Periodic response characteristics on a piecewise hysteresis nonlinear system

Abstract

A piecewise hysteresis nonlinear dynamic model with nonlinear stiffness and damping is established for a system with alternating elastic constraints and hysteresis nonlinearity. First, the amplitude–frequency response equation of the system is solved by using the averaging method under periodic excitation. Two frequency regions with multiple solutions are then identified in the system, and the amplitude–frequency response characteristics under different system parameters are obtained. Thus, the influence law of different piecewise nonlinear factors on system stability is explored. Second, the bifurcation behavior of the system under different external disturbances is analyzed. Given the change of perturbation parameters, the system is found to be a complex dynamic system with alternating periodic, double periodic, and chaotic motions, and many other forms of movement. Moreover, lower buffer damping leads to the complex and unpredictable chaotic state of the system’s dynamic behavior.