Eigenfrequencies of symmetric planar trusses via weighted graph symmetry and new canonical forms

Abstract

Purpose

The purpose of this paper is to describe how the method recently developed for mass‐spring systems and frame structures is modified to include the free vibration of trusses.

Design/methodology/approach

Here, two methods are presented for calculating the eigenfrequencies of structures. The first approach is graph theoretical and uses graph symmetry. The graph models are decomposed into submodels and healing processes are employed such that the union of the eigenvalues of the healed submodels contain the eigenvalues of the entire model. The second method has an algebraic nature and uses special canonical forms. The present method is illustrated through three simple examples with odd and even number of bays.

Findings

The inter‐relation for the mechanical properties of elements is established using new weighted graphs, enabling easy calculation of the eigenvalues involved. Two methods are presented for calculating the eigenfrequencies of the truss structures.

Originality/value

Symmetry is used for easy calculation of the eigenfrequencies of structures.

Citation

Kaveh, A. and Shahryari, L. (2010), "Eigenfrequencies of symmetric planar trusses via weighted graph symmetry and new canonical forms", Engineering Computations, Vol. 27 No. 3, pp. 409-439. https://doi.org/10.1108/02644401011029952