Nonlinear dynamic analyses on a magnetopiezoelastic energy harvester with reversible hysteresis

This paper presents a systematic approach through a series of nonlinear analyses to predict and design the nonlinear resonance characteristics and energy-harvesting performance of a magnetopiezoelastic vibration energy harvester with reversible hysteresis. To this end, a mathematical model of the energy harvester system, composed of a bimorph cantilever beam along with three permanent magnets, is first derived. With this model, frequency response analyses are conducted using the methods of multiple scales and harmonic balance. In the case of weak excitation, the system's stationary forced response is obtained through multiple-scale analysis (MSA). With this MSA solution, analytical design criteria in terms of the position parameters of the magnets are derived to determine the hysteresis type of the nonlinear resonance (stiffness hardening or stiffness softening). However, in the case of a relatively strong excitation, the high-dimensional harmonic balance analysis (HDHBA) shows that the stiffness-softening effect tends to strengthen for the oscillation amplitude in a specific condition, and this effect can even lead to hysteresis transition or potential well escape. Using the HDHBA, design criteria are set up and evaluated in terms of source vibration strength to detect the hysteresis transition or the condition required to determine the potential well escape. Finally, based on the present systematic analyses, the complicated resonant responses and energy-harvesting performance of the present system are examined with respect to several design parameters, and the results are discussed in detail.