TY - JOUR ID - 22071 TI - Canonical forms and rotationally repetitive matrices for eigensolution of symmetric structures JO - Scientia Iranica JA - SCI LA - en SN - 1026-3098 AU - Kaveh, A. AU - Rahmani, P. AD - School of Civil Engineering, Iran University of Science and Technology, Narmak, Tehran-16, Iran Y1 - 2021 PY - 2021 VL - 28 IS - 1 SP - 192 EP - 208 KW - canonical forms of matrices KW - graphs KW - regular structures KW - Eigenvalues KW - Laplacian KW - bilateral symmetric systems KW - rotationally repetitive (circulant) matrices KW - dome structures DO - 10.24200/sci.2020.56639.4827 N2 - 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. UR - https://scientiairanica.sharif.edu/article_22071.html L1 - https://scientiairanica.sharif.edu/article_22071_ad5577cb11d7a5df2a62a9fe6bd24b88.pdf ER -