Dynamic phononic crystals with spatially and temporally modulated circuit networks

Elastic wave mitigation covering multiple broad bands is highly demanded for modern applications in wave control. Here, we report both theoretically and experimentally on the complete investigation of a series of dynamic phononic crystal beams integrated with circuit networks decorated with both spatial and temporal modulation. They are capable of practicing multi-band flexural wave mitigation with convenient tunability and broadband operability. The electromechanical interaction through piezoelectric shunts allows for energy exchange between electrical and mechanical modes and gives rise to Bragg forbidden bands. The key contribution of this work lies in the inclusion of spatial and temporal modulation that is applied solely in circuit networks and improves wave mitigation abilities in terms of operable frequency range. Specifically, the spatial modulation of circuit network effectively broadens the wave attenuation band by creating space-Bragg forbidden bands for electrical modes and thus extending the electromechanical coupling range. The temporal modulation, on the other hand, generates time-Bragg band gaps by linearly translating the fundamental electromechanical mode in terms of frequency. More importantly, both seemingly complicated approaches are simply based on the convenient tuning of a single resistor in the circuit network. This advantage later facilitates the experimental evidences of the transmission characteristics of the spatially and temporally modulated configurations. We believe the dynamic phononic crystals are highly promising for the next-generation applications such as tunable multi-band filters.