Comparison of harmonic balance and multi-scale method in characterizing the response of monostable energy harvesters

Harmonic balance and multi-scale methods have been widely applied to investigate the nonlinear dynamics and performance enhancement methods of nonlinear vibration energy harvesters. However, there are rare works considering the relative accuracy of the two methods in characterizing the response of nonlinear harvesters. Therefore, new insights into the analytical accuracy of harmonic balance and multi-scale methods are provided based on a monostable energy harvester in this paper. Frequency response functions of displacement and voltage for a monostable harvester are derived according to harmonic balance expansion and multi-scale method respectively. Monostable system parameters identified from experimental measurements are obtained for numerical investigation of the theoretical solution from harmonic balance and multi-scale methods. Results demonstrate that harmonic balance method is more accurate to characterize the frequency response under different acceleration levels, as well as the amplitude response for various excitation frequencies. While for multi-scale method, it is of great importance to choose proper keeping parameter to describe the nearness of excitation frequency to the resonance frequency.