Study on characteristics of the piezoelectric energy-harvesting from the torsional vibration of thin-walled cantilever beams

In this paper, a piezoelectric energy-harvesting structure based on the torsional vibration in the second mode is presented, which is composed of a thin-walled cantilever beam with PZT piezoelectric material and an eccentric proof mass. It has some advantages, such as small displacement amplitudes, uniform strain, and lower natural frequency. Firstly, based on the torsion theory of thin-walled bar (or beam), the static and dynamic theoretical torsion models of the harvester structure are established and its static and dynamic characteristics are derived. Then based on constitutive equation of piezoelectric materials, some characteristics of piezoelectric output such as open voltage are derived. The advantage of the models we made is that the analytical solutions of output characteristics clearly and concisely show the relationship between the related parameters and the output results. After modeling, we have made relevant theoretical calculations, numerical simulations and experiments by using PZT-5H as the piezoelectric material. The results show that the second modal frequency of the structure is 124.72 Hz. Under this condition, the open circuit voltage can reach 1.82 V when the excitation acceleration is 10 m/s²; the torsion angle can reach 0.341° when the excitation acceleration is 3 m/s². From the results of mechanical and electrical output obtained by theoretical calculations, numerical simulations and experiments, it is found that they are all in good agreement with each other.