Analysis of repetitive and near-repetitive structures by transformation to equivalent circulant structures

Abstract

Purpose There are many structures that have a repetitive pattern. If a relationship can be established between a repetitive structure and a circulant structure, then the repetitive structure can be analyzed by using the properties of the corresponding circulant structure. The purpose of this paper is to develop such a transformation. Design/methodology/approach A circulant matrix has certain properties that can be used to reduce the complexity of the analysis. In this paper, repetitive and near-repetitive structures are transformed to circulant structures by adding and/or eliminating some elements of the structure. Numerical examples are provided to show the efficiency of the present method. Findings A transformation is established between a repetitive structure and a circulant structure, and the analysis of the repetitive structure is performed by using the properties of the corresponding circulant structure. Originality/value Repetitive and near-repetitive structures are transformed to circulant structures, and the complexity of the analysis of the former structures is reduced by analyzing the latter structures.

Matrix Analysis of Repetitive Circulant Structures: New-block and Near Block Matrices

“…Also they presented various types of circulant structures. Some irregular structures were analyzed by applying modifications [9,10]. Static, modal analysis and free vibration of structures with some repetitive patterns have been studied [11], also some structures with different patterns are introduced.…”