Nonlinear mode localization in boundary–interior coupled structures by an asymptotic approach

Abstract

Boundary–interior coupled structures are an important class of complex combined structural systems, with one component kinematically excited at its boundary and the other excited by a coupling force in its interior domain. Nonlinear mode localization of boundary–interior coupled structures is fully investigated in this paper, with a general asymptotic formulation being developed for construction of localized/global/hybrid nonlinear normal modes (NNMs), leading to a nonlinear interpretation of mode localization in boundary–interior​ structures. It is found that localized and global NNMs are induced at the same time as NNMs pairs, if the linear component frequencies are away from each other, while four non-trivial hybrid NNMs associated with two different nonlinear frequencies are produced, if the linear component frequencies are close to each other. Furthermore, the general asymptotic procedure is applied to a beam–beam coupled system with cubic nonlinearity, and various localized/global/hybrid NNMs are explicitly constructed.