Steady‐State Oscillation of Hysteretic Differential Model. II: Performance Analysis

The present study involves two aspects associated with the steady‐state performance of the versatile Bouc‐Wen hysteretic model. First, influence of the model parameters on steady‐state responses and hysteresis loops of the single‐degree‐of‐freedom (SDOF) hysteretic system is studied by the proposed Galerkin/ Levenberg‐Marquardt (GLM) method. The dynamic behavior corresponding to five kinds of hysteresis loops is identified. Second, the steady‐state characteristics of the Bouc‐Wen hysteretic model used for representing inelastic constitutive laws are recognized. As endochronic constitutive relationship, this smooth hysteretic model may locally violate the Drucker's (or Ilyushin's) stability postulate of plasticity when the steady‐state hysteresis loops are exhibited with intermediate unloading‐reloading. The study is emphasized on the energy dissipation properties in small unloading‐reloading cycles starting at an arbitrary deformation previously reached. The extent of local violation of the Drucker's postulate under steady‐state circumstances is observed through numerical analysis. The mitigation of this violation is addressed by parameter studies.