Free and forced vibration of repetitive structures

In this paper, the vibration problems of some repetitive structures, including symmetric, cyclic periodic, linear periodic, chain, and axi-symmetric structures is investigated. Eigen-value problems derived from the vibration equations of these structures are established based on their continuous models. The special properties of the structural modes of these structures are deduced. Applying these properties can provide effective reduction approach to solving the natural and forced vibration problems of these structures by either numerical or experimental methods. Furthermore, these properties can be applied in other aspects such as evaluating the reasonableness of the discrete models of these repetitive structures.