Dynamical response and vibrational resonance of a tri-stable energy harvester interfaced with a standard rectifier...

This paper investigates the dynamical response and vibrational resonance (VR) of a piecewise electromechanically coupled tri-stable energy harvester (TEH), which is driven by dual-frequency harmonic excitations. To achieve a stable DC output, the TEH is interfaced with a standard rectifier circuit. Using the harmonic balance method combined with the separation of fast and slow variables, a steady-state response together with the analytical expressions of displacement and harvested power is derived. The multi-solution feature in the amplitude-frequency response is observed and can improve the harvesting performance of the TEH under a low-frequency environment. There is an optimal time constant ratio and electromechanical coupled coefficient to maximize the harvested DC power. Meanwhile, the VR phenomenon of the TEH is explored through the response amplitude of the low-frequency input signal, which implies that an appropriate combination can induce the occurrence of VR and improve the rectified voltage. Similarly, the nonlinear stiffness coefficients can be adjusted by changing the magnet distance to induce the appearance of VR. The theoretical solutions are well supported by numerical simulation and experimental verification. Specifically, the theoretical analysis and experimental evidence illustrate that the harvested power under the VR effect is much higher than that without VR.