Piezomagnetoelastic vibration energy harvesting with superharmonic resonance

Nonlinearities give rise to secondary resonances such as superharmonic and subharmonic resonances. The superharmonic resonance can activate large-amplitude responses when the excitation frequency is a fraction of the fundamental frequency of the system. These low frequency excitations are very beneficial for energy harvesting systems. This paper presents an analytical investigation of vibrational energy harvesters with superharmonic excitation in a pietzomagnetoelastic configuration. A piezomagnetoelastic power generator is assumed to operate in the monostable and bistable modes. Nonlinear differential equations governing the oscillations of the system is solved using the method of multiple scales. System responses to the superharmonic resonance including the cantilever tip displacement and the output voltage are determined. It is found that employing the superharmonic resonance can increase the amount of harvested energy in the system. The root mean square value of the output voltage is obtained for several cases in both monostable and bistable modes. The power generated in monostable and bistable modes is then compared through numerical simulations. It is observed that the bistable mode is more convenient for harvesting energy. In addition, a Rung-Kutta numerical scheme is used to solve the differential equations. It is shown that the perturbation solution is in a close agreement with the numerical solution.