Evolution of tunable phononic frequency combs via three-mode interaction in curved piezoelectric micromachined ultrasonic transducers.

Phononic frequency combs are the mechanical counterparts of optical frequency combs, representing a pivotal progression in nonlinear studies of micro-electromechanical systems. This work presents the generation of tunable frequency combs based on three-mode interaction through combination internal resonance and a ferroelectric thin film in curved piezoelectric micromachined ultrasonic transducer. The experimental results demonstrate rich three-mode coupled nonlinear dynamics and how this coupling leads to frequency comb generation under specific input actuation parameters. The comb spacing and the number of spectral lines can be tuned by modulating the applied DC voltage, as well as the AC input voltage and frequency. Unlike previous studies on three-mode comb analysis, a theoretical model is systematically developed using nonlinear von Kármán plate theory to elucidate the experimentally observed dynamics of nonlinear three-mode intermodal coupling through combination internal resonance and its role in comb generation. Our findings demonstrate resonance coupling between the first and third asymmetric modes and the second symmetric modes, underscoring the generation of tunable multimode phononic frequency combs. This advancement paves the way for further progress in nonlinear phononics, enabling diverse applications in sensors, acoustic imaging, and phonon computation.