Strong–weak modal coupling in finite structures with antinode-concentrated resonators

Dynamic vibration absorbers (DVAs) and locally resonant metamaterials share a common physical foundation: subwavelength resonators coupled to a host structure. The two paradigms, however, have developed along parallel lines. DVA design on continuum hosts traditionally proceeds mode by mode, relying on modal truncation and iterative tuning. Metamaterial design rests on Bloch analysis of infinite periodic arrays, whose assumptions do not transfer to bounded structures with a finite number of resonators. As a result, neither paradigm captures the host–resonator interaction in such finite systems within a single governing relation. In this work, a unified modal-domain framework is proposed for bounded continuum hosts equipped with a finite number of antinode-concentrated resonators. The host and attachment coordinates are condensed into an Attachment Condensed Characteristic Equation (ACCE), whose global determinant retains the coupling between the target-mode direction and its residual complement. Reduced strong and residual equations identify modal origin and become independent characteristic equations only under explicitly stated invariance conditions. Within this framework, a strong–weak mode-coupling mechanism is identified. Target-mode splitting bounds a broad finite-structure response-reduction interval, while S − 1 resonator-origin modes may remain as clustered peaks inside it. The analysis also distinguishes shifted non-target host modes from exact dark and weakly coupled modes. One-dimensional finite-element calculations, three-dimensional simulations, and beam experiments reproduce the principal spectral trends. A reciprocal force–moment extension further demonstrates a feasible mechanism for the experimentally observed downward shift of the clustered-mode center, without treating its effective eccentricity as an independently identified physical parameter.