Non-linear modelling of elastic hysteretic damping in the time domain

Elastic hysteretic damping is defined as the dissipation of energy at a rate that is weakly dependent on frequency of vibration. In this article, we propose that the elastic hysteretic damping can be achieved by a simple modification to the viscous damping model. The proposed modification is based on computing an instantaneous correction factor that recursively depends on the state variables of the system. This correction factor is related to the rate by which the velocity changes with respect to the displacement. The new model compares quite favourably with the other existing solutions in the time-domain and differences between the solutions become evident for higher damping ratios. It is found that the new model predicts consistently the weak variation in the loss factor as a function of frequency. In addition to its simple mathematical formulation, the proposed model is superior to the existing solutions in that it does not require knowledge of the past history of motion neither the knowledge of the excitation frequency and is extensible to any type of loading. Various aspects pertaining to the linearity of the proposed approach are finally discussed.