陀螺系统辛子空间迭代法

An adjoint simplectic subspace iteration method of a large gyroscopic system

转子系统的有限元分析可以导出陀螺系统的本征值问题,而陀螺本征值问题可在哈密顿体系下求解。基于辛子空间迭代法的思想,提出了一种求解陀螺系统本征值问题的算法。首先引入对偶变量,将陀螺动力系统导入哈密顿体系,将问题化为了哈密顿矩阵的本征值问题,由于稳定的陀螺系统其本征值必为纯虚数,利用这个特点,提出了对应陀螺系统的辛子空间迭代法,从而可以求出系统任意阶的本征值及其振型。算例证明了这种算法的有效性。

The finite element analysis of rotor dynamics can be induced to an eigenvalue problem of a large Hamiltonian matrix which can be solved in Hamiltonian system. In this paper, based on an adjoint symplectic subspace iteration method, an iteration method is proposed to solve eigenvalue problem of gyroscopic system. Introducing dual variables of the original variables, Hamiltonian dual equations are presented, so Hamiltonian solution system can be applied to this gyroscopic system. The property that the eigenvalues are only pure imaginary for stable gyroscopic system is used, an adjoint symplectic subspace iteration method of gyroscopic system is presented which can solve any order eigenvalue and eigenvector. This paper demonstrates by examples that the algorithm is valid and has good stability because of the property of subspace iteration method.