Probabilistic Response Analysis of Nonlinear Tristable Energy Harvester Under Gaussian Colored Noise

Purpose: In this paper, probabilistic response and performance analysis of a nonlinear tri-stable energy harvesting with piezoelectric coupling driven by exponentially correlated Gaussian colored noise are investigated. The effects of the system parameters, depth of potential well function, noise intensity and its correlation time on the mean square voltage are studied. Methods: The joint probability density function (PDF) as well as the voltage generated are obtained by numerically solving the four dimensional Fokker-Plank (FP) equation for the coupled electromechanical system. The results as obtained using the FP solution are verified using the Monte Carlo simulations (MCS). Results: A relative comparison of single, double and triple well potential functions on energy harvesting is presented. It is observed that the electromechanical coupling coefficient, damping ratio, intensity of noise and time constant and the shape of the potential wells have significant effects on the harvested energy. Under random excitation, for lower intensity of noise the energy harvester with single potential well outperforms the harvester with multiple deep potential wells. Beyond a threshold value of noise intensity, energy harvester with multiple well potentials outperforms as the jump from one potential well to another becomes more frequent with inter-well dynamics functioning. It is found that the probability of jumps between potential wells is enhanced with increase in the noise intensity and corresponding increase in the mean power generation. Nevertheless, this enhancement is weakened with increase in correlation time of noise. Conclusion: The study has shown that, the energy harvested can be optimized by suitable choice of the potential function, coupling parameters, the noise intensity and its correlation time.