Manipulation of non-Hermitian skin effect in elastic media

Non-Hermitian skin effects, rooted in non-trivial point-gap topologies, have been widely demonstrated in systems with discrete nonreciprocal hoppings, yet their physical realization and manipulation in continuous elastic media remain largely unexplored. Here, we establish a framework for manipulating the non-Hermitian skin effect in 2D linear elastic solids exhibiting Parity-Time ($\mathcal{PT}$) symmetry. The elastic solid is equipped with two active non-Hermitian controls: active body forces that break parity-inversion symmetry and generate point-gap topology, giving rise to higher-order skin modes, and active stress tractions applied at the boundary that preserve parity-inversion symmetry and counteract eigenmode localization. We demonstrate that the interplay between these two controls enables continuous tuning of the eigenmode localization, allowing active steering, funneling, and on-demand suppression of the non-Hermitian skin effect -- all while preserving the intrinsic non-Hermiticity and the underlying point-gap topology of the elastic solid. We further reveal unconventional extended skin modes, such as \textit{extended diagonal skin modes}, which feature coexisting corner-localized and bulk-extended states -- arising from complementary mechanisms introduced by the active stress tractions at the solid boundary. These results establish a physically grounded framework for steering and reshaping non-Hermitian skin effects in continuous elastic media, opening new avenues for programmable topological mechanical metamaterials with spatially controlled wave localization and energy transport.