Abstract
A computational method for calculating the exact eigenvalues of partially rotationally periodic structures is presented, where the eigenvalues are the natural frequencies of undamped free vibration analysis or the critical load factors of buckling problems. In particular, the method can be used to find efficiently the eigenvalues of the following structural systems: (1) rotationally periodic structures with arbitrary boundary conditions; (2) rotationally periodic substructures which can be connected in any required way and at any number of connecting nodes to an arbitrary parent structure. The stiffness matrix method of structural analysis is used and an existing algorithm is employed to ensure that no eigenvalues are missed. The successful combination of this algorithm with harmonic analysis and substructuring techniques makes the method presented very efficient. Finally, several non-trivial examples are given.
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