Semi-analytical model and vibrational energy recovery efficiency of piezoelectric beams with quasi-periodic additional acoustic black holes

Based on the energy aggregation effect of acoustic black holes (ABHs) structures, they can be used as bending wave traps for energy harvesting applications and help to greatly improve the efficiency of energy recovery. In this paper, a quasi-periodic additional acoustic black holes (Q-IABHs) piezoelectric beam structure for efficient energy recovery of low-frequency broadband energy is proposed in response to the current embedded piezoelectric ABHs that lead to weakening of the structural strength. Firstly, the electromechanical coupling model of Q-IABHs is established according to the characteristics of the thickness power rate distribution in ABHs, based on the theory of Gaussian expansion method and coupled spring technology. Compared with the commonly adopted finite element method (FEM), this method has obvious advantages in terms of greatly improving the computational efficiency and perfectly adapting to arbitrary boundary conditions with thickness gradient changes. The accuracy of the theoretical modeling method is verified by numerical simulation with FEM. Then, the mechanism of the key structural parameters of the Q-IABHs piezoelectric beam on the energy recovery power is investigated, and the enhancement mechanism of the piezoelectric sheet size and position on the broadband recovery power is revealed. Then, the enhancement mechanism of the energy aggregation effect of the Q-IABHs piezoelectric beam structure on the energy recovery power is revealed through comparative analysis. Finally, 6063 aluminum alloy material is used to complete the preparation of Q-IABHs piezoelectric beam structure by machining black hole features through CNC milling, and the experimental platform for piezoelectric energy recovery is built. The results show that the recovery efficiency of Q-IABHs piezoelectric beams in the range of 0-471.27 Hz is significantly higher than that of additional uniform piezoelectric beams (Q-UNIs), which verifies the effectiveness of the Q-IABHs structure to improve the efficiency of broadband energy recovery, and lays a foundation for the advancement of the ABHs structure from theoretical research to the application in the field of practical engineering.