Parametric study and optimization of linear and nonlinear vibration absorbers combined with piezoelectric energy harvester

In this work, a harmonically excited generalized two degree of freedom nonlinear system is used to manifest the functions of both the vibration absorber and energy harvester simultaneously. The generalized system has been reduced to a linear primary system with linear/nonlinear absorber and harvester or nonlinear primary system with linear/nonlinear absorber and harvester. Multi harmonic balance method (MHBM) along with arc length continuation is used for generating frequency response plots for different absorber and energy harvester system parameters with constant primary system parameters and excitation amplitude. The frequency response plot shows multiple branches of stable periodic solutions and jump at certain frequency ranges for systems with non-linearity. The absorber and energy harvester parameters are optimized using an optimization procedure based on genetic algorithm in combination with response surface methodology. The method is validated with analytical solutions available in the literature for a linear primary system with linear absorber and harvester and nonlinear primary system with nonlinear absorber alone. This study demonstrates that the proposed optimization framework along with MHBM is suitable for generating the optimal frequency response for multi functional energy harvesting systems or systems with nonlinear absorber. The frequency response plots with optimal parameter values reiterates the fact that the absorber system with nonlinear element perform better compared to its linear counterpart over a wider band of frequencies. This study also reports the comparison of the performance of a combined nonlinear absorber harvester system with that of a nonlinear energy sink (NES) absorber harvester system.