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.