A modified precise integration method based on Magnus expansion for transient response analysis of time varying dynamical structure

2016 ◽  
Vol 89 ◽  
pp. 40-46 ◽  
Author(s):  
Cong Yue ◽  
Xingmin Ren ◽  
Yongfeng Yang ◽  
Wangqun Deng
Keyword(s):  
Transient Response ◽  
Integration Method ◽  
Response Analysis ◽  
Dynamical Structure ◽  
Time Varying ◽  
Magnus Expansion ◽  
Precise Integration ◽  
Precise Integration Method ◽  
Transient Response Analysis

scholarly journals Precise Integration Method for Solving Noncooperative LQ Differential Game

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Hai-Jun Peng ◽  
Sheng Zhang ◽  
Zhi-Gang Wu ◽  
Biao-Song Chen
Keyword(s):  
Differential Equation ◽  
Differential Game ◽  
Integration Method ◽  
Transformation Method ◽  
Linear Quadratic ◽  
Riccati Differential Equation ◽  
Precise Integration ◽  
Precise Integration Method ◽  
Direct Integration Method ◽  
Two Parameters

The key of solving the noncooperative linear quadratic (LQ) differential game is to solve the coupled matrix Riccati differential equation. The precise integration method based on the adaptive choosing of the two parameters is expanded from the traditional symmetric Riccati differential equation to the coupled asymmetric Riccati differential equation in this paper. The proposed expanded precise integration method can overcome the difficulty of the singularity point and the ill-conditioned matrix in the solving of coupled asymmetric Riccati differential equation. The numerical examples show that the expanded precise integration method gives more stable and accurate numerical results than the “direct integration method” and the “linear transformation method”.

Transient Vibration of High-Speed, Lightweight Rotors Due to Sudden Imbalance

1983 ◽  
Vol 105 (3) ◽  
pp. 480-486 ◽  
Author(s):  
M. Sakata ◽  
T. Aiba ◽  
H. Ohnabe
Keyword(s):  
Transient Response ◽  
High Speed ◽  
Rotor System ◽  
Response Analysis ◽  
Transient Vibration ◽  
Flexible Shaft ◽  
Shaft System ◽  
Transient Response Analysis ◽  
Flexible Disk ◽  
Blade Loss

In the field of rotor dynamics, increased attention is being given to the transient response analysis of the rotor, since the effects of impact loading and vibrations of the rotor arising from blade loss can be studied by a time transient solution of the rotor system. As recent trends in rotating machinery have been directed towards lightweight, high-speed flexible rotors, the effect of flexibility on transient response analysis is becoming of increasing importance. In the present paper, a transient vibration analysis is carried out on a flexible-disk/flexible-shaft system or rigid-disk flexible-shaft system subjected to a sudden imbalance that is assumed to represent the effect of blade loss. To solve the basic equation governing a rotating flexible disk the Galerkin’s method is used, and the equation of motion of the rotor system is numerically solved by employing the Runge-Kutta-Gill’s method. Experiments were conducted on a model rotor having a blade loss simulator; the shaft vibrations were also measured. The validity of the anaytical results was demonstrated by comparison with the experimental results.

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