Spatiotemporal modulations in acoustics: From nonreciprocity to mechanical computing

Spatially graded materials have been a cornerstone of acoustic metamaterials for decades, enabling wave manipulation across different length scales. Likewise, structures with time-varying material properties have gained traction in wave filtering applications. Put together, systems exhibiting concurrent spatial and temporal modulations of one or more parameters (e.g., stiffness or phase) can unlock an array of new features ranging from nonreciprocal propagation to frequency-dependent wave beaming. In this talk, we will introduce the notion of dynamic phase gradients, i.e., a spatial phase shift between neighboring elements (of a metasurface) or transducers (of a phased array) which also varies in time. Through theory and experiments, we will demonstrate that the resultant systems are capable of (a) generating multiple scattered harmonics of a single input which simultaneously propagate in different directional lanes, each carrying a unique frequency footprint, and (b) exhibiting non-identical beaming patterns in transmission and reception by breaking time invariance. We will present an application of this concept in the development of a mechanical neural network via reconfigurable elastic metasurfaces, designed to perform a computational task. Since the frequency channels of a spatiotemporally-modulated metasurface are independently tunable, they can be assigned distinct tasks, thus allowing parallel operations in mechanical computing systems.