黏弹性夹层环形薄板自由振动的理论解

doi:10.6052/1000-0879-12-380

力学与实践 ›› 2013, Vol. 35 ›› Issue (5): 42-46.DOI: 10.6052/1000-0879-12-380

黏弹性夹层环形薄板自由振动的理论解

廖明建^1,2, 李映辉²

1. 中国工程物理研究院总体工程研究所, 四川绵阳621900;
2. 西南交通大学力学与工程学院, 成都610031

收稿日期:2012-10-09 修回日期:2013-03-11 出版日期:2013-10-08 发布日期:2013-10-22
通讯作者: 廖明建,1976年生,男,硕士,工程师,主要从事结构振动与控制研究.E-mail:zhaoliaofei2005@aliyun.com
基金资助:
国家自然科学基金(11072204),中央高校业务费专项(SWJTU11ZT15)和中国工程物理研究院科学技术发展基金(2010A0203007)重点资助项目.

ANALYTICAL SOLUTION OF THE FREE VIBRATION OF VISCOELASTIC SANDWICH ANNULAR PLATE

LIAO Mingjian^1,2, LI Yinghui²

1. Institute of Systems Engineering, China Academy of Engineering Physics, Sichuan, Mianyang 621900, China;
2. School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, China

Received:2012-10-09 Revised:2013-03-11 Online:2013-10-08 Published:2013-10-22

摘要/Abstract

摘要：

基于薄板小挠度理论和Kelvin-Voigt 黏弹性本构方程,建立了黏弹性夹层环形薄板振动控制方程.采用分离变量法计算了内边固支、外边自由黏弹性夹层环形薄板的固有频率和振型,并与有限元计算结果进行比较. 分别讨论了夹心层比和内外半径比对固有频率及衰减系数的影响. 研究表明:系统频率随夹心层厚度增大,先增大后减小,而衰减系数一直增大;系统频率和衰减系数随内外半径比增大而增大.

关键词:

黏弹性夹层环形薄板|自由振动|分离变量法

Abstract:

On the basis of the theory of thin plate of small deflection and the constitutive equation of KelvinVoigt, the governing equation of the viscoelastic annular plate is established. The natural frequencies and modes are calculated, respectively, in consideration of the boundary of the clamped inner edge and the free outer edge by employing the method of separation of variables. The results are compared with those obtained by the finite element method. The effects of the core ratio and the inner-outer radius ratio on the natural frequencies and the damping coefficient are discussed. Conclusions are as follows: the natural frequencies increase at first, then decrease with the increase of the core ratio,however,the damping coefficient increases with the increase of the core ratio. The natural frequencies and the damping coefficient also increase with the increase of the inner-outer radius ratio.

Key words:

viscoelastic sandwich annular plate|free vibration|method of separated variables

中图分类号:

O327

廖明建, 李映辉. 黏弹性夹层环形薄板自由振动的理论解[J]. 力学与实践, 2013, 35(5): 42-46.

LIAO Mingjian, LI Yinghui. ANALYTICAL SOLUTION OF THE FREE VIBRATION OF VISCOELASTIC SANDWICH ANNULAR PLATE[J]. Mechanics in Engineering, 2013, 35(5): 42-46.

参考文献

1 吴强,凌道盛,徐兴. 黏弹性几何非线性夹层梁动态响应分析. 计算力学学报, 1997, 14(1): 36-42 (Wu Qiang, Ling Daosheng,Xu Xing. Dynamic response analysis of geometrical nonlinearity viscoelastic sandwich beam. Journal of Compu-tational Mechanics, 1997, 14(1): 36-42 (in Chinese))

2 韩强,张年梅,杨桂通. 非线性黏弹性梁在随动载荷作用下的混沌运动. 力学与实践, 1998, 20(6): 21-24 (Han Qiang, ZhangNianmei, Yang Guitong. Chaotic motion of a nonlinearviscoelastic beam under a follower force. Mechanics in En-gineering, 1998, 20 (6): 21-24 (in Chinese))

3 梁天锡,廖文冬,陈强洪等. 基于ANSYS 二次开发进行黏弹性结构动力学分析. 力学与实践, 2006, 28(4): 41-45 (Liang Tianxi, Liao Wendong, Chen Qianghong, et al. Modalanalysis of elastic-viscoelastic composite structure based onANSYS secondary development. Mechanics in Engineer-ing, 2006, 28(4): 41-45 (in Chinese))

4 李相辉. 轴向运动黏弹性夹层梁的横向振动分析. [硕士论文].成都: 西南交通大学, 2011 (Li Xianghui. Transverse vibra-tion analysis on axially moving viscoelastic sandwich beam.[Master Thesis]. Chengdu: Southwest Jiaotong University,2011 (in Chinese))

5 王慧彩,赵德有. 黏弹性阻尼夹层板动力特性分析及其试验研究.船舶力学, 2005, 9(4): 109-118 (Wang Huicai, Zhao Deyou.Dynamic analysis and experiment of viscoelastic dampedsandwich plate. Journal of Ship Mechanics, 2005, 9(4):109-118 (in Chinese))

