约束层阻尼板的有限元建模研究

粘弹性材料（VEM）的本构关系随频率和温度的变化而变化，对粘弹结构难以进行动特性分析及控制研究。基于Hamilton原理，给出了一种建立约束层阻尼（CLD）板动力学方程的新建模方法，建模时，考虑到VEM的纵向位移影响，并引入虚拟自由度，导出了标准二阶定常线性系统模型，从而避免因粘弹性材料导致的高阶非线性方程。采用GHM方法描述VEM的本构关系，它能直接与有限元法融合。算例分析了夹芯层为ZN—1型粘弹性材料的CLD悬臂板的动态特性，并与相关文献中的计算及试验结果进行比较，计算结果更加准确，表明新建模方法是准确的。

STUDY ON THE MODEL OF FINITE ELEMENT OF CONSTRAINED LAYER DAMPING PLATE

A new modeling method for a sandwich plate with voscoelastic core is presented. It is difficult to perform the dynamical analysis and control research by conventional methods because the constitutive relations of viscoelastic materials (VEM) vary with the frequency and temperature. In order to get over this defect, the finite element method (FEM) is combined with the GHM(Golla-Hughes-Mctavish) model of VEM to model a cantilever plate with constrained layer damping (CLD). It employs the GHM method to describe the dynamic characteristics of VEM. FEM is used to model the dynamic model of sandwich plate with a VEM core. The standard second order time invariant linear system model is derived so as to avoid high order nonlinear equations resulted from VEM. In the numerical example the analysis for a cantilever plate with VEM of ZN-1 is performed and compared with related literatures. The results show that the proposed new modeling method is more accurate and reliable than the other methods and closer to the test results. It could be used to develop the active constrained layer damping technique, which combines the robustness, reliability of passive constrained layer damping and effectiveness, adaptability of active control.