Locally resonant metamaterial plate with cantilever spiral beam-mass resonators and various piezoelectric defects for energy harvesting

In this paper, a locally resonant metamaterial sandwich plate with different types of piezoelectric defects is proposed by selectively replacing the cantilever spiral beam-mass resonator with that containing two piezoelectric material layers. Firstly, a mechanical model of the piezoelectric cantilever spiral beam is considered, and its cross-sectional bending stiffness and equivalent stiffness are derived. The natural frequency and response voltage are theoretically calculated and analyzed. It is found that the thicknesses of piezoelectric layer and the spiral beams have a crucial influence on the natural frequency and response voltage of the system. The dynamic equations governing the vibration of the defect locally resonant metamaterial sandwich plate is given. Within the framework of the plane wave expansion method, the band gap structure and defect band frequency are analytically obtained. On this basis, the influence of various defects of the metamaterial sandwich structures, including various point defect and line defect on the transmission loss and response voltage are explored. The results indicate that two-point defects exhibit significant advantages in energy concentration and capture efficiency when the resistance is high. While as the number of defects increases, the energy localization effect gradually disperses, leading to gradual weakening in capture efficiency. Present work achieves the combination of vibration control and energy harvesting in the same system, and provides new ideas for fields such as piezoelectric energy harvesting structures and self-powered devices.