Analytical method for an excitation adaptive bistable wave energy converter

As a nonlinear mechanism, bistablity provides a promising idea for high efficiency and wideband energy harvesting. In order to solve the bottleneck problem of the worse performance for the traditional bistable mechanism under small excitations, a rack-pinion-lever-spring bistable mechanism with a dynamic constraint is proposed and applied to a point absorber wave energy convertor (WEC). Different from the traditional bistable system, the WEC with a dynamic constraint based bistable Power Take-Off (PTO) is characterized as a one-and-half-degree of freedom dynamic model. The approximate analytical solution of the bistable WEC is derived combined with harmonic balance method and Arc-length continuation method. The superior wave height adaptability for the bistable WEC under regular wave is revealed by using numerical and analytical solutions. The intrinsic complex nonlinear behaviors are analyzed by using bifurcation diagrams and phase portraits. The results show that the WEC with a dynamic constraint based bistable PTO can greatly improve the capture efficiency of low frequency energy compared with the WEC with a fixed constraint based bistable PTO, especially for the wave conditions of small wave amplitudes. The stability of the WEC with a dynamic constraint based bistable PTO is better under large amplitude. The bistable mechanism with a dynamic constraint proposed in this paper can provide reference for capture of low frequency wave energy.