Journal of Dynamics and Control
1672-6553
2013
11
4
336
342
10.6052/1672-6553-2013-040
article
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
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 viscoelastic circular plate is established. The analytical expression of natural frequency and modes of free 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 influence 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.
粘弹性夹层圆板,自由振动,Kelvin-Voigt,分离变量法
viscoelastic sandwich circular plate,free vibration,Kelvin-Voigt,method of separated variables
廖明建,李映辉
Liao Mingjian and Li Yinghui
jdc/article/abstract/20130408