弹性-粘弹性复合结构的Krylov子空间模型降阶方法

针对弹性-粘弹性复合结构的动力学模型降阶问题，提出用Krylov子空间作为投影子空间进行模型减缩的方法。首先介绍了二阶时不变动力学模型的Krylov子空间的定义，并证明了经Krylov子空间方法降阶得到的模型具有与原模型的部分低频矩量相等的特性。然后给出了计算Krylov向量的算法。最后以一表面部分粘贴约束阻尼结构的正交异性悬臂板为例，分别用Krylov子空间方法和迭代动力缩聚法进行了模型降阶，并对原模型和降阶模型进行了频率响应分析，结果表明，采用Krylov子空间降阶后的模型能较好地保持原模型的动力学特性且降阶幅度大。

Model Reduction Method for Elastic-viscoelastic Composite Structure Based on Krylov Subspace

A model reduction method adoping Krylov subspace as the projection subspace for composite structure was proposed.The definition of Krylov subspace as the projection subspace for composite structure was proposed.The definition of Krylov subspace of second-order linear time-invariant dynamics model was introduced,and it was proved that part of the low-frequency moments is preserved after model reduction based on Krylov subspace.The algorithm of calculating Krylov subspace was presented.A clamped plate of orthotropic materials with partially bonded constrained damping layer treatment was employed,its dynamics finite element model was reduced using the Krylov subspace method and iterative dynamic reduction method respectively,and then the frequency response analysis about the above mentioned models was carried out.The example demonstrates that model reduced by using Krylov subspace can preserve more desirably the dynamic characteristics of original model,while the dimension was reduced greatly.