Complexity and response of bio-inspired energy harvesters based on wing-beat pattern

Abstract This paper aims to investigate the dynamical mechanism of bio-inspired energy harvesters based on wing-beat pattern under harmonic excitation. Due to the existence of the gravity force in the established model, the harmonic balance method is utilized to calculate the theoretical results, which has the advantage to keep the influence of gravity force. Multiple solutions are found in the high frequency region, and they are very close in the amplitude of displacement and voltage due to the special structure of the bio-inspired energy harvester. Direct time-domain analysis verifies the effectiveness of theoretical results. The influence mechanism of the equivalent stiffness is also explored, which leads to the appearance of different states. Then, the root mean square (RMS) voltage and average power are analyzed. It is observed that a smaller damping coefficient and equivalent capacitance enhance the average electrical output and achieve greater output power. Subsequently, the bifurcation and complexity properties of the harvester are discussed. Complex phenomena are observed under different external excitations and equivalent damping, including double periodic bifurcation, multiple periodic bifurcation, and chaos phenomena. The complexity analyses confirm the effectiveness of the bifurcation results. The distribution of complexity also exhibits significant fluctuations, closely correlated with the trend of the bifurcation diagram.