估计多自由度系统振动基频的一个算法

尽管计算机和有限元软件的发展已使复杂结构固有频率的计算变得很容易，但在某些场合仍然使用简便方法来估计振动系统的基频，文中基于瑞雷法，导出计算多自由度系统振动基频的新算法，并就两个算例与文献所提供的其他方法进行比较，理论分析和算例比较表明。（1）新算法计算量约是瑞雷法的两倍，但无须假设基频振型，即可得到精确的基频。（2）适用于柔度矩阵已知的情形。

ALGORITHM TO ESTIMATE THE MINIMUM NATURAL FREQUENCY OF MULTI-DEGREE FREEDOM VIBRATION SYSTEM

Although the high development of computer and finite element software have facilitated the natural frequency computation of very complicated structures, the simplified algorithms are still applied to estimating the Minimum Natural Frequency of Multi-degree Freedom Vibration System. A new algorithm was deduced out from the conventional Rayleigh method, and the comparison of operational precision and computation efficiency was conducted on 2 examples. The theoretical analysis and example comparison show that, firstly the computation amount is 2 times as that of Rayleigh method, but with the new method, the accuracy minimal natural frequency can be obtained without presumption of the modal shapes, secondly, the new method is applicable to the situation under which the flexibility matrix is accessible.