关于线性离散系统模态阻尼比矩阵和系统阻尼比矩阵的研究

System on the Model Damping Ratio Matrix and System Damping Ratio Matrix for MDOF System

本文将单自由度系统阻尼比的概念推广到多自由度系统,在临界阻尼矩阵的基础上提出了系统阻尼比矩阵和模态阻尼比矩阵的概念.进而,本文还导出了判断系统各模态上的振动性质(过阻尼、欠阻尼、临界阻尼或混合阻尼)的判据式.系统阻尼比矩阵和模态阻尼比矩阵对由实验得出的实模态阻尼系统的阻尼比提供了一种直观的表达,在复模态情况下,模态阻尼比矩阵和实验测定值在定性的意义上也是完全一致的.

This paper presents a concept of system damping ratio matrix and modal damping ratio matrix based on the critical damping matrix, extending the concept of damping ratio to the MDOF system from SDOF system.Furthe-rmore, this paper proposes several criterions of determining vibration nature in modes of system (overdamping, underdamping, critical damping or mixed damping).Modal damping ratio matrix offers a partial physical interpretation of measured modal damping ratios for non-proportionally damped systems.