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

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.

On the basis of the theory of thin plate of small deflection and the constitutive equation of Kelvin- Voigt, 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.