Modal dynamics of boundary-interior coupled structures. Part 2: An asymptotic interpretation of mode localization

This Part 2 (continued from Part 1 [1]) focuses on mode localization phenomenon in boundary-interior coupled structures, aiming to establish an asymptotic interpretation based upon the general operator formulation given in Part 1, i.e., without referring to particular structure types. It is found that a large mass ratio of combined components is the key condition causing generic mode localization in the essential coupling domain (with uncoupled component frequencies being not too distant). Three different coupled modes closely related with mode location, i.e., local/global modes (with energy localized in one component) and hybrid modes (with energy distributed over the combined structure), are first predicted qualitatively by employing a proper ordering analysis of the frequency nonlinear equation and the explicit modal shapes (derived in Part 1 [1]). Then they are refined through a detailed multi-scale expansion/construction in a quantitative manner, leading to a general asymptotic interpretation of mode localization phenomenon in the boundary-interior coupled structures. Briefly, the main conclusion is that a large mass ratio will lead to local and global modes, if the coupled frequency approaches the component’s uncoupled frequency, and in particular, if the two component frequencies are themselves very close to each other, two hybrid modes will be induced for a large mass ratio.