Noise-induced stochastic internal resonance in nonlinear energy harvesting

We analytically study the dynamic behavior of a linear mechanical energy harvester nonlinearly coupled to a linear oscillating mode, driven by stochastic Gaussian forces. Using renormalization theory and Feynman diagrams, we determine the renormalization of three key system parameters: the natural frequencies of the oscillating components and the parameter associated with the driving force amplitude. Our results show that random forces can induce the well-known internal resonance state, where the renormalized quantities exhibit a nontrivial dependence on the working frequency. In this state, coherent synchronization between the two oscillatory systems leads to qualitative changes in their respective spectral densities, with direct implications for the harvested electrical energy. Finally, we numerically validate our analytical findings.