Least-Square Effective Stiffness to be Used for Equivalent Linear Model

This work introduces a method for the identification of linear stiffness and viscous damping parameters from a one-degree-of-freedom force-displacement cycle. Using an original approach, the stiffness parameter is derived by a least-square formula from the discrete input force-displacement point coordinates of the loop. The damping ratio is obtained in a classic manner from the quotient of absorbed and elastic energy. The obtained stiffness and damping parameters are proposed to be used, with the known mass, as an equivalent linear mass-spring-damper that should predict the response to a known load for the original nonlinear system associated to the input force-displacement cycle. As an example study, the effectiveness of such prediction is qualitatively shown in the case of the steady-state response to a harmonic load for a particular hysteretic numerical model, by using a range of values for some dimensionless parameters. This kind of study is susceptible to be extended to other kinds of loading and/or numerical and experimental hysteretic models, as well as to other identification procedures available in the literature.