轴力作用下多点约束杆件的横向振动及稳定简化分析方法  

Simplified analysis method for the transverse vibration and stability of multi-point constrained bars under axial force

作　　者：陈飘华 张慧健 黄仕平[1,2] 袁兆勋 CHEN Piaohua;ZHANG Huijian;HUANG Shiping;YUAN Zhaoxun(School of Civil Engineering and Transportation,South China University of Technology,Guangzhou 510640,China;China-Singapore International Joint Research Institute,Guangzhou 510700,China)

机构地区：[1]华南理工大学土木与交通学院,广州510640 [2]中新国际联合研究院,广州510700

出　　处：《振动与冲击》2022年第22期241-245,300,共6页Journal of Vibration and Shock

基　　金：国家自然科学基金项目(11672108,11911530692);中央高校基本科研业务费专项资金资助。

摘　　要：结构振动频率是其动力特性的重要指标,是结构动力分析及控制的重要参数。该研究采用特征函数集和相应的特征值建立基本结构的势能泛函方程,利用拉格朗日乘子法考虑泛函中的附加约束条件,推导了轴向力作用下多点约束杆件横向振动的频率方程,同时获得了振动频率及欧拉临界力的解析解。通过有限元模拟验证了端部支承方式为简支和固支两种情况下该公式计算的准确性和有效性。该方法适合快速估算轴力下复杂约束杆件的振动频率及欧拉临界荷载,优化布设约束位置及数量。The structural vibration frequency is an important index of its dynamic characteristics and an important parameter of the structural dynamic analysis and control.The potential energy functional equation of the basic structure was established by using a set of eigenfunctions and corresponding eigenvalues.By using the Lagrange multiplier method and considering additional constraint conditions in the functional,the frequency equation of the transverse vibration of a multi-point constrained bar under axial force was derived.At the same time,an analytical solution of vibration frequency and Euler critical force were obtained.Through finite element simulation,the accuracy and effectiveness of the formula were verified in the cases of simple supports and fixed supports.The method is suitable for fast estimation of the vibration frequency and Euler critical force of complex constraint bars under axial force,and also for the optimization of constraint locations and quantities.

关 键 词：振动频率 多点约束 欧拉临界力 有限元模拟 

分 类 号：O32[理学—一般力学与力学基础]