On time-dependence of mechanical metamaterials properties

The study focuses on wave propagation in time-periodic mechanical matamaterials, such as beams with time-modulated elastic modulus. The time-dependence of the elastic modulus results in a system with a frequency-periodic dispersion diagram. Flat bands originate at the intersections of the dispersion branches, signaling zero group velocity modes. Through an analytic approach, we obtain approximate expressions for the range of wavenumbers associated to flat bands, as well as their dependence on the modulation parameters. It is shown that the flat bands lead to unbounded growth of the displacement field, which is due to the interaction between the structure’s dynamics and the energy provided to it by means of the elastic modulus variation. If such phenomenon is properly confined over a limited time window, it provides a way to filter wave propagation over a ultra-wide frequency range by property choosing the modulation parameters. Numerical simulations, obtained by implementing a FDTD scheme, verify the theoretical findings. Finally, an experimental validation of the results is discussed, which employs piezoelectric patches and time-dependent negative capacitance shunted circuits.