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

摘要
图/表
参考文献(15)
相关文章 (15)

全文: PDF (1554 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)

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。本文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。本文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。
关键词：振动频率；多点约束；欧拉临界力；有限元模拟

	服务

	把本文推荐给朋友
	加入我的书架
	加入引用管理器
	E-mail Alert
	RSS
	作者相关文章
	陈飘华1
	张慧健1
	黄仕平1
	2
	袁兆勋1

关键词 ：振动频率, 多点约束, 欧拉临界力, 有限元模拟

Abstract：Structural vibration frequency is an important index of its dynamic characteristics and an important parameter of structural dynamic analysis and control. The potential energy functional equation of the basic structure is established by using a set of eigenfunctions and the corresponding eigenvalues. By using the Lagrange multiplier method and considering the additional constraint conditions in the functional, the frequency equation of the transverse vibration of a multi-point constrained bar under axial force is derived. At the same time, an analytical solutions of the vibration frequency and Euler critical force are obtained. Through the finite element simulation, the accuracy and effectiveness of the formula are verified in the case of simple support and fixed support. This method is suitable for fast estimation of vibration frequency and Euler critical force of complex constraint bar under axial force, and optimization of constraint locations and quantities.
Key words: vibration frequency; multi-point constraints; Euler critical force; finite element simulation

Key words： vibration frequency multi-point constraints Euler critical force finite element simulation

收稿日期: 2021-06-24 出版日期: 2022-11-28

引用本文:

陈飘华1，张慧健1，黄仕平1,2，袁兆勋1. 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[J]. 振动与冲击, 2022, 41(22): 241-245.
CHEN Piaohua1， ZHANG Huijian1， HUANG Shiping1,2， YUAN Zhaoxun1. Simplified analysis method for the transverse vibration and stability of multi-point constrained bars under axial force. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(22): 241-245.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2022/V41/I22/241

[1] 黄小清，陆丽芳，何庭蕙. 材料力学[M]. 第2版. 广州：华南理工大学出版社，2011：229-234.
HUANG Xiao-qing, LU Li-fang, HE Ting-hui. Mechanics of Materials [M]. 2nd Edition. Guangzhou: South China University of Technology Press, 2011: 229-234.
[2] 刘晶波，杜修力，李宏男，等. 结构动力学[M]. 北京：机械工业出版社，2005：166-167.
LIU Jing-bo, DU Xiu-li, LI Hong-nan, et al. Structural Dynamics [M]. Beijing: China Machine Press, 2005: 166-167.
[3] HUANG Yong-hui, GAN Quan, HUANG Shi-ping, et al. A dynamic finite element method for the estimation of cable tension [J]. Structural Engineering and Mechanics, 2018, 68(4): 399-408.
[4] 孙秀荣，张立娟，赵洁妤，等. 考虑分布轴向力的细长杆横向振动与失稳分析[J]. 力学与实践，2021，43(1)：74-83.
SUN Xiu-rong, ZHANG Li-juan, ZHAO Jie-yu, et al. Transverse vibration and instability of slender rod with consideration of distributed axial force [J]. Mechanics in Engineering, 2021, 43(1): 74-83.
[5] 李梦瑶. 考虑剪力滞效应和附加轴力的箱梁自振分析[J]. 交通科学与工程，2020，36(4)：94-100.
LI Meng-yao. The natural vibration analysis of box girder considering shear lag effect and additional axial force [J]. Journal of Transport Science and Engineering, 2020, 36(04): 94-100.
[6] 滕兆春，李世荣. 轴向力作用下非对称支承Euler-Bernoulli梁在过屈曲前后的横向自由振动[J]. 振动与冲击，2004，23(4)：88-90+150.
TENG Zhao-chun, LI Shi-rong. Pre-buckling and post-buckling transverse free vibration of an asymmetrically supported Euler-Bernoulli beam subjected to axial force [J]. Journal of Vibration and Shock, 2004 (4): 88-90+150.
[7] 楼梦麟，洪婷婷. 预应力梁横向振动分析的模态摄动方法[J].工程力学，2006，23(1)：107-111.
LOU Meng-lin, HONG Ting-ting. Mode perturbation method for lateral vibration analysis of prestressed beams [J]. Engineering Mechanics, 2006, 23(1): 107-111.
[8] 陈红永，李上明. 轴向运动梁在轴向载荷作用下的动力学特性研究[J]. 振动与冲击，2016，35(19) ：75-80.
CHEN Hong-yong, Li Shang-ming. Dynamic characteristics of an axially moving Timoshenko beam under axial loads [J]. Journal of Vibration and Shock, 2016, 35(19): 75-80.
[9] 赵雨皓，杜敬涛，许得水. 轴向载荷条件下弹性边界约束梁结构振动特性分析[J]. 振动与冲击，2020，39(15) ：109-117.
ZHAO Yu-hao, DU Jing-tao, XU De-shui. Vibration characteristics analysis for an axially loaded beam with elastic boundary restraints [J]. Journal of Vibration and Shock, 2020, 39 (15): 109-117.
[10] 吴晓. 多跨连续长索的横振固有频率[J]. 振动与冲击，2005，24(4) ：127-128+146.
Wu Xiao. Natural transversal vibrating frequency of continuous long cable with multi-spans [J]. Journal of Vibration and Shock, 2005, 24(4): 127-128+146.
[11] 黄翀，吴晓. 支承不在同一直线上多跨索的固有振动分析[J]. 振动与冲击，2011，30(12)：250-252+264.
HUANG Chong, WU Xiao. Natural vibration analysis of a multi-span cable supports on different straight lines [J]. Journal of Vibration and Shock, 2011, 30(12): 250-252+264.
[12] 荆洪英，张利，金基铎，等. 轴向受压中间支承梁的横向振动和稳定性[J]. 振动与冲击，2010，29(6)：101-104+238-239.
JING Hong-ying, ZHANG Li, JIN Ji-duo, et al. Stability analysis of the beam with intermediate support subjected to axial force [J]. Journal of Vibration and Shock, 2010, 29(6): 101-104+238-239.
[13] XIAO W S, WANG F D, Liu J . Analysis of axial compressive loaded beam under random support excitations [J]. Journal of Sound and Vibration, 2017, 410: 378-388.
[14] 王勖成. 有限单元法[M]. 北京：清华大学出版社，2003：273-277.
WANG Xu-cheng. Finite Element Method [M]. Beijing: Tsinghua University Press, 2003: 273-277.
[15] SAIBEL E. Vibration Frequencies of Continuous Beams [J]. Journal of the Aeronautical Sciences, 1944, 11(1): 88-90.