Data‐based model‐free representation of complex hysteretic MDOF systems

A general approach is presented for developing data-based, model-free representations of complex non-linear (including hysteretic) multi-degree-of-freedom (MDOF) systems under arbitrary dynamic loads. Only the excitation forces and corresponding response is needed to implement the procedure: the system mass need not be known. The approach utilizes a two-stage procedure: in the first stage, least-squares techniques are used to identify the system matrices of an equivalent linear MDOF system; in the second stage, the non-linear system restoring force vector is determined, and transformed into the ‘modal space’ associated with the eigenvectors of the linearized system. Subsequently, non-parametric identification techniques are used to represent the transformed restoring force surface in terms of suitable state variables. The robustness of the method is illustrated by means of a 3DOF system incorporating non-linear features associated with friction, hysteresis, and limited-slip phenomena, as typically encountered in ‘joints.’ Copyright © 2005 John Wiley & Sons, Ltd.