Canonical forms and rotationally repetitive matrices for eigensolution of symmetric structures

In this paper, all canonical forms that exist in the literature for bilateral symmetry are derived from the formula for rotationally repetitive structures (systems) considering the rotation angle as 180 degrees. Different nodal numberings lead to different patterns for matrices associated with bilaterally symmetric structures. This study shows that all these forms are of the same nature and can be considered as particular forms of circulant matrices associated with rotationally repetitive structures. Simply put, some numerical examples are investigated using both the classic approach and the canonical forms.