Active Metamaterials with Tunable Shear Nonreciprocity and Nonlinear Dynamics.

Actively and smoothly tunable mechanical metamaterials are in high demand for adaptive, variable-stiffness structures in smart machines. However, existing designs are largely restricted to tunable transverse deformation, reciprocal response, and linear dynamics. Here, we propose a novel gear-based design paradigm-using Taiji planar gears and planetary gear assemblies as building blocks-that overcomes these limitations by enabling simultaneous control of translational and torsional stiffnesses, shear nonreciprocity, and programmable nonlinear dynamics. Our metamaterials achieve in situ, continuous tuning of shear stiffness by 30-100×, break reciprocity under positive versus negative loads, and allow the nonreciprocity ratio to be tuned by over 100×. Meta-resonators constructed from these units showcase an application example exhibit broadly tunable transverse and torsional resonant frequencies. Furthermore, we demonstrate that static nonreciprocity serves as a precise control knob for dynamic nonlinearity-a property traditionally fixed and nearly impossible to tune in conventional materials. Analytical models and analyses elucidate the underlying mechanisms and extendable design freedoms. This work bridges the critical gaps in mechanical metamaterials and dynamics, offering a practical pathway to control both linear and nonlinear structural deformations, elastic waves, and vibrations.