Development of a Modified Bouc-Wen Model for Butterfly Hysteresis Behaviors

Butterfly hysteresis effects are complicated nonlinear behaviors. In comparison with single-loop hysteresis behaviors, butterfly hysteresis loops are composed of two single hysteresis loops and the directions of the butterfly hysteresis loop include both clockwise and counter-clockwise. Therefore, it brings a great challenge to build a proper model to describe the butterfly hysteresis behaviors, since most available hysteresis models are applied to describe the single-loop hysteresis. To solve this problem, a modified Bouc-Wen model with an absolute excitation function and modified elastic polynomials is developed in this paper. Experimental results are carried out via a dielectric elastomer actuator (DEA) to validate the effectiveness of the proposed model.