Damped free vibration with initial conditions

Translational and rotational basic connector components as well as translational-rotational combination connections are tested in damped, free vibration analyses. A series of simple, 2-node connector element models verify the connections described in Table 1. Two-dimensional, three-dimensional, and axisymmetric cases are examined where appropriate. In each case all available components of relative motion produce the same free, damped sinusoidal response based on the initial displacements. In Abaqus/Standard linear geometry is used to avoid nonlinear coupling for finite rotation connection types.

The verification analyses consist of two steps in Abaqus/Standard and one step in Abaqus/Explicit. The initial displacements for the dynamic response are defined as follows. The first step in the Abaqus/Standard analysis prescribes the connector motion with a static step to apply an initial displacement to the “free” end node of the connector. The Abaqus/Explicit analysis defines reference lengths and angles for constitutive response that are different from those calculated from the initial geometry. In the dynamic analysis the free node end of the connector element undergoes damped, free vibration in response to the initial displacement.