Time-Periodic Stiffness Modulation in Elastic Metamaterials for Selective Wave Filtering: Theory and Experiment.

Elastic waveguides with time-modulated stiffness feature a frequency-periodic dispersion spectrum, where branches merge at multiple integers of half the modulation frequency and over a finite wave number range. In this range, frequency becomes complex, with its real part remaining constant. The vanishing group velocity associated with these flat bands leads to frequency-selective reflection at an interface between a nonmodulated medium and a time-modulated one, which converts a broadband input into a narrow-band output centered at the half modulation frequency. This behavior is illustrated in an elastic waveguide in transverse motion, where modulation is implemented experimentally by an array of piezoelectric patches shunted through a negative electrical capacitance controlled by a switching circuit. The switching schedule defines the modulation frequency and allows the selection of the output frequency. This implementation is suitable for the investigation of numerous properties of time-space modulated elastic metamaterials, such as nonreciprocity and one-way propagation, and can lead to the implementation of novel functionalities for acoustic wave devices operating on piezoelectric substrates.