Temporal refraction and reflection in time-modulated mechanical metabeams: theory and physical observation

The wave reflection and refraction in time-varying media challenge traditional conservation laws in those in space-varying media. This study presents the first experimental demonstration of the refraction and reflection of flexural waves across a temporal boundary in a continuum-based mechanical metabeam. The temporal metabeam comprises an elastic beam attached to an array of piezoelectric patches connected to the time-varying transfer function. Frequency conversions in refraction and reflection are physically observed in the time-modulated elastic metabeam with a single temporal interface. These results are well interpreted using formulated temporal Snell's law and Fresnel's equations for temporal interfaces. Further, we illustrate the manipulation of amplitude and frequency spectra of flexural wave refraction and reflection through multi-stepped temporal interfaces. Finally, by implementing the smooth time-varying transfer function, we numerically and experimentally demonstrate the capabilities of the temporal metabeam for smart waveform morphing and information coding. Our findings lay the foundation for developing time-mechanical metamaterials and time-phononic crystals, offering new avenues for advanced phonon manipulation in both wave amplitude and frequency.