José R. F. Arruda | Searcharxiv

arXiv2026

Comparing Spatially Periodic Feedback and Space-Time Modulation for Unidirectional Wave Propagation in a 1D Mass-Spring-Damper System

Unidirectional wave propagation has emerged as a key concept in the dynamics of non-reciprocal mechanical and acoustic metamaterials. This work investigates two fundamentally distinct strategies for achieving directional wave propagation in a periodic one-dimensional mass-spring-damper lumped system: space-time modulation and spatially periodic feedback. In the first approach, the stiffness is modulated periodically in both space and time. The resulting space-time periodic system is analyzed using a Plane Wave Expansion (PWE) formulation based on the Bloch-Floquet theory to obtain the dispersion relation. The traveling modulation produces asymmetric dispersion diagrams and directional band gaps, within which elastic waves propagate preferentially in a single direction due to broken time-reversal symmetry. In the second approach, non-reciprocity is introduced through a spatially periodic feedback action. The force can depend on the displacement and/or its derivatives, such as velocity or acceleration, and is applied to the masses along the system. The lumped system with a finite number of unit cells is modeled using classical mechanics principles, yielding a state-space model of the system. The active mechanism can generate directional amplification or attenuation via the non-Hermitian skin effect (NHSE), characterized by boundary-localized modes identified by a topological invariant, the winding number. The stability of the space-time periodic system is assessed through the Lyapunov-Floquet theory. In the periodic feedback case, stability is investigated using the eigenvalues of the state matrix. These results provide design guidelines for directional wave propagation in elastic waveguides.

physics.app-ph↗

arXiv2018

Edge states and topological pumping in elastic lattices with periodically modulated coupling

We investigate the dispersion topology of elastic lattices characterized by spatial stiffness modulation. The modulation is defined by the sampling of a two-dimensional surface, which provides the lattices with topological properties that are usually attributed to two-dimensional crystals. We show that the cyclic variation of the phase of the stiffness modulation leads to a Berry phase accumulation for the Bloch eigenmodes, which is characterized by integer valued Chern numbers for the bands and associated gap labels. The resulting non-trivial gaps are spanned by edge modes localized at one of the boundaries of the considered 1D lattices. The edge mode location is governed by the phase of the stiffness distribution, whose spatial modulation drives these modes to transition from one edge to the other, through a bulk state that occurs when the corresponding dispersion branch touches the bulk bands. This property enables the implementation of a topological pump that is obtained by stacking and coupling a family of modulated 1D lattices along a second spatial dimension. The gradual variation of the stiffness phase modulation drives the adiabatic transition of the edge states, which transition from their localized state at one boundary, to a bulk mode and, finally, to another localized state at the opposite boundary. Similar effects were illustrated under the assumption of quasiperiodic modulation of the lattice interactions. We here demonstrate that a topological pump can be achieved also in periodic media, and illustrate this for the first time in elastic discrete lattices.

cond-mat.mes-hall↗