In many technical applications (like those in automotive engineering or in structural mechanics) the mechanical system studied can be considered composed by two or many identical subsystems or parts. These kind of symmetries of the structure can be used in order to simplify the analysis of the vibrations and permit to reduce the dimension of the differential equations that describe the motion. In the paper we proof that in case of such technical systems with elastic elements composed of two identical subsystems, the eigenvalues of the subsystems associated to the identical parts are eigenvalues of the whole structure as well. The demonstrated property allows the simplification of the calculation of the problem of eigenvectors and eigenvalues for this kind of structure.
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