Twisting Kelvin Cells for Enhanced Vibration Control

TL;DR

This paper explores how twisting Kelvin-cell lattices alters wave propagation, enabling enhanced vibration control through symmetry-breaking geometric modifications that activate multiple attenuation mechanisms.

Contribution

It introduces a novel twisting approach to Kelvin-cell lattices that preserves topology while enabling tunable wave filtering without added mass or resonators.

Findings

Twisting induces both Bragg and polarization-dependent band gaps.

Wave attenuation up to 20 dB was experimentally validated.

Material viscoelasticity significantly affects wave propagation predictions.

Abstract

This work investigates the propagation of elastic waves in periodic Kelvin-cell chains, focusing on symmetry-breaking geometric modifications induced by twisting the cell's faces. By imposing such twists, the original lattice topology is preserved, while mirror symmetries are strategically broken through modifying a single geometric parameter, allowing wave characteristics to be adjusted without additional resonators or mass augmentation. The complex-valued Bloch-Floquet analysis reveals that twisting activates two distinct wave attenuation mechanisms: Bragg-type band gaps associated with periodicity-induced scattering, and polarization-dependent band gaps arising from longitudinal-torsional mode coupling and avoided crossings. To obtain qualitative and quantitative insight into these mechanisms, a simplified analytical model with coupled translational and rotational degrees of freedom is considered. The finite-element wave transmission calculations are experimentally validated on SLA-printed three-cell specimens, for which wave attenuation reaches up to 20 dB within the predicted band-gap frequencies. Note that high prediction accuracy requires accounting for viscoelastic material behavior, underscoring the importance of material behavior on the wave propagation characteristics. Overall, the findings show that modest geometric modifications to a classical Kelvin-cell lattice can enhance wave-filtering behavior, offering a tractable design strategy for vibration control in lightweight architected lattices.