Bandgap prediction of single cantilever beam piezoelectric phononic crystals

Piezoelectric phononic crystals (PPCs) exhibit effective control over elastic wave bandgaps, demonstrating applicability in resolving vehicle low-frequency vibration and piezoelectric energy harvesting issues. Targeted modulation of bandgaps constitutes a key research focus in PPCs. Under scenarios involving rapid variations in target frequencies, fast and accurate prediction of bandgap characteristics is critically significant for achieving targeted modulation of bandgaps. This paper proposes a bandgap prediction method for single cantilever beam PPCs, which quantitatively characterizes the characteristic frequencies of the bandgap using calculation formulas. This method enables rapid acquisition of bandgap characteristics through structural parameters of PPCs, significantly enhancing targeted modulation efficiency during rapid target frequency variations. The bandgap calculation method based on plane wave expansion method and the equivalent elastic modulus calculation method for piezoelectric patches based on the long-wave approximation are first briefly described. Subsequently, an equivalent dynamic stiffness calculation method considering bending moments is proposed. Then a bandgap prediction model specific to single cantilever beam PPCs is developed, and a method is proposed for calculating proximity factors through analyzing the impact of material and dimensional parameters on them. Finally, the effectiveness of the bandgap prediction method is verified by simulation and experiment.