Improving energy harvesting from low-frequency excitations by a hybrid tri-stable piezoelectric energy harvester

This paper presents the design of a novel hybrid tri-stable piezoelectric energy harvester (HTPEH) that improves the energy harvesting efficiency of piezoelectric energy harvesters operating at low frequencies. The proposed HTPEH is an extension of a conventional tri-stable cantilever piezoelectric energy harvester with an elastic base (TPEH + EB), and it incorporates vertical and rotational elastic amplifiers that are installed between the mass block at the left end of a cantilever beam and the left side of a U-shaped frame to enhance the system's nonlinear characteristics. By utilizing Hamilton's principle, a HTPEH's nonlinear electromechanical equation is formulated, and the harmonic balance method is used to obtain analytical solutions for the displacement amplitude, voltage amplitude, and power amplitude. The study investigates the effects of various parameters, including the elastic amplifier-to-base stiffness ratio and elastic amplifier-to-piezoelectric cantilever beam mass ratio on the energy harvesting performance of the HTPEH. The results indicate that the displacement and voltage amplitude of the HTPEH exhibit two peaks as the external excitation frequency increases, and adjusting the relative mass and stiffness between the elastic amplifier and the piezoelectric cantilever beam can alter the frequency band interval where the two response peaks of the system are located. This allows the HTPEH to enter inter-well motion at low-level external excitation, resulting in high output power. The HTPEH outperforms the TPEH + EB in terms of energy harvesting efficiency under low-frequency environmental excitation.