Extreme Localization via a Singular Edge Mode in an Asymmetric Linkage System
Abstract
Mechanical localized modes generally retain exponentially decaying tails, whereas confinement to a single structural unit is difficult to achieve without resonators, flat-band lattices or topological design. To address this need, an asymmetric linkage system is introduced in which geometry tunes a boundary mode from finite localization to its extreme limit. Each cell comprises two unequal rigid bars connected by a torsional spring and is described by one generalized coordinate. Linearization and coordinate transformation yield a tridiagonal model and closed-form expressions for the edge mode frequency and spatial decay ratio. The analysis identifies the configurations supporting a singular edge mode at which its decay ratio vanishes, leaving only the boundary cell active in the linear regime. Simulations show near-complete localization under finite-amplitude excitation, and experiments reproduce the configuration-dependent transition from bulk transmission to boundary confinement. These results establish a minimal and analytically tunable platform for mechanical localization
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BibTeX
@misc{joo2026extreme,
title = {{Extreme Localization via a Singular Edge Mode in an Asymmetric Linkage System}},
author = {Myeonggyun Joo and Dongwook Kwak and Rajesh Chaunsali and Panayotis G. Kevrekidis and Jinkyu Yang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15041},
eprint = {2610.15041},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15041},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Extreme Localization via a Singular Edge Mode in an Asymmetric Linkage System
AU - Myeonggyun Joo
AU - Dongwook Kwak
AU - Rajesh Chaunsali
AU - Panayotis G. Kevrekidis
AU - Jinkyu Yang
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.15041
UR - https://arxiv.org/abs/2610.15041
AB - Mechanical localized modes generally retain exponentially decaying tails, whereas confinement to a single structural unit is difficult to achieve without resonators, flat-band lattices or topological design. To address this need, an asymmetric linkage system is introduced in which geometry tunes a boundary mode from finite localization to its extreme limit. Each cell comprises two unequal rigid bars connected by a torsional spring and is described by one generalized coordinate. Linearization and coordinate transformation yield a tridiagonal model and closed-form expressions for the edge mode frequency and spatial decay ratio. The analysis identifies the configurations supporting a singular edge mode at which its decay ratio vanishes, leaving only the boundary cell active in the linear regime. Simulations show near-complete localization under finite-amplitude excitation, and experiments reproduce the configuration-dependent transition from bulk transmission to boundary confinement. These results establish a minimal and analytically tunable platform for mechanical localization
ER -