3.2.1 Modal dynamic analysis with baseline correction

Product: ABAQUS/Standard  

Elements tested

B23    CAX4H   

Features tested

Baseline correction of simple accelerogram record.

Primary and secondary base motions.

Problem description

This section illustrates the *BASELINE CORRECTION and *BASE MOTION options by two examples.

The first example (pmodbase.inp, pmodbas2.inp, and pmodbas2a.inp) is a modal dynamic, time history analysis that is performed on a one-element cantilever structure using a B23 element. As the base motion record, a simple sine-shaped accelerogram is assumed for the time of one sine period. The record is corrected for the total time of the record duration. The choice of the base motion record as a sine function allows the analytical calculation of the parabolic correction to the record using the formulę from Baseline correction of accelerograms, Section 6.1.2 of the ABAQUS Theory Manual. The values of the three constants for the parabolic correction are = –0.8308, = 0.4207, and = 2.1717; and the corrected accelerogram is

where . Integrating twice gives the corresponding displacement record:

The second example (pmodbas3.inp and pmodbas4.inp) illustrates the application of multiple base motions in a time history modal dynamic analysis in which part of the structure is fixed while another part of it is subjected to excitation. The structure analyzed is a quarter-symmetry axisymmetric model of a cylinder made of rubberlike material. An 8 × 8 mesh with CAX4H elements is employed for the analysis. The structure is first preloaded in compression statically in the axial direction by a rigid platen, which is modeled as a rigid surface in pmodbas3.inp and as a rigid body in pmodbas4.inp; perfect bonding between the platen and the top surface of the cylinder is assumed. The response to applied axial (acceleration) excitation at the rigid surface reference node is sought. The acceleration records are the same as those used in the first problem. Since both fixed boundary conditions and applied acceleration boundary conditions occur in the same global (axial) direction in different parts of the structure, we use two *BASE MOTION options to specify these boundary conditions, treating the fixed boundary conditions as a primary base motion and the applied accelerations as a secondary base motion.

Results and discussion

The results for the first example are confirmed by running the input files pmodbase.inp, pmodbas2.inp, and pmodbas2a.inp and postprocessing the results file output. Although the three models differ in their “base” organizations—namely, the base in the first input file is handled as a primary base and that in the second and third input files is handled as a secondary base—the results they generate are identical. The plot of the total displacement of the cantilever tip will show the considerable difference between the uncorrected and corrected records.

The results obtained for the second example by the two different input files, pmodbas3.inp and pmodbas4.inp, are the same.

Input files

pmodbase.inp

Invokes *BASE MOTION without the BASE NAME parameter.

pmodbas2.inp

Invokes *BASE MOTION with the BASE NAME parameter.

pmodbas2a.inp

Invokes *BASE MOTION with TYPE=DISPLACEMENT.

pmodbas3.inp

Tests multiple base motions and rigid surface.

pmodbas4.inp

Tests multiple base motions and rigid element.