required for calculation,thereby enhancing computational efficiency.
作者
李直兵
靳国永
仲赛凤
叶天贵
杨铁军
LI Zhibing;JIN Guoyong;ZHONG Saifeng;YE Tiangui;YANG Tiejun(College of Power and Energy Engineering,Harbin Engineering University,Harbin 150001,China)
出处
《哈尔滨工程大学学报》
北大核心
2025年第6期1169-1178,共10页
Journal of Harbin Engineering University
基金
国家自然科学基金项目(5225109,52241101,52271309)
黑龙江省优秀青年科学基金项目(YQ2022E104)。
关键词
梁耦合结构
动刚度矩阵
精确解析解
强迫振动
动力学分析
计算效率
计算精度
有限元分析
beam-coupled structures
dynamic stiffness matrix
exact analytical solution
forced vibration
dynamic analysis
calculation efficiency
calculation accuracy
finite element analysis
