Non-Hermitian elastodynamics in gyro-odd continuum media

Abstract Linear elasticity has long been considered a well-established research area using conservative field theory. However, the discovery of odd-elasticity challenges essential energy conservation assumption, which together with gyroscopic ingredients compromise fundamental theory elasticity, but to same effect, enable new directions in active elastodynamics. Here, we consider two-dimensional continuum mechanics more general framework containing constituents from both and odd-elastic effects, gives rise non-reciprocal non-Hermitian elastic waves highly unconventional guise. We discuss how these unusual media can extract engine cycles comprising remarkable features stability transitions, exchange process reverses. Beyond bulk waves, akin unidirectional characteristics 2D quantum-Hall insulator, demonstrate existence Rayleigh surface which, contrast classical ones passive solids, display one-way interference-free transport characteristics, even remain resilient finite sharp or curved geometries. The findings reported here may provide possibilities manipulate ways.