两个计算固有频率新的简便近似公式

本文给出两个计算多自由度线性系统振动固有频率的简便近似公式。对三自由度系统振动,能简便地求出各阶固有频率。弥补了Rayleigh法、Dunkerley法实际上只能给出基频上下限的不足。对四自由度以上的系统振动,也可以求出基频的下限和最高频的上限。而基频下限的精确度始终比Dunkerley法更高,计算过程比Rayleigh法更简便。

TWO NEW AND SIMPLE APPROXIMATE FORMULAS ON THE NATURAL FREQUENCIES

Two new approximate formulas on the natural frequencies ofvibration of Multi-Degree-of-Freedom linear systems arepresented in this paper.Applying these formulas we can calculateall classes of natural frequencies of the Three-Degree-of-Free-dom system.They supplement the Rayligh's and Dunkerley'smethods which only give the upper and lower limit of the funda-mental.For the vibration of more than Four-Degree-of-Freedom-system,the lower limit of the fundamental and superior limit oftop frequency can be found by thses formulas in this paper.Thelower limit of the fundamental computed by these formulas in thispaper is more precise than that computed by Dunkerley's and issimpler than that computed by Rayleigh's.