Analytical investigation and optimization of a vortex-induced piezoelectric energy harvester by differential transform method and response surface methodology

Linear piezoelectric energy harvesters exhibit coupled vibration phenomena under external excitation. This study proposes a novel semi-analytical method for examining the vibration response of linear piezoelectric energy harvesters in vortex-induced vibration environments. In this study, the governing equations of a vortex-induced piezoelectric energy harvester, derived with the help of Euler–Lagrange equation, are solved using the multi-step differential transform-Padé approximation method. The accuracy of this method is validated against the fourth-order Runge–Kutta method. Furthermore, the influences of the bluff body’s diameter and the length of piezoelectric beam on the system’s output power are examined. Finally, optimization of the model is conducted using the non-dominated sorting genetic algorithm II with the objectives of maximizing output power and minimizing system mass, in which response surface methodology is employed to tackle with the time-consuming problem in computation process. The results indicate that the output power at the turning points calculated through idealized points is 13.37% greater than that of the initial design point, while the total system mass is reduced by 3.06%.