A General Rule for the Influence of Physical Damping on the Numerical Stability of Time Integration Analysis

The influence of physical damping on the numerical stability of time integration analysis is an open question since decades ago. In this paper, it is shown that, under specific very general conditions, physical damping can be disregarded when studying the numerical stability. It is also shown that, provided the specific conditions are met, analysis of structural systems involved in extremely high linear-viscous damping is unconditionally stable. A secondary achievement is that, when the linear-viscous damping increases, the numerical damping may increase or decrease.