Multi-solution phenomena and nonlinear characteristics of tristable galloping energy harvesters with magnetic coupling nonlinearity

Different from linear energy harvesters, nonlinear energy harvesters have multi-solution phenomena and nonlinear characteristics, some of which are beneficial for high-performance energy harvesting. This paper employs the incremental harmonic balance method to deduce the semi-analytical solutions of bistable and tristable nonlinear galloping energy harvesters. The traditional harmonic balance method is used to select the initial values for the incremental harmonic balance method, and the two points tracing algorithm is used to track each solution curve. The stabilities of the semi-analytical solutions are determined by the Floquet theory. The multi-solution phenomena and nonlinear characteristics of tristable galloping energy harvesters and bistable galloping energy harvesters are revealed. The root-mean-square voltage and response frequency of the bistable galloping energy harvester have three non-zero solutions and only one is stable. Those of the tristable galloping energy harvester have nine non-zero solutions (two of which are stable) and the tristable galloping energy harvester has two cut-in wind speeds. Subsequently, cases with different nonlinear stiffness coefficients are studied. Overall, this paper provides a framework for the theoretical analysis of nonlinear flow-induced vibration energy harvesters.