求解杆系结构自由振动问题的力法

杆系结构的静力分析有两类方法——力法和位移法,而自由振动分析却仅有位移法。针对这一缺失,提出杆系结构自由振动的力法分析方法。通过放松某个位移约束并施加相应的动内力来建立力法的基本体系。当动内力的频率等于结构自振频率时被放松的约束位移重新得到满足,此时基本体系与原结构等价,由此建立力法的控制方程。该控制方程为频率的非线性方程,对该方程的求解建立了Newton法的迭代格式。数值算例表明该法是一个精确、高效、实用的方法。

FORCE METHOD FOR FREE VIBRATION PROBLEMS OF FRAMED STRUCTURES

There are two major methods in the static analysis of framed structures, i.e. the displacement method and the force method. But only the displacement method is available in free vibration analysis. This paper presents a force method for the free vibration analysis of framed structures. The primary system is established by releasing one of the displacement constraints with the corresponding internal force exposed. The released constraint is satisfied when the trial frequency equals to any of the original structure’s free vibration frequencies. Thus the nonlinear governing equation can be established. The Newton iteration procedure will be set up for solving this nonlinear equation. Typical numerical examples are presented to show the validity, applicability, accuracy and efficiency of the proposed method.