Electrically controllable behaviors in defective phononic crystals with inductive-resistive circuits

Research in defective phononic crystals (PnCs) has garnered increasing interest for their unique properties of energy localization and bandpass filtering. Despite their utility, conventional defective PnCs suffer from a fixed defect band, limiting adaptability in scenarios requiring frequency adjustments. Addressing this limitation, this study proposes a novel approach—integrating inductive-resistive circuits into defective PnCs—to introduce electrically controllable defect bands. Key findings include the emergence of additional defect bands through electrical resonance in inductive and inductive-resistive circuits. Notably, the phenomenon of defect-band splitting is newly observed when mechanical and electrical resonance frequencies align. An essential observation is the superiority of inductive circuits in maximizing transmittance efficiency. Conversely, resistive or inductive-resistive circuits exhibit limitations, such as rapid transmittance decrease. The significance of this work lies in two main contributions. First, it presents a pioneering approach to build a bridge between inductive-resistive circuits and defective PnCs, offering tunable narrow bandpass filters to users. Second, this study offers a comprehensive guideline for selecting optimal electrical circuit configurations to maximize transmittance. These endeavors aim to advance the field of tunable energy-localized behaviors in defective PnCs, opening up new avenues for future research and practical applications, such as enhancing ultrasonic sensors and actuators for structural health monitoring and medical imaging.