Implementation and Performance of Bell-Shaped Damping Model

A new proportional damping model, named as bell-shaped, has recently been proposed to address the limitations of existing models for simulating un-modeled energy dissipation in large-scale structures subjected to seismic loading. This model relies on an expanded damping coefficient matrix in a sparse matrix form in order to maintain the same computational efficiency as Rayleigh model for the response solution process, so that it can be used for structures with a large number of degrees of freedom. This study investigates two storage schemes: COO (coordinate list) and BST (binary search tree) for constructing and storing the expanded coefficient matrix. The results show that both schemes require a computational complexity of $$O\left(nnz\mathrm{log}\left(nnz\right)\right)$$ , which is the optimum in the state-of-the-art technologies and is less than the complexity of the solution process. This study also develops an application for computing model parameter values via optimization to match a user-specified damping ratio curve in the structural frequency domain.