Delay Correlation of Mechanical Hysteresis and Damping

This paper presents a procedure for calculating the effective equivalent structural properties (stiffness and damping) of hysteretic systems from the time histories of their dynamic response. The method is based on the finding that the effective dynamic damping is proportional to the product of the structural natural frequency and the delay between the overall restoring force and the structural displacement. The delay is calculated from the time-shifted cross correlation between the structural force and displacement; and the same procedure also allows us to compute the instantaneous period of the response. It is then shown how, by computing the standard deviations of the force and displacement signals, it is possible to compute both the equivalent damping and the linearized stiffness. By implementing this procedure sequentially through moving windows, it is possible to monitor the nonlinear evolution in time. Some proofs are given for some easily tractable mathematical cases such as for linear simple harmonic and seismic responses, conjecturing that the method can be equally applied for transient forcing functions of nonlinear systems.