Low-frequency broadband vibration suppression of periodic piezoelectric acoustic black hole beams

Objective Conventional acoustic black hole (ABH) structures are primarily effective for high-frequency vibration suppression but exhibit limited performance below the cutoff frequency. This study proposes a periodic piezoelectric ABH beam to broaden its low-frequency broadband vibration attenuation band.

Method Based on Euler beam theory and Bloch’s theorem for periodic structures, a virtual spring energy method is proposed to address periodic boundary conditions. The equivalent medium method is employed to homogenize piezoelectric patches coupled with external resistor–inductor (RL) shunt circuits, and the vibration governing equations of a single unit cell, infinite periodic ABH beams, and finite periodic ABH beams are established. COMSOL finite element simulations are conducted to verify the accuracy of the proposed theoretical model. Parametric analyses are performed to investigate the effects of unit cell size, truncation thickness, number of periodic units and circuit parameters on bandgap characteristics and vibration transmissibility.

Results Periodic arrangement generates multiple low-frequency Bragg attenuation bandgaps within the range of 22–1263 Hz below the ABH cutoff frequency. Increasing the unit cell size shifts the bandgaps toward lower frequencies, while increasing the truncation thickness broadens the bandwidth. Beams with 3–6 periodic units exhibit optimal damping performance. By adjusting the shunt inductance and resistance, resonance peaks can be selectively suppressed, achieving a maximum transmissibility reduction of 24.5 dB at the target frequencies. The proposed structure significantly enhances vibration attenuation performance over the broadband frequency range of 20–1000 Hz.

Conclusion The combination of periodic arrangement and piezoelectric shunt damping overcomes the inherent low-frequency limitations of single ABH structures. The proposed beam achieves excellent low-frequency broadband vibration suppression performance and provides an innovative structural solution for low-frequency noise control in underwater vehicles.