A highly stable and accurate computational method for eigensolutions in structural dynamics
A highly stable and accurate computational method for eigensolutions in structural dynamics
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DOI：
10.1016/j.cma.2005.08.007
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发表时间：
2006-07
影响因子：
7.2
通讯作者：
Zhaohui Qi;D. Kennedy;F. Williams
中科院分区：
文献类型：
--
作者：
Zhaohui Qi;D. Kennedy;F. Williams
提出了一种新的结构动力学线性特征解的计算方法。从理论上将特征值问题转化为一个常微分方程的初值问题。基于动刚度矩阵符号计数的物理意义，设计了稳定控制装置，并将其与四阶龙格-库塔法相结合。该方法能同时求出特征值和特征向量，具有高精度和高稳定性。数值算例表明，当特征值之间存在很大的幅度差异时，以及当某些特征值非常接近时，该方法仍能给出高精度的解.
A new computational method for the linear eigensolution of structural dynamics is proposed. The eigenvalue problem is theoretically transformed into a specific initial value problem of an ordinary differential equation. Based on the physical meaning of the sign count of the dynamic stiffness matrix, a stability control device is designed and combined with the fourth-order Runge–Kutta method. The resulting method finds the eigenvalues and eigenvectors at the same time, with high accuracy and high stability. Numerical examples show that the proposed method still gives high accuracy solutions when there is a great difference in magnitude among the eigenvalues, and also when some eigenvalues are very close to each other.