Dynamic analysis of vibro-impact energy harvester with acoustic black hole

In order to improve the energy harvesting efficiency of acoustic black hole (ABH) structures under low-frequency excitation, this paper proposed a vibro-impact energy harvester, which can greatly improve the energy output through collision under such conditions. The equations of motion are established by using the Bernoulli-Euler beam theory and Rayleigh-Ritz method. Subsequently, the nonlinear impact force and contact stiffness can be gained by the Hertz contact theory. The Chebyshev polynomials of the first kind are employed to form the mode shape functions. The natural frequency and mode shape are obtained by solving the eigenvalue problem, and the vibration responses under base excitation and collision are calculated by the Duhamel integration and time-stepping iteration method. Finally, the energy output of the system is obtained using the piezoelectric theory. By comparing with the experimental results, the proposed method can accurately solve the vibration response and energy output of the piezoelectric cantilever beam under continuous impact. The advantages and reasons of ABH beam in energy harvesting compared with uniform beam and stepped beam are analyzed by numerical calculation. The results show that the pasting position of piezoelectric sheet, external resistance, impact distance, impact position, excitation frequency and excitation amplitude play important roles on the energy output of the system.