Low-threshold subharmonic generation in composites structures with Cantor-like code

We show experimental evidence of extremely low thresholds for subharmonic generation of ultrasonic waves in one-dimensional artificial piezoelectric plates with Cantor-like structure, as compared to the corresponding homogeneous periodic plates. The origin of this apparent anomaly is theoretically investigated by studying anharmonic coupling between normal modes. We demonstrate that the large enhancement of nonlinear interaction results from the more favorable frequency and spatial matching of coupled modes (fractons and phonons) in the Cantor-like structure, with no need to invoke anomalous modifications of the nonlinear elastic constants.