Triggering high-energy orbits of 2-DOF bistable rotational energy harvesters through phase difference

In recent years, energy harvesting technology has provided a promising solution for powering low-power sensors. Rotational motions are ubiquitous in nature and human activities, making the design and study of rotational energy harvesters highly significant for the development of the Internet of Things. Previous studies have shown that nonlinear bistability and multiple degrees of freedom (MDOF) can significantly enhance the output power and operating frequency bandwidth of rotational energy harvesters. However, the bistability introduces the nonlinear stiffness into the MDOF harvester, resulting in the oscillations in high-energy or low-energy orbits that both may occur depending on the system condition. Therefore, this paper proposes a method to excite the high-energy orbit of two degree-of-freedom rotational bistable energy harvesters (2-DOF-RBEH) at ultra-low frequencies utilizing the phase difference of equivalent excitation. A theoretical model describing its dynamic response and output voltage is derived based on Hamilton's principle. Experiments are conducted to validate the model, and the output voltage responses of the harvester with zero phase difference (HZPD) and the harvester with half phase difference (HHPD) are compared. Results show that the HHPD more easily enter into the high-energy orbit at ultra-low rotational frequencies. Due to this, the output power of HHPD is increased by up to 2187% compared to HZPD, and the frequency bandwidth entering the highenergy orbit is increased by up to 466%. In addition, this study analyzes the dynamic mechanism by which the equivalent excitation phase difference triggers the high-energy orbit and explores the effect of excitation angles on the dynamic response and performance of the HHPD. These investigations offer new insights for the design of high-performance ultra-low-frequency bistable rotational energy harvesters.