Free oscillations of an elasto-plastic oscillator with kinematic hardening are analyzed in this paper. A bilinear hysteretic model is used to represent the material non-linearity. The coefficient of kinematic hardening is used as a problem parameter in the equations of motion. By solving the governing equations on each branch of the hysteretic cycle and matching the transition conditions, an iterative map is obtained for the plastic displacements. The map is analyzed and a bifurcation of the system's dynamic behavior due to change in the hardening parameter is discussed. A theorem is presented to identify two distinct subranges of this parameter, and the dynamic behavior of the oscillator is discussed in each subrange.
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Pratap et al. (1994) studied this question.
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