利用Lanczos方法求解复合结构特征问题

EIGENVALUE PROBLEM ANALYSIS OF ELASTIC VISCOELASTIC COMPOSITE STRUCTURES USING LANCZOS METHOD

本文研究由弹性材料和粘弹性材料构成复合结构的动力学问题。在文［１］的基础上，建立了复合结构的动力学状态方程。为了对复合结构进行动力学分析，本文提出一种扩展的Ｌａｎｃｚｏｓ方法，用来求解复合结构的复模态参数。通过数值算例分析，证明了本文方法具有较高的计算精度和计算效率。

This paper investigates the vibration problems of composite structures constructed with elastic and viscoelastic materials. Introduced the concept of dissipation displacement, the equation of motion is transformed into the first order differential equation in state space. The modal analysis is carried out. Then, the Lanczos method to solve eigenvalue problem is discussed in detail. Finally, sample examples are given to illustrate the theory in the paper.