静位移法求解理论力学中单自由度系统的自由振动问题

Determining Free Vibration in Single Degree of Freedom System with Static Displacement Method in Theoretical Mechanics

在用静位移法求质量-弹簧系统自由振动固有频率的基础上,进一步推导出由外力(外力偶)作用下产生的静位移(静角位移)来求一般单自由度系统微幅自由振动固有频率的方法,且通过实例分析,说明此方法简洁有效,可用于理论力学教学的补充。

In this paper,based on determining natural frequency of the free vibration for mass-spring system with static displacement method,a new method of obtaining the natural frequency was developed,with which the static displacement(or static angle displacement) generated by the external force(external force couple) is further derived to obtain the natural frequency of small amplitude free vibration,within the general single-degree-of-freedom system.Via example demonstration,the method is then proved to be effective,simple and can be used to supplement the teaching of theoretical mechanics.