Numerical Evaluation of Bell-Shaped Proportional Damping Model for Softening Structures

. A new type of proportional damping models, called bell-shaped proportional damping model, has recently been proposed. This new model has not only addressed the spurious damping forces, but also maintained the same order of computational efficiency as the Rayleigh model. This model has also been further improved such that, by using the tangent stiffness approach, it becomes suitable for structures experiencing softening response with negative stiffness. The improved model allows users to have flexible control of modal damping ratio for all interested frequency intervals, including those associated with negative stiffness. In this study, the performance of bell-shaped damping model is evaluated numerically in a response history analysis of a multi-storey building under seismic loading. The results show that, compared to the Rayleigh model, the bell-shaped model performs excellently in terms of always giving desirable positive energy dissipation even when the structure is experiencing softening response.