n维空间二次特征值问题的分解定理-《郑州大学学报(工学版)》

文章信息/Info

Title:: n -dimensional space secondary feature value problem decomposition theorem

Author(s):: Cheng Shui; Liu Renjie;; Henan Provincial Economic Commission, Zhengzhou Institute of Technology,

Keywords:: About the matrix; the Cronek matrix charging; the matrix equation group

摘要:: n 自由度线性阻尼振动系统的二次特征值问题,一般是在2n 维空间求得复数精确解,或在小阻尼、弱非比例阻尼情况下,在 n 维空间求得近似解.本文提出并证明了一个分解定理,即在一定条件下,n 维空间二次特征值问题可化为 n 维空间两个普通特征值问题,用标准算法求得精确解,大大降低了解题难度,简化了计算方法,节约了计算时间。

Abstract:: n The secondary feature value of the linear damping vibration system is generally obtained by obtaining complex solutions at 2N dimensional spaces, or in the case of small damping and weak non -proportional damping, the N -dimensional space finds approximate solution. This article proposes and proves a decomposition theorem, that is, under certain conditions, the second characteristic value problem of N -dimensional space can be turned into two common feature values of N -dimensional space. Reduce the difficulty of understanding the problem, simplify the calculation method, and save the calculation time.