6 张敬莹. 黏弹性夹层板振动特性的有限元分析. [硕士论文]. 大连: 大连理工大学, 2007 (Zhang Jingying. Transverse vibra-tion analysis on axially moving viscoelastic sandwich beam.[Master Thesis]. Dalian: Dalian University of Technology,2007 (in Chinese))

7 周银锋,王忠明. 轴向运动黏弹性板的横向振动特性. 应用数学与力学, 2007, 28(2): 191-199 (Zhou Yinfeng, Wang Zhong-ming. Transverse vibration characteristics of axially mov-ing viscoelastic plate. Applied Mathematics and Mechan-ics, 2007, 28(2): 191-199 (in Chinese))

8 高正,杨晓东. 轴向运动黏弹性板横向振动特性分析的有限差分法. 沈阳航空工业学院学报, 2009, 26(3): 14-18 (Gao Zheng,Yao Xiaodong. Finite difference method of transverse vi-bration characteristics of an axially moving viscoelasticplates. Journal of Shenyang Institute of Aeronautical En-gineering, 2009, 26(3): 14-18 (in Chinese))

9 黄勇,李胜宏,刘先斌. 宽带噪声作用下黏弹性板的矩Lyapunov指数. 力学学报, 2011, 43(3): 551-560 (Huang Yong,LiShenghong,Liu Xianbin. On the moment Lyapunov ex-ponent of a viscoelastic plate subjected to the excitationof wide band noises. Chinese Journal of Theoretical andApplied Mechanics, 2011, 43(3): 551-560 (in Chinese))

10 李中华,李映辉. 轴向运动黏弹性夹层板的多模态耦合横向振动. 复合材料学报, 2012, 29(3): 219-225 (Li Zhonghua, LiYinghui. Muti-mode coupled transverse vibration of ax-ially moving viscoelastic sandwich plate. Acta MateriaeCompositae Sinica, 2012, 29(3): 219-225 (in Chinese))

11 Yu Shann-Chewn, Huang Shyh-Chin. Vibration of a three-layered viscoelastic sandwich circular plate. MechanicalScience, 2001, 43(10): 2215-2236

12 Li Longfei, Wang Xingzhe, ZhouYouhe. Dynamic charac-teristics of traveling waves for a rotating laminated circularplate with viscoelastic core layer. Journal of Sound andVibration, 2011, 330(12): 2836-2847

13 曹志远. 板壳振动理论. 北京: 中国铁道出版社, 1989

[1]	叶梓佑, 刘龙飞, 吴荣平, 吴孟臻, 许向红. CED400型高速受电弓精细动力学模型影响因素研究 ¹⁾[J]. 力学与实践, 2019, 41(3): 265-269.
[2]	刘祥, 叶茂, 曹文斌. 人体-结构系统的水平振动实验[J]. 力学与实践, 2017, 39(4): 365-370.
[3]	费恒孝, 谢季佳, 范学军, 武晓雷. 金属管线高温环境下的断裂失效分析[J]. 力学与实践, 2017, 39(1): 30-34,55.
[4]	高永毅, 唐果, 万文, 邹声华. 非线性因素对隔振器隔振效果影响的研究[J]. 力学与实践, 2015, 37(5): 590-596,602.
[5]	马宏伟, 聂振华. 桥梁安全监测最新研究进展与思考[J]. 力学与实践, 2015, 37(2): 161-170,181.
[6]	陈玉骥. 一种计算多自由度结构基频的较简便方法[J]. 力学与实践, 2013, 35(6): 75-77.
[7]	韩芳, 钟冬望, 蔡路军. 考虑瞬态反应影响的结构动力放大系数研究[J]. 力学与实践, 2013, 35(4): 64-65.
[8]	张维峰, 范传帅. 车架结构动力修改与力响应模拟技术研究[J]. 力学与实践, 2012, 34(4): 19-23.
[9]	路玲玲, 王曦, 黄晨光. 结构健康监测系统中传感器优化布置组合算法[J]. 力学与实践, 2012, 34(1): 80-84,51.
[10]	钱波岳华英. 变截面梁横向振动固有频率数值计算[J]. 力学与实践, 2011, 33(6): 45-49.
[11]	张雷, 孙秀荣. 铅直圆筒内细长杆柱在屈曲位移激励下的横向振动仿真¹⁾[J]. 力学与实践, 2019, 41(5): 526-533.
[12]	刘永春, 赵艳影. 一种悬臂梁模态测试方法¹⁾[J]. 力学与实践, 2019, 41(5): 571-578.
[13]	孙秀荣, 张立娟, 赵洁妤, 宋杨. 考虑分布轴向力的细长杆横向振动与失稳分析¹⁾[J]. 力学与实践, 2021, 43(1): 74-83.

黏弹性夹层环形薄板自由振动的理论解

ANALYTICAL SOLUTION OF THE FREE VIBRATION OF VISCOELASTIC SANDWICH ANNULAR PLATE

PDF (PC)

可视化

被引次数

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 13

编辑推荐

Metrics

本文评价