A non-linear model for elastic hysteresis in the time domain: Implementation for multiple degrees of freedom

A model that captures the weak frequency sensitivity of elastic hysteretic damping is proposed for the time-domain simulation of structures with multiple degrees of freedom (MDOF) under free or forced vibration. The model is based on a recently proposed modification to the conventional single degree of freedom (SDOF) viscous damping model, utilising a correction factor computed based on the local instantaneous response to adjust the damping coefficient such that the dissipated energy remains insensitive to the frequency characteristics of the motion. The model compares favourably to the well-established viscous (incl. Collar’s frequency correction), Rayleigh and Reid MDOF models, is applicable to any type of loading and, unlike other classes of damping models, such as Rayleigh, modal, Bouc-Wen, Biot, and Collar/Neumark, does not require extensive calibration, knowledge of the past history of motion, or a priori knowledge of the excitation characteristics and frequency.