Modal dynamics of boundary-interior coupled structures. Part 1: A general approach using components Green’s function

Abstract

In Part 1 of this series papers (Part 1 & Part 2 (Guo and Rega, 2020) [1]), a general operator-based boundary analysis approach is proposed for free vibrations of coupled structural systems, with the new coupled modal frequencies and modal shapes being directly extracted in a systematic manner from the uncoupled components Green’s functions. Therefore, ad-hoc re-modelling of the whole augmented structural system is avoided. It turns out that a hybrid decomposition of the original coupled system into two sub-problems at the coupling interface, i.e., one excited kinematically at the boundary and the other excited by an interaction force in its interior domain, is of vital importance. Using general operator arguments and reciprocity-based operator equality, the dynamic coupling is imposed by combining the boundary kinematic effects and interaction force effects. The orthogonality of the coupled modal shapes is further established (and in Part 2 (Guo and Rega, 2020) [1] a general full interpretation of mode localization phenomenon will be presented). Finally, two coupled structural systems, i.e., string-oscillator and string-beam, are attacked by this operator formulation as examples, with coupled frequencies/modal shapes being obtained in a systematic way.