Abstract: Consider the hysteretic characteristic of processed material, a bilinear hysteresis model is utilized to describe the dynamical behavior of a kind of vibrating crusher. The equivalent coefficients of damping and stiffness to the hysteresis can be deduced by means of asymptotic method. Nonlinear dynamics techniques, such as Poincaré sections, bifurcation diagrams and the largest Lyapunov exponents, are employed to ascertain dynamics responses of a SDOF model of vibrating crasher with bilinear hysteresis. A variety of nonlinear dynamic responses of the nonlinear system underg- oing periodic, quasi-periodic and chaotic vibrations are observed, and some design recommendations are provided.

Key words: Bilinear hysteretic model, Chaotic behavior, Equivalent damping, Equivalent stiffness