Vibration mode localization in two-dimensional systems with multiple substructural modes

Free vibration mode localization in randomly disordered weakly coupled two-dimensional cantilever-mesh-spring arrays, in which S substructural modes are considered for each cantilever, is studied in this paper. A method of regular perturbation is applied to determine the localization factors, which are defined in terms of the angles of orientation and characterize the average exponential rates of growth or decay of the amplitudes of vibration. Iterative formulations are derived to determine the amplitudes of vibration of the cantilevers. In the diagonal directions, a transfer matrix formulation is obtained. The localization behaviour of the system in the diagonal directions is similar to that of a one-dimensional cantilever-spring array with multiple substructural modes. Applicability of the single-substructural-mode and two-substructural-modes approximations is investigated.