DYNAMICS OF NONLINEAR CYCLIC SYSTEMS WITH STRUCTURAL IRREGULARITY

The dynamics of weakly coupled, nonlinear cyclic assemblies are invest igated in the presence of weak structural mistuning. The method of mul tiple scales is used to obtain a set of nonlinear algebraic equations which govern the steady-state, synchronous ('modal-like') motions for the structures. Considering a degenerate assembly of uncoupled oscilla tors, spatially localized modes are computed corresponding to motions during which vibrational energy is spatially confined to one oscillato r (strong localization) or a subset of oscillators (weak localization) . In the limit of weak substructural coupling, asymptotic solutions ar e obtained which correspond to (i) spatially extended, (ii) strongly l ocalized, and (iii) weakly localized modes for fully coupled systems. Throughout the analysis, the influence of structural mistunings on the resulting solutions are discussed. Additionally, numerical solutions (including linearized stability characteristics) are obtained for prot otypical two-and three-degree-of-freedom (DoF) systems with various st ructural mistunings. The numerical results provide insight into the st rong influence of structural irregularities on the dynamical behavior of nonlinear cyclic systems, and demonstrate that the combined influen ces of structural mistunings and nonlinearities do not lead to uniform improvement of motion confinement characteristics.