Study on bandgap modulation of partially covered cantilever-type piezoelectric phononic crystals

Low-frequency vibration and noise control remain critical challenges in automotive systems, rail transportation, and precision equipment. Cantilever-based piezoelectric phononic crystals (PPCs) exhibit wide bandgaps, strong attenuation, and compact configurations, offering considerable potential for low-frequency vibration suppression. However, conventional fully covered piezoelectric layouts suffer from limited tunability and inefficient material utilization. This study proposes a partially covered cantilever-type PPC and investigates its bandgap characteristics through theoretical modeling, numerical simulation, and experimental validation. An electromechanically coupled model is established based on Timoshenko beam theory and the Precise Integration Method, and the band structure is derived using the Transfer Matrix Method. Finite element simulations demonstrate high accuracy of the proposed formulation in predicting localized resonance bandgaps. Vibration transmissibility experiments conducted on a six-period prototype further confirm the predicted bandgap locations and support the validity of the theoretical model. The influence of different shunt circuit configurations is analyzed, showing that RC circuits effectively suppress electrical resonance and improve bandgap stability. A modulation factor is introduced to quantify tunability, and its dependence on key geometric parameters is examined. The results show that, for the same short-circuit bandgap center frequency of 702 Hz, the partially covered design expands the tunable bandgap range from 615–764 Hz to 589–791 Hz. Consequently, the tuning efficiency is improved by 7.67% while the piezoelectric material usage is reduced by 38.69%. The underlying mechanism is further clarified by showing that the enhanced tunability arises from the competition between electrically induced stiffness modulation and inertia effects, which governs the effectiveness of piezoelectric material distribution. These findings demonstrate enhanced tunability and material utilization efficiency.