Decomposition of symmetric mass–spring vibrating systems using groups, graphs and linear algebra

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The main objective of this article is to develop a methodology for an efficient calculation of the eigenvalues for symmetric mass–spring systems in order to reduce the size of the eigenproblem involved. This is achieved using group‐theoretical method, whereby the model of a symmetric mass–spring system is decomposed into appropriate submodels. The eigenvalues of the entire system is then obtained by calculating the eigenvalues of its submodels. The results are compared to those of the existing methods based on graph theory and linear algebra. Examples are provided to illustrate the simplicity and efficiency of the present method.