Green’s Function Approach to Model Vibrations of Metamaterials with Spatiotemporally Modulated Properties

Acoustic and elastic metamaterials with space- and time-dependent material properties have received great attention recently as a means to realize systems that are not linear-time-invariant, usually with the goal to induce nonreciprocal wave propagation. However, for finite systems the set of modulation parameters that yield a strong mode-coupling response is not well characterized. In this work, we derive the Green’s function for finite elastic beams with spatiotemporally-modulated material properties. We show for the particular case of flexural wave modes in a thin finite beam that spatiotemporal modulation of the Young’s modulus can lead to the splitting and shifting of the resonances of the system.