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

• 应用研究 • 上一篇    下一篇

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. 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 Mingjian1,2, LI Yinghui2   

  1. 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:

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

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