LI Ming-wu, ZHAO Yan, ZHONG Wan-xie. Dynamic Analysis of Linear Damped Systems With the Symplectic Eigenspace Expansion Method[J]. Applied Mathematics and Mechanics, 2015, 36(1): 1-15. doi: 10.3879/j.issn.1000-0887.2015.01.001
 Citation: LI Ming-wu, ZHAO Yan, ZHONG Wan-xie. Dynamic Analysis of Linear Damped Systems With the Symplectic Eigenspace Expansion Method[J]. Applied Mathematics and Mechanics, 2015, 36(1): 1-15.

# Dynamic Analysis of Linear Damped Systems With the Symplectic Eigenspace Expansion Method

##### doi: 10.3879/j.issn.1000-0887.2015.01.001
Funds:  The National Natural Science Foundation of China（General Program）（11472067）; The National Basic Research Program of China(973 Program)（2014CB046803）
• Rev Recd Date: 2014-11-29
• Publish Date: 2015-01-15
• A symplectic eigenspace expansion method was proposed for the dynamic analysis of linear systems with damping and gyroscopic effect. The modal expansion method based on the Rayleigh quotient had been widely used in the dynamics of complex structures. However, the applicability of the modal expansion method was restricted since the gyroscopic effect was not taken into account. Herein, the relation between the Rayleigh quotient eigenvalue problems and the symplectic eigenvalue problems was established firstly. For these two types of problems, it was found that the latter was more general and can be reduced to the former through neglection of the gyroscopic effect. Then, the symplectic eigenspace expansion method was derived to conduct the dynamic analysis of linear damped gyroscopic systems. Finally, effectiveness of the proposed method is shown with the numerical examples of damped systems with and without gyroscopic effect simulated respectively.
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沈阳化工大学材料科学与工程学院 沈阳 110142