Document Type: Research Paper
For a symmetric structure the degrees of freedom (DOFs) in two sides of the axis of
symmetry can be either symmetric or anti-symmetric. If there is no active DOF on the axis of
symmetry, then we will have the Form II symmetry for the structural matrices, and alternatively if
we have some active DOFs on the axis, we will have Form III symmetry. These forms are already
developed and employed in structural dynamics and stability analysis of frame structures.
However, for the structures having both symmetric DOFs and anti-symmetric DOFs,
simultaneously, we will have different canonical forms, defined in this paper as the Form A and
Form B symmetry. Thus the main objective is to develop these forms and explore the governing
relationships. The presented method is then applied to the analysis of symmetric structures.