Alternative characterization of time integration schemes Original Research Article

This work presents an alternative definition of the numerical angular frequency and numerical damping ratio, within the framework of direct time integration of second-order differential equations. The classical approach, based on the amplification matrix concept, deals with the ability of the numerical schemes to deliver an accurate response in time for problems with free vibration behaviour. It is well suited to the study of the schemes, both explicit and implicit, used in transient dynamic analysis. The alternative approach emphasizes the capability of the scheme to deliver an accurate resonant response for problems with forced vibration behaviour. Such frequency viewpoint is helpful in the study of the implicit schemes used in civil engineering applications.