A SYMMETRIC STATE-SPACE FORMAT FOR MOMENTUM CONSERVING TIME INTEGRATION ALGORITHMS WITH ENERGY DISSIPATION

摘要

A symmetric state-space format is presented for momentum conserving time integration algorithms, and two schemes for introduction of algorithmic damping are described. The balanced damping is formulated in terms of the original state-space variables variables, leading to a linear increase of damping with frequency in the low-frequency region. In the extended state-space algorithm auxiliary variables introduce damping via discrete first order filters. By this method the low-frequency damping is lifted to third order in frequency. Both algorithms have full symmetry in the state-space variables.