An efficient seismic analysis of regular skeletal structures via graph product rules and canonical forms

  • Kaveh, A. (Centre of Excellence for Fundamental Studies in Structural Engineering, School of Civil Engineering, Iran University of Science and Technology) ;
  • Zakian, P. (Centre of Excellence for Fundamental Studies in Structural Engineering, School of Civil Engineering, Iran University of Science and Technology)
  • Received : 2015.06.02
  • Accepted : 2015.10.28
  • Published : 2016.01.25


In this study, graph product rules are applied to the dynamic analysis of regular skeletal structures. Graph product rules have recently been utilized in structural mechanics as a powerful tool for eigensolution of symmetric and regular skeletal structures. A structure is called regular if its model is a graph product. In the first part of this paper, the formulation of time history dynamic analysis of regular structures under seismic excitation is derived using graph product rules. This formulation can generally be utilized for efficient linear elastic dynamic analysis using vibration modes. The second part comprises of random vibration analysis of regular skeletal structures via canonical forms and closed-form eigensolution of matrices containing special patterns for symmetric structures. In this part, the formulations are developed for dynamic analysis of structures subjected to random seismic excitation in frequency domain. In all the proposed methods, eigensolution of the problems is achieved with less computational effort due to incorporating graph product rules and canonical forms for symmetric and cyclically symmetric structures.


seismic analysis;regular skeletal structures;graph product rules;canonical forms


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