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计及二阶效应的梁杆系统动力响应分析方法研究
引用本文:王佳,张宏生,陆念力.计及二阶效应的梁杆系统动力响应分析方法研究[J].工程力学,2012,29(7):275-282.
作者姓名:王佳  张宏生  陆念力
作者单位:哈尔滨工业大学机电工程学院, 哈尔滨 150001
基金项目:国家科技支撑计划项目(2006BAJ12B03-2)
摘    要:基于动力刚度法和有限元理论提出了一种考虑二阶效应计算梁杆动力响应的新方法。通过求解轴向力作用下Bernoulli-Euler 梁横向和轴向挠度自由振动微分方程,利用位移边界条件反解出待定系数,得到了动态精确形函数;使用经典有限元方法推导了考虑截面自身旋转惯量的质量阵和考虑二阶效应的刚度阵,该质量阵和刚度阵各元素均为轴力和圆频率的超越函数;建立了杆系结构瞬态动力学分析的动力平衡方程,给出了稳定和高效的求解方案。对几个典型的算例进行了计算分析,并与通用软件ANSYS 的计算结果进行了比较。计算结果表明:该分析梁杆系统动力响应的新方法具有较高的计算精度和效率,特别是能够准确地计入轴力对于梁杆动力响应的影响。

关 键 词:有限单元法    瞬态动力学    精确形函数    二阶效应    梁杆系统
收稿时间:2010-09-28

THE STUDY OF DYNAMIC RESPONSE ANALYSIS OF BEAM-ROD SYSTEM CONSIDERING SECOND-ORDER EFFECTS
WANG Jia,ZHANG Hong-sheng,LU Nian-li.THE STUDY OF DYNAMIC RESPONSE ANALYSIS OF BEAM-ROD SYSTEM CONSIDERING SECOND-ORDER EFFECTS[J].Engineering Mechanics,2012,29(7):275-282.
Authors:WANG Jia  ZHANG Hong-sheng  LU Nian-li
Affiliation:School of Mechatronics Engineering, Harbin Institute of Technology, Harbin 150001, China
Abstract:Based on the dynamic stiffness method and finite element method,a new method for calculating the dynamic response of a beam-rod system considering the second-order effect is proposed.By solving the differential equation of the free vibration for an axially loaded Bernoulli-Euler beam and the displacement boundary conditions used to get the undetermined coefficient,the dynamic exact shape function is obtained.The mass matrix and stiffness matrix considering the second-order effect are deduced by a classic finite element method,each element of the mass matrix and stiffness matrix is transcendental functions of the axial force and circular frequency.The dynamic equilibrium equation to analyze the transient dynamic response of a beam-rod system is established,and a stable and efficient solution scheme is proposed to solve the equations.The proposed method are used to analyze various typical numerical examples and compared with that of ANSYS.The results show that the new method for calculating the dynamic response of a beam-rod system has a high computational accuracy and efficiency,especially for the impact of an axial force to the dynamic response of beam structures accurately.
Keywords:finite element method  transient dynamics  exact shape function  second-order effects  beam-rod system
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