Harvesting base vibration energy by a piezoelectric inverted beam with pendulum

We proposed a two-degrees-of-freedom inverted piezoelectric beam with pendulum to promote the performance of vibration energy harvesting. This configuration is composed of an inverted elastic beam and a pendulum attached to its free end. The electromechanical equations governing the nonlinear system were derived. The harmonic balance method (HBM) is applied to solve the equation and the results prove that there exists a 1:3 super-harmonic resonance. The simulation results show that owing to the particular nonlinearity, there appears a special bending effect in the amplitude-frequency response, i.e., bending right for the first natural frequency and left for the second natural frequency, which is beneficial for harvesting vibration energy. The HBM results are verified by the entity simulations. Furthermore, over a relatively wide range of power spectral density, it could reach a dense jumping and give a dense high pulse voltage.