Enhanced sensitivity and wave-structure interaction in nonsingular flat-band lattices with compact localized states

Abstract

This paper investigates the dynamics of compact localized modes in one-dimensional flat-band elastic lattices. Flat dispersion arises from destructive interference between neighboring elements, resulting in a zero group velocity across all momenta. This unique condition enables the formation of wave modes that are not only highly localized in space and inherently non-propagative – protected by the flatness of the dispersion relation – but also exceptionally sensitive to structural variations due to enhanced wave-structure interaction. These features are first explored on a simple spring–mass lattice and later applied to a microelectromechanical (MEMS) system of oscillators. By exploring the role of flat-band dispersion in mechanics, this work provides new insights into their fundamental dynamics while opening new opportunities for applications in vibration control and the sensitivity analysis of mechanical structures.