非经典粘性阻尼离散系统随机振动响应分析

摘要

To decouple the equation of non-classical viscous damping random dynamic systems, Paired Complex Modal Displacement (PCMD), which denotes paired displacement for the complex modal and its conjunction, is introduced in this paper. The modal decoupling approach for the equation of non-classical viscous damping random dynamic systems, based on the PCDM is applied to linear discrete systems. The implementation leads to a simpler method of random response analysis under random excitations. Furthermore, the pseudo excitation method for power spectral density matrix analysis is applied in this paper. Compared to traditional methods of the correlation matrix and power spectral density matrix analysis, it is demonstrated that the efficiency of random vibration analysis could be further improved.%为了解耦非经典粘性阻尼离散系统随机动力方程，本文引进“复模态对位移”（Paired Complex Modal Displacement - PCMD）的概念，用以表示复模态及其共轭复模态的配对位移。基于这一新概念，给出了非经典粘性阻尼线性离散系统的解耦分析，由此构成一个在随机激励作用下随机响应分析的简洁方法。另外，还采用了虚拟激励法进行功率谱密度矩阵分析，与传统方法进行响应的功率谱密度矩阵分析相比，这一方法大大提高了随机振动分析的效率。