Dynamical analysis of a tri-stable piezoelectric energy harvester with stops driven by narrow-band random noise

The tri-stable vibrational energy harvester (VEH) is commonly designed to achieve the large-orbit motion, but it is always trapped in one potential well and performs an intra-well motion under weak vibration excitations. To solve this problem, a tri-stable piezoelectric VEH with stops is proposed in this paper. The analytic expressions of the first-order and second-order moments for system response are derived based on the multiple scale method. It is found that the harvesting frequency bandwidth of the tri-stable VEH becomes wider under an optimal impact distance. Compared with the tri-stable VEH without stops, the consideration of stops can help the system achieve the multiple high-energy solutions. The choice of high-stiffness stops at high frequencies can enhance the harvesting efficiency of the tri-stable VEH with stops. Moreover, the experimental results and analysis also are presented to verify the obtained theoretical results. It is found that the energy harvesting efficiency can be increased to 140% of the unrestricted state at the optimal impact distance. Compared with the tri-stable VEH with rubber and stiff springs, the one with silica gel stops has a higher output voltage.