Analytical and experimental investigation of the centrifugal softening and stiffening effects in rotational energy harvesting

Depending on its mounting orientation, the rotational piezoelectric harvester can be subjected to the centrifugal softening or stiffening effects, which may pose a positive or negative influence on the energy harvesting performance. This paper firstly presents the comprehensive comparison of the centrifugal softening and stiffening harvesters with a unified dimensionless analytical model. The analytical expressions of the optimum short-circuit and open-circuit rotational frequencies, the optimum resistances and the optimum centrifugal coefficients are derived to reveal the influence mechanism of the centrifugal effects. The proposed model is validated experimentally and used for case studies to compare the centrifugal softening and stiffening harvesters. Results illustrate that the centrifugal softening harvester has a superior energy harvesting performance at low rotational frequencies while the centrifugal stiffening harvester is better at high rotational frequencies. Furthermore, the peak power of the centrifugal softening harvester is higher while the frequency bandwidth of the centrifugal stiffening harvester is wider. In addition, it is found that the centrifugal stiffening harvester is more sensitive to the centrifugal coefficient. Based on the centrifugal stiffening effect, the self-tuning harvester can be achieved with a wide frequency bandwidth. Meanwhile, this requires that the centrifugal coefficient is precisely determined, and the fundamental natural frequency of the harvester without the centrifugal force should be low enough when operating at low rotational frequencies. Compared with the centrifugal stiffening effect, the centrifugal softening effect may be more suitable to be used in MEMS/NEMS applications since it can reduce the fundamental resonant frequency of the harvester during the rotation.