MULTIPLE-EIGENVALUES ARISING FROM A CLASS OF REPETITIVE SUBSTRUCTURES

The dynamic substructure method in state space was employed to study e igenvalue problems for structures with a class of repetitive substruct ures, which share a common interface. The block properties of the resu lting synthesized system matrices are discussed. A very interesting re sult on multiple eigenvalues of the considered structures was obtained : each fixed interface eigenvalue of the single repetitive substructur e appeared as at least (n - alpha) multiple eigenvalues of the whole s tructure, where n is the number of repetitive substructures; alpha is a number depending on the azimuth distributions of the repetitive subs tructures. It takes at most nine, and it takes three in the special ca ses when the repetitive substructures are oriented by rotation around a fixed axis. The mode shapes associated with the (n - alpha) multiple eigenvalues were obtained and the nondefectiveness of the obtained mu ltiple eigenvalues is discussed. Physical explanation and numerical ex amples were also attempted and are given.