Enhanced Modeling Method of Asymmetric Nonlinear Magnetic Force for Multi-stable Energy Harvesters

The nonlinear multi-stable piezoelectric energy harvesters have attracted a great quantity attention for the performance enhancement. Due to the fact that the nonlinear restoring force plays an important role in dynamic behavior, it is necessary to model the nonlinear restoring force accurately. However, previous models mainly focus on the symmetric system, but the influencing mechanism of widely used asymmetric systems has not been discussed. Therefore, this paper presents an enhanced modelling method of nonlinear restoring force for asymmetric multi-stable energy harvesters. The magnetic charge method is applied to deduce the theoretical expression of magnetic force between the tip magnet and the rotatable magnets. Then, numerical results of magnetic force have verified the effectiveness of proposed method for asymmetric multi-stable energy harvesters. The influence of different structural position parameters of rotatable magnets on nonlinear magnetic force is analyzed. Moreover, the dynamic responses of asymmetric multi-stable energy harvesters with different potential well shapes are compared by directly changing structural parameters.