1.9.1 Damped free vibration with initial conditions

Products: ABAQUS/Standard  ABAQUS/Explicit  

Elements tested

CONN2D2    CONN3D2   

Problem description

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 1.9.1–1. 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 uses the *CONNECTOR MOTION option with a *STATIC procedure to apply an initial displacement to the “free” end node of the connector. The ABAQUS/Explicit analysis uses the *CONNECTOR CONSTITUTIVE REFERENCE option to define 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.

Table 1.9.1–1 Connection types for damped, free vibration verification analyses.

Connection TypeDOFs AffectedDimensions
AXIALTranslational Basic2-D, 3-D, Axisymmetric
CARTESIANTranslational Basic2-D, 3-D, Axisymmetric
PROJECTION CARTESIANTranslational Basic3-D
RADIAL-THRUSTTranslational Basic3-D
SLIDE-PLANETranslational Basic3-D
SLOTTranslational Basic2-D, 3-D, Axisymmetric
CARDANRotational Basic3-D
EULERRotational Basic3-D
FLEXION-TORSIONRotational Basic3-D
PROJECTION FLEXION-TORSIONRotational Basic3-D
REVOLUTERotational Basic3-D
ROTATIONRotational Basic2-D, 3-D, Axisymmetric
UNIVERSALRotational Basic3-D
AXIAL/EULERCombination3-D
CARTESIAN/CARDANCombination3-D
CARTESIAN/ROTATIONCombination2-D, 3-D, Axisymmetric
JOIN/FLEXION-TORSIONCombination3-D
LINK/UNIVERSALCombination3-D
RADIAL-THRUST/ CONSTANT VELOCITYCombination3-D
SLIDE-PLANE/REVOLUTECombination3-D
SLOT/ALIGNCombination2-D, 3-D, Axisymmetric
PROJECTION CARTESIAN/PROJECTION FLEXION-TORSIONCombination3-D

Model:

Initial relative displacement0.1
Initial relative rotation0.1

Material:

Translational spring stiffness48.0
Translational damping coefficient5.0
Mass12.0
Torsional spring stiffness480.0
Torsional damping coefficient50.0
Rotary inertia (isotropic)120.0

Results and discussion

ABAQUS provides the expected solution for all cases.

Input files

ABAQUS/Standard input files

conn_std_free_2d.inp

Connector elements in two dimensions.

conn_std_free_3d.inp

Connector elements in three dimensions.

conn_std_free_axi.inp

Connector elements in axisymmetric analyses.

ABAQUS/Explicit input files

conn_xpl_free_2d.inp

Connector elements in two dimensions.

conn_xpl_free_3d.inp

Connector elements in three dimensions.

conn_xpl_free_axi.inp

Connector elements in axisymmetric analyses.