Dynamics of time-varying elastic metamaterials

Abstract

This talk explores the fascinating dynamics of elastic metamaterials under time-varying modulation, shedding light on the transformation of both standing and wave modes. In the first part, the focus is on standing mode transformations in topological and nontopological structures driven by slow and fast time modulation. The critical role of modulation velocity in enabling edge-to-edge energy transfer is highlighted, with the transition between successful and unsuccessful transformations explained using the adiabatic theorem. These ideas are discussed through numerical simulations of spring-mass lattices and experimental demonstrations on time-varying electromechanical beams. The second part is instead focused on wave mode transformations in time-modulated systems, where intriguing phenomena such as frequency conversion, wave steering, trapping, and mode conversion take center stage. These effects are illustrated with examples from spring-mass lattices and elastic half-planes. The talk wraps up with early steps toward implementing these concepts in micro-electromechanical systems.