Dynamics of a coupled nonlinear energy harvester under colored noise and periodic excitations

Vibration energy harvester (VEH) has proven to be a favorable potential technique to supply continuous energy from ambient vibrations and its performance is greatly influenced by the design of potential structures. Motivated by the enhancement of energy harvesting performance, an electromechanical coupled VEH under colored noise and periodic excitations is investigated theoretically and numerically, and comparisons of the effects of mono-, bi- and tri-stable potentials are analyzed in detail. An uncoupled equivalent system, together with its joint probability density function (PDF), are derived by using the generalized harmonic transformation and the stochastic averaging based on energy-dependent frequency. For three kinds of different potentials, the effects of the periodic excitation, colored noise, potential shape and other crucial system parameters are explored on the dynamical behaviors. Results show that tri-stable VEH outperforms the mono- and bi-stable VEHs in mean harvested power and can achieve better stochastic resonance (SR) effect and higher power conversion efficiency by choosing the optimal system parameters, such as noise intensity, electromechanical coupling coefficient and time constant ratio. Moreover, the periodic excitation can change the topological characteristic of transient PDF, and larger periodic force can enhance SR effect but will weaken the power conversion efficiency. The theoretical results obtained by the proposed stochastic averaging method are well validated by numerical simulations.