Harvesting electricity from random vibrations via a nonlinear energy sink

Abstract

Integration of a vibration absorber and an energy harvester is a promising approach to achieve simultaneously vibration reductions and vibratory energy harvesting. The present work investigates random responses of a nonlinear energy sink (NES) combined with a giant magnetostrictive energy harvester (GMEH). When a structure is modeled as a one-degree-of-freedom oscillator subjected to a random excitation, the structure with the integrated NES-GMEH is governed by two simultaneous nonlinear stochastic differential equations coupled with a nonlinear algebraic equation. The Ferrari formula is applied to decouple the algebraic equations from the stochastic differential-algebraic equations. The resulting stochastic algebraic differential equations are transformed into the steady Fokker-Planck-Kolmogorov equations. A fourth finite difference scheme is used to solve numerically the FPK equations. The FPK equations based solutions are qualitatively verified via Monte Carlo simulations. The parametric effects on vibration suppression and electricity production are examined, where the electricity is indicated by the square expectations of voltage and power. The responses of the structure, the structure with the NES only and the structure with both NES-GMEH are compared under the same Gaussian white noise and system parameters. It is found that the integrated NES-GMEH system achieves the best vibration suppression. It is demonstrated that a properly designed NES-GMEH device can simultaneously suppress vibration and produce electricity under Gaussian white noise excitations.