canonical forms and rotationally repetitive matrices for eigensolution of symmetric structures

In this paper, symmetry of graph models (structures) is investigated. all canonical forms previously derived in literature for bilateral symmetry are derived from the formula for rotationally repetitive structures (systems) considering the angle of rotation as 180 degrees. different nodal numberings result in different patterns for matrices associated with bilaterally symmetric structures. in this study, it is shown that all these forms have the same nature and can be considered as particular forms of circulant matrices associated with rotationally repetitive structures. in order to clarify this point, some numerical examples are investigated using both the classic approach and the canonical forms.