Eigenfrequencies of symmetric planar frames with semi-rigid joints using weighted graphs

The main aim of this paper is to extend the recently developed methods for calculating the free vibration analysis of planar symmetric frames to include the effect of semi-rigidity of the joints. This is achieved by decomposing a symmetric weighted graph model into two submodels and using canonical forms in such a manner that the union of the eigenvalues of the submodels result in the eigenvalues of the entire model. Thus the eigenfrequencies of the frame is obtained in an efficient manner. Here, only the free vibration of frames with linear behavior is studied.