Comparison of damping parameters based on the half-power bandwidth methods of viscous and hysteretic damping models

The half-power bandwidth method is usually used to calculate structural damping parameters by frequency response function (FRF). In this note, the half-power bandwidth methods for the displacement FRF, the velocity FRF, and the acceleration FRF are proposed based on viscous and hysteretic damping models, respectively. Comparison results show that the application conditions of half-power bandwidth methods for the displacement and acceleration FRFs are limited. They can only be used to calculate the small damping ratio/loss factor. The application condition of half-power bandwidth method for the velocity FRF is not limited. It can be used to calculate the large or small damping ratio/loss factor, which should be the first choice for calculating damping parameters. Besides, when the damping ratio is less than 0.2546 or the loss factor is less than 0.5658, the relative difference between the loss factor and twice the damping ratio is less than 10%. With the increase of the damping ratio or loss factor, the relative difference will increase rapidly, and the approximate relationship is no longer applicable.

Effect of the elastic hysteresis term formulation and response to non-harmonic periodic excitations of a non-linear SDOF dynamical model with weak frequency-dependency in the time domain

We elaborate a SDOF time-domain model for elastic hysteretic damping, by modifying the viscous damping model to introduce an instantaneous correction factor that recursively depends on the state variables of the system, such that the response exhibits weak dependency on frequency, corresponding to a large array of engineering materials. The effect of different formulations for calculating the instantaneous correction factor on the predicted hysteresis loops and the potential manifestation of singularities is studied. Hysteresis loops anticipated by the model are plotted and forced vibration responses to harmonic and other periodic non-harmonic excitations are simulated and discussed, also in comparison to the conventional viscous and Reid’s damping models.