粘弹性夹层圆板自由振动的理论解  

ANALYTICAL SOLUTION OF THE FREE VIBRATION OF VISCOELASTIC SANDWICH CIRCULAR PLATE

作　　者：廖明建[1,2] 李映辉[1] 

机构地区：[1]西南交通大学力学与工程学院,成都610031 [2]中国工程物理研究院总体工程研究所,绵阳621900

出　　处：《动力学与控制学报》2013年第4期336-342,共7页Journal of Dynamics and Control

基　　金：国家自然科学基金(11072204);中央高校业务费专项(SWJTU11ZT15);中国工程物理研究院科学技术发展基金重点资助项目(2010A0203007)~~

摘　　要：研究了粘弹性夹层圆板的自由振动特性.基于经典弹性薄板理论和Kelvin-Voigt粘弹性本构方程,建立了粘弹性夹层圆板振动控制方程.采用分离变量法导出了粘弹性夹层圆板的自然频率及振型解析表达式,计算了固支和简支粘弹性夹层圆板的自然频率,并与有限元计算结果进行比较;讨论了粘弹性夹层圆板的夹心层比率对自然频率及衰减系数的影响.研究表明:(1)随着夹心层厚度的增大,系统频率先增大后减小,高阶时该趋势表现更为明显;(2)随着夹心层厚度的增大,衰减系数一直增大,高阶时该趋势表现更为明显.Free vibration characteristics of viscoelastic sandwich circular plate is presented. Based on the basic assumption of elastic thin plate and Kelvin-Viogt constitutive equation, the vibration control equation of the visco- elastic circular plate is established. The analytical expression of natural frequency and modes of fi＇ee vibration is derived by employing the method of separated variables. The natural frequency of fixed and simply supported sandwich circular plate are calculated respectively. The results are compared with finite element method. The in- fluence of core ratio on natural frequency and damping coefficient is discussed. Conclusions are as follows ： （ 1 ） The natural frequency increases at first, then decreases with the increase of core ratio. It is more obvious for high order frequency. （2） The damping coefficient always increases with the increase of core ratio.

关 键 词：粘弹性夹层圆板 自由振动 Kelvin-Voigt 分离变量法 

分 类 号：O322[理学—一般力学与力学基础]