粘弹性阻尼夹层梁的振动分析

Vibration Analysis of Sandwich Beams with Viscoelastic Damping

本文采用横截面位移的几何相似假设,建立更为一般的粘弹性阻尼夹层梁的振动方程.同时给出相应的自然边界条件,然后简化到DTMM方程。基于粘弹性材料本构关系的微分算子描述,时域形式的振动方程在概念上更为清晰、严格。从时频转换角度来看,剪切参量不再存在依赖频率含糊的问题.文中还讨论了几何、物理参量对阻尼频率及损耗因子的影响,并推导出阻尼梁强迫振动稳态响应的正交模态解,指出阻尼结构的自感应现象。

The assumption of geometric similarity has been used to replace the assumption of plane cross sections for each layer in present paper. New equations governing the vibration of sandwich beams with viscoelastic damping together with their boundary conditions have been obtained, and then the DTMM eguations have also been obtained from simplifying them. The expression of viscoelastic stress-strain relations for the core in differential time operator has made the vibration equations much clearer and more exact. Based on the transformation of time—frequency domains, there is not the problem of the shear parameter depending on frequency. The normal modal solution for the forced vibration has been come out. Effects of geometric and physical parameters on damping frequency and loss factor have been discussed. The phenomenon of self—induction in damped structures has been pointed.