Interval combination method of time domain finite element analysis for gyroscopic systems
SUI Yongfeng1,2,3,4，PAN Huibin1,3,4，SUI Yi3,4，ZHONG Wanxie2
1.Central Research Institute, Hangzhou Steam Turbine & Power Group Co., Ltd., Hangzhou 310022, China;
2.State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116023, China;
3.Zhejiang Gas Turbine Innovation Center, Hangzhou 310022, China;
4.Zhejiang Rancon Turbine Machinery Co., Ltd., Hangzhou 311199, China
Abstract：Based on the variational principle, time domain finite element method of gyroscopic systems is presented and applied to gyroscopic rotor dynamics. The corresponding trial function matrix, element stiffness matrix and inhomogeneous force are given. The interval combination method of time domain FEM is subsequently proposed which has higher efficiency. This method inherits the property of symplectic conservation and enhances computational accuracy. The examples comparing the numerical results obtained from different methods: time domain FEM and Newmark method demonstrate the advantages of time domain FEM.
隋永枫1,2,3,4，潘慧斌1,3,4，隋艺3,4，钟万勰2. 陀螺转子动力学系统的时间有限元内点法[J]. 振动与冲击, 2020, 39(14): 75-79.
SUI Yongfeng1,2,3,4，PAN Huibin1,3,4，SUI Yi3,4，ZHONG Wanxie2. Interval combination method of time domain finite element analysis for gyroscopic systems. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(14): 75-79.
[1] Zienkiewicz O C and Taylor R. The finite element method. 5-th ed. [M].McGraw-Hill, NY, 2000.
[2] 冯康，秦孟兆. Hamilton体系的辛计算格式[M]. 浙江科技出版社，2004.
Feng Kang,Qin Meng-zhao.Symlectric Geometric Algorithms for Hamiltonian Systems[M]. Zhejiang Science & Technology Press,2004.
[3] 钟万勰. 分析结构力学与有限元[J]. 动力学与控制学报，2006,2(4):1-8.
ZHONG Wan-xie. Analytical Structural Mechanics and Finite Element[J]. Journal of Dynamics and Control, 2006,2(4):1-8.
[4] 钟万勰. 应用力学对偶体系[M].科学出版社，2002.
ZHONG Wan-xie. DualSystem in Applied Mechanics[M]. Science Press,2002.
[5] 钟万勰，姚征. 时间有限元与保辛[J]. 机械强度，2005,27(2)：178-183.
ZHONG Wan-xie,YAO Zheng. Time Domain FEM and Symplectic Conservation[J]. Journal of Mechanical Strength， 2005,27(2)：178-183.
[6] SUI Y F and ZHONG W X. An Adjoint Simplectic Subspace Iteration Method of Gyroscopic Dynamic System and the Application In Rotor Dynamic System[C], the Fourth ECCOMAS 2004.
[7] 隋永枫，钟万勰.大型不正定陀螺系统本征值问题[J].应用数学和力学，2006，27(1): 13-20.
SUI Yong-feng, ZHONG Wan-xie. Eigenvalue Problem of a Large Scale Indefinite Gyroscopic Dynamic System[J].Applied Mathematics and Mechanics,2006,27(1): 13-20.
[8] 张娟娟，崔升，冯永新.多支承转子系统辛空间传递矩阵法及应用[J].振动与冲击，2017，36(16)：32-36,62.
ZHANG Juan-juan，CUI Sheng，FENG Yong-xin. A transfer matrix method for a multi-support rotor system in the symplectic space and its application[J]. Journal of Vibration and Shock，36(16)：32-36,62.
[9] 隋永枫，高强，钟万勰.陀螺系统时间有限元方法[J].振动与冲击,2012，31（13）：95-98.
SUI Yong-feng，GAO Qiang，ZHONG Wan-xie. Time domain finite element method for gyroscopic systems[J]. Journal of Vibration and Shock,2012，31（13）：95-98.
[10] 隋永枫.转子动力学的求解辛体系及其数值计算方法[D].大连：大连理工大学博士论文，2006.
SUI Yong-feng, A Symplectic systematic methodology of rotor dynamics and the corresponding numerical computational methods[D].Dalian：Dalian University of Technology,2006.
[11] 李强,马龙,许伟伟等.椭圆轴承—转子耦合系统动力学特性研究[J].振动与冲击,2016,35(11):174-179.
LI Qiang,MA Long,Xu Wei-wei,et al. Dynamic characteristics analysis of an elliptical bearing-rotor coupled system[J]. Journal of Vibration and Shock,2016,35 (11) :174-179.
