Least-square effective stiffness to be used with equivalent viscous damping as equivalent linear model

Abstract

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 for 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 numerical and experimental hysteretic models as well as to other identification procedures available in the literature